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<!DOCTYPE html> <html lang="en"> <head> <meta content="text/html; charset=utf-8" http-equiv="content-type"/> <title>A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials</title>  <meta content="width=device-width, initial-scale=1, shrink-to-fit=no" name="viewport"/> <link href="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/css/bootstrap.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/ar5iv.0.7.9.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/ar5iv-fonts.0.7.9.min.css" rel="stylesheet" type="text/css"/> <link href="/static/browse/0.3.4/css/latexml_styles.css" rel="stylesheet" type="text/css"/> <script src="https://cdn.jsdelivr.net/npm/bootstrap@5.3.0/dist/js/bootstrap.bundle.min.js"></script> <script src="https://cdnjs.cloudflare.com/ajax/libs/html2canvas/1.3.3/html2canvas.min.js"></script> <script src="/static/browse/0.3.4/js/addons_new.js"></script> <script src="/static/browse/0.3.4/js/feedbackOverlay.js"></script> <base href="/html/2406.13190v1/"/></head> <body> <nav class="ltx_page_navbar"> </nav> <div class="ltx_page_main"> <div class="ltx_page_content"> <article class="ltx_document ltx_authors_1line ltx_fleqn"> <div class="ltx_para" id="p1"> <p class="ltx_p" id="p1.1">[1]<span class="ltx_ERROR undefined" id="p1.1.1">\fnm</span>Weilu <span class="ltx_ERROR undefined" id="p1.1.2">\sur</span>Gao</p> </div> <div class="ltx_para" id="p2"> <p class="ltx_p" id="p2.1">1]Department of Electrical and Computer Engineering, The University of Utah, Salt Lake City, UT, USA</p> </div> <div class="ltx_para" id="p3"> <p class="ltx_p" id="p3.1">2]J.A. Woollam Co., Inc., Lincoln, NE, USA</p> </div> <h1 class="ltx_title ltx_title_document">A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials</h1> <div class="ltx_authors"> <span class="ltx_creator ltx_role_author"> <span class="ltx_personname"><span class="ltx_ERROR undefined" id="id1.1.id1">\fnm</span>Jichao <span class="ltx_ERROR undefined" id="id2.2.id2">\sur</span>Fan </span></span> <span class="ltx_author_before"> </span><span class="ltx_creator ltx_role_author"> <span class="ltx_personname"><span class="ltx_ERROR undefined" id="id3.1.id1">\fnm</span>Ruiyang <span class="ltx_ERROR undefined" id="id4.2.id2">\sur</span>Chen </span></span> <span class="ltx_author_before"> </span><span class="ltx_creator ltx_role_author"> <span class="ltx_personname"><span class="ltx_ERROR undefined" id="id5.1.id1">\fnm</span>Minhan <span class="ltx_ERROR undefined" id="id6.2.id2">\sur</span>Lou </span></span> <span class="ltx_author_before"> </span><span class="ltx_creator ltx_role_author"> <span class="ltx_personname"><span class="ltx_ERROR undefined" id="id7.1.id1">\fnm</span>Haoyu <span class="ltx_ERROR undefined" id="id8.2.id2">\sur</span>Xie </span></span> <span class="ltx_author_before"> </span><span class="ltx_creator ltx_role_author"> <span class="ltx_personname"><span class="ltx_ERROR undefined" id="id9.1.id1">\fnm</span>Nina <span class="ltx_ERROR undefined" id="id10.2.id2">\sur</span>Hong </span></span> <span class="ltx_author_before"> </span><span class="ltx_creator ltx_role_author"> <span class="ltx_personname"><span class="ltx_ERROR undefined" id="id11.1.id1">\fnm</span>Yingheng <span class="ltx_ERROR undefined" id="id12.2.id2">\sur</span>Tang </span></span> <span class="ltx_author_before"> </span><span class="ltx_creator ltx_role_author"> <span class="ltx_personname"> </span><span class="ltx_author_notes"> <span class="ltx_contact ltx_role_email"><a href="mailto:weilu.gao@utah.edu">weilu.gao@utah.edu</a> </span> <span class="ltx_contact ltx_role_affiliation">[ </span> <span class="ltx_contact ltx_role_affiliation">[ </span></span></span> </div> <div class="ltx_abstract"> <h6 class="ltx_title ltx_title_abstract">Abstract</h6> <p class="ltx_p" id="id13.id1">The ability to design and dynamically control chiroptical responses in solid-state matter at wafer scale enables new opportunities in various areas. Here we present a full stack of computer-aided designs and experimental implementations of a dynamically programmable, unified, scalable chiroptical heterostructure containing twisted aligned one-dimensional (1D) carbon nanotubes (CNTs) and non-volatile phase change materials (PCMs). We develop a software infrastructure based on high-performance machine learning frameworks, including differentiable programming and derivative-free optimization, to efficiently optimize the tunability of both excitonic reciprocal and linear-anisotropy-induced nonreciprocal circular dichroism (CD) responses. We experimentally implement designed heterostructures with wafer-scale self-assembled aligned CNTs and deposited PCMs. We dynamically program reciprocal and nonreciprocal CD responses by inducing phase transitions of PCMs, and nonreciprocal responses display polarity reversal of CD upon sample flipping in broadband spectral ranges. All experimental results agree with simulations. Further, we demonstrate that the vertical dimension of heterostructure is scalable with the number of stacking layers and aligned CNTs play dual roles – the layer to produce CD responses and the Joule heating electrode to electrically program PCMs. This heterostructure platform is versatile and expandable to a library of 1D nanomaterials and electro-optic materials for exploring novel chiral phenomena and photonic and optoelectronic devices.</p> </div> <section class="ltx_section" id="Sx1"> <h2 class="ltx_title ltx_title_section">Introduction</h2> <div class="ltx_para" id="Sx1.p1"> <p class="ltx_p" id="Sx1.p1.1">Manipulating chiroptical responses in solid-state materials and their photonic and optoelectronic devices has enabled various applications, including sensing <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib1" title="">1</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib2" title="">2</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib3" title="">3</a>]</cite>, imaging <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib4" title="">4</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib5" title="">5</a>]</cite>, neuromorphic computing <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib6" title="">6</a>]</cite>, and light-driven synthesis <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib7" title="">7</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib8" title="">8</a>]</cite>. In particular, the interaction of circularly polarized light with quantum materials has profound implications on quantum photonic applications <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib9" title="">9</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib10" title="">10</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib11" title="">11</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib12" title="">12</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib13" title="">13</a>]</cite>. Chiroptical responses, such as circular dichroism (CD) that is the differential attenuation between the left- and right-handed circularly polarized (LCP and RCP) light, generally have two prominent contributions with distinct features <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib14" title="">14</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib15" title="">15</a>]</cite>. The first one is an intrinsic isotropic reciprocal response due to molecular or structure-induced chirality, which is invariant upon sample orientation. The second one is a linear anisotropy-induced nonreciprocal response, leading to opposite handednesses from opposite sides of the same sample. Leveraging both contributions of chiroptical responses can enrich functionalities, improve efficiencies, and reduce costs of chiral photonic and optoelectronic devices <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib16" title="">16</a>]</cite>.</p> </div> <div class="ltx_para" id="Sx1.p2"> <p class="ltx_p" id="Sx1.p2.1">Recently, twisted stacks of self-assembled aligned 1D nanomaterials, such as carbon nanotubes (CNTs), have emerged as a high-performance chiral photonic material platform <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib17" title="">17</a>]</cite>. For example, a 3-layer twisted stack of aligned CNTs has demonstrated the highest CD response compared to all other material and metamaterial platforms in the deep ultraviolet spectral range, because of the strong room-temperature quantum-confinement effects in CNTs <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib18" title="">18</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib19" title="">19</a>]</cite> compared to natural molecules and self-assembled conventional metallic or dielectric materials without quantum-relevant properties <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib20" title="">20</a>]</cite>. Further, the optical properties of 1D nanomaterials can be structurally and dynamically tuned in a broadband spectral range from ultraviolet to infrared frequencies. In addition, in contrast to engineered metamaterials, whose top-down manufacturing requires sophisticated nanofabrication facilities and processes to create artificial symmetry-breaking structures and is challenging to scale up <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib21" title="">21</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib22" title="">22</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib23" title="">23</a>]</cite>, bottom-up self-assembly of 1D nanomaterials is low-cost and at wafer scale <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib24" title="">24</a>]</cite>. Although hybridizing metamaterials with materials or structures whose optical properties or geometries can be electrically, thermally, or mechanically controlled enables dynamic tunability <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib25" title="">25</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib26" title="">26</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib27" title="">27</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib28" title="">28</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib29" title="">29</a>]</cite>, this hybridization further increases manufacturing complexity and the design of dynamically tunable metametarials using full-wave simulations is time-consuming and computation-intensive <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib30" title="">30</a>]</cite>. Moreover, nonreciprocal chiroptical responses are occasionally reported in a few solid-state films of organic materials without systematic designs <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib15" title="">15</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib16" title="">16</a>]</cite>, and are largely ignored or missing in metamaterial reports. Hence, a fully programmable, unified, wafer-scale chiroptical platform, whose reciprocal and nonreciprocal chiroptical responses can both be efficiently designed through programming and can be electrically tuned and dynamically programmed, is lacking.</p> </div> <div class="ltx_para" id="Sx1.p3"> <p class="ltx_p" id="Sx1.p3.9">Here, we present such a platform that is a heterostructure of twisted aligned 1D nanomaterials and non-volatile chalcogenide phase change materials (PCMs). The demonstrated 1D nanomaterial and PCM are CNT and germanium-antimony-tellurium (Ge<sub class="ltx_sub" id="Sx1.p3.9.1">2</sub>Sb<sub class="ltx_sub" id="Sx1.p3.9.2">2</sub>Te<sub class="ltx_sub" id="Sx1.p3.9.3">5</sub> or GST), respectively. The material phases of PCMs can be fast electrically programmed to be crystalline or amorphous using a short electrical pulse with a substantial dielectric function modulation in broadband spectral ranges <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib31" title="">31</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib32" title="">32</a>]</cite>. Further, the phases can be preserved after programming without external stimulus for <math alttext=">10" class="ltx_Math" display="inline" id="Sx1.p3.4.m4.1"><semantics id="Sx1.p3.4.m4.1a"><mrow id="Sx1.p3.4.m4.1.1" xref="Sx1.p3.4.m4.1.1.cmml"><mi id="Sx1.p3.4.m4.1.1.2" xref="Sx1.p3.4.m4.1.1.2.cmml"></mi><mo id="Sx1.p3.4.m4.1.1.1" xref="Sx1.p3.4.m4.1.1.1.cmml">></mo><mn id="Sx1.p3.4.m4.1.1.3" xref="Sx1.p3.4.m4.1.1.3.cmml">10</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx1.p3.4.m4.1b"><apply id="Sx1.p3.4.m4.1.1.cmml" xref="Sx1.p3.4.m4.1.1"><gt id="Sx1.p3.4.m4.1.1.1.cmml" xref="Sx1.p3.4.m4.1.1.1"></gt><csymbol cd="latexml" id="Sx1.p3.4.m4.1.1.2.cmml" xref="Sx1.p3.4.m4.1.1.2">absent</csymbol><cn id="Sx1.p3.4.m4.1.1.3.cmml" type="integer" xref="Sx1.p3.4.m4.1.1.3">10</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx1.p3.4.m4.1c">>10</annotation><annotation encoding="application/x-llamapun" id="Sx1.p3.4.m4.1d">> 10</annotation></semantics></math> years with zero static energy consumption. We implemented simulation software based on machine learning frameworks, including graphics processing unit (GPU)-powered differentiable programming enabled by gradient backpropagation algorithm and derivative-free Bayesian optimization, to efficiently design and optimize the dynamic tunable ranges of reciprocal and nonreciprocal CD responses in the heterostructure with experimentally obtained optical constants of materials. Further, we experimentally implemented designed heterostructures through wafer-scale low-cost self-assembly of aligned CNTs and wafer-scale deposition of GST and dielectric films, and experimentally observed strong dynamic tunability. In particular, we demonstrated tunable nonreciprocal CD responses, which displayed opposite signs or polarity reversal of measured CD signals in a broadband visible range when opposite sides of the same heterostructure were probed. All measured spectra agreed with the simulations. In addition, we demonstrated that not only the lateral dimension of the heterostructure was at wafer scale, but also the vertical dimension was scalable with a large number of stacking layers to enhance CD responses. Moreover, we showed that aligned CNTs in the heterostructure played dual roles – the active material to produce CD responses and the Joule heating electrode material to electrically program GST phases. The demonstrated heterostructure architecture is versatile and can be extended to incorporate a wide range of 1D nanomaterials, such as transition metal dichalcogenides nanotubes <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib33" title="">33</a>]</cite>, boron nitride nanotubes <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib34" title="">34</a>]</cite>, nanotube heterostructures <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib35" title="">35</a>]</cite>, and encapsulated CNTs with 1D atomic chains <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib36" title="">36</a>]</cite>, and different PCMs and electro-optic materials <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib37" title="">37</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib38" title="">38</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib39" title="">39</a>]</cite>, such as antimony sulfide (Sb<sub class="ltx_sub" id="Sx1.p3.9.4">2</sub>S<sub class="ltx_sub" id="Sx1.p3.9.5">3</sub>), antimony selenide (Sb<sub class="ltx_sub" id="Sx1.p3.9.6">2</sub>Se<sub class="ltx_sub" id="Sx1.p3.9.7">3</sub>), lithium niobate (LiNO<sub class="ltx_sub" id="Sx1.p3.9.8">3</sub>) and electro-optic organic materials. This versatile chiroptical platform will provide opportunities for novel chiral photonic and optoelectronic devices, such as chiral quantum light emitters <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib13" title="">13</a>]</cite>, and provide a new platform for exploring optical and non-optical chiral phenomena, such as chirality-induced spin selectivity effects <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib40" title="">40</a>]</cite>.</p> </div> </section> <section class="ltx_section" id="Sx2"> <h2 class="ltx_title ltx_title_section">Results</h2> <section class="ltx_subsection" id="Sx2.SSx1"> <h3 class="ltx_title ltx_title_subsection">Programmable heterostructure architecture</h3> <div class="ltx_para" id="Sx2.SSx1.p1"> <p class="ltx_p" id="Sx2.SSx1.p1.9">Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F1" title="Figure 1 ‣ Programmable heterostructure architecture ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">1</span></a>a schematically illustrates the programmable heterostructure architecture containing multiple layers of anisotropic aligned CNTs and other isotropic materials, including PCMs and dielectrics. The quantum confinement along CNT circumferences induces the formation of subbands and excitonic interband transitions across subbands. These transitions span broadband spectral ranges and are dependent on the atomic structures of CNTs <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib18" title="">18</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib19" title="">19</a>]</cite>. Further, the 1D geometry of CNTs leads to anisotropic excitonic electric dipoles and optical absorption under the excitation of linearly polarized light. We used a shaking-assisted vacuum filtration (SAVF) process to prepare aligned CNT films and measured their linear-polarization-dependent absorption spectra. The linear shaking occurring during the vacuum filtration dictated the alignment direction of obtained aligned CNT films; see Methods and Supplementary Fig. 1 for more details. The deterministic control of CNT alignment direction in the SAVF process is advantageous over conventional vacuum filtration without direction control and facilitates the scalable stacking of multiple layers in the heterostructure. As shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F1" title="Figure 1 ‣ Programmable heterostructure architecture ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">1</span></a>b, when the polarization of incident light is parallel to the CNT axis, strong absorption occurs through M<sub class="ltx_sub" id="Sx2.SSx1.p1.9.1"><span class="ltx_text ltx_font_italic" id="Sx2.SSx1.p1.9.1.1">11</span></sub> transition in CNTs at 730 nm and the <math alttext="M" class="ltx_Math" display="inline" id="Sx2.SSx1.p1.2.m2.1"><semantics id="Sx2.SSx1.p1.2.m2.1a"><mi id="Sx2.SSx1.p1.2.m2.1.1" xref="Sx2.SSx1.p1.2.m2.1.1.cmml">M</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p1.2.m2.1b"><ci id="Sx2.SSx1.p1.2.m2.1.1.cmml" xref="Sx2.SSx1.p1.2.m2.1.1">𝑀</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p1.2.m2.1c">M</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p1.2.m2.1d">italic_M</annotation></semantics></math> point transition (labeled ‘<math alttext="\pi_{\parallel}" class="ltx_Math" display="inline" id="Sx2.SSx1.p1.3.m3.1"><semantics id="Sx2.SSx1.p1.3.m3.1a"><msub id="Sx2.SSx1.p1.3.m3.1.1" xref="Sx2.SSx1.p1.3.m3.1.1.cmml"><mi id="Sx2.SSx1.p1.3.m3.1.1.2" xref="Sx2.SSx1.p1.3.m3.1.1.2.cmml">π</mi><mo id="Sx2.SSx1.p1.3.m3.1.1.3" xref="Sx2.SSx1.p1.3.m3.1.1.3.cmml">∥</mo></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p1.3.m3.1b"><apply id="Sx2.SSx1.p1.3.m3.1.1.cmml" xref="Sx2.SSx1.p1.3.m3.1.1"><csymbol cd="ambiguous" id="Sx2.SSx1.p1.3.m3.1.1.1.cmml" xref="Sx2.SSx1.p1.3.m3.1.1">subscript</csymbol><ci id="Sx2.SSx1.p1.3.m3.1.1.2.cmml" xref="Sx2.SSx1.p1.3.m3.1.1.2">𝜋</ci><csymbol cd="latexml" id="Sx2.SSx1.p1.3.m3.1.1.3.cmml" xref="Sx2.SSx1.p1.3.m3.1.1.3">parallel-to</csymbol></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p1.3.m3.1c">\pi_{\parallel}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p1.3.m3.1d">italic_π start_POSTSUBSCRIPT ∥ end_POSTSUBSCRIPT</annotation></semantics></math>’) at 282 nm <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib41" title="">41</a>]</cite>. The absorption resonance wavelength is dependent on the diameters and atomic structures of CNTs <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib42" title="">42</a>]</cite>. In contrast, different <math alttext="M" class="ltx_Math" display="inline" id="Sx2.SSx1.p1.4.m4.1"><semantics id="Sx2.SSx1.p1.4.m4.1a"><mi id="Sx2.SSx1.p1.4.m4.1.1" xref="Sx2.SSx1.p1.4.m4.1.1.cmml">M</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p1.4.m4.1b"><ci id="Sx2.SSx1.p1.4.m4.1.1.cmml" xref="Sx2.SSx1.p1.4.m4.1.1">𝑀</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p1.4.m4.1c">M</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p1.4.m4.1d">italic_M</annotation></semantics></math> point transition transition (labeled ‘<math alttext="\pi_{\perp}" class="ltx_Math" display="inline" id="Sx2.SSx1.p1.5.m5.1"><semantics id="Sx2.SSx1.p1.5.m5.1a"><msub id="Sx2.SSx1.p1.5.m5.1.1" xref="Sx2.SSx1.p1.5.m5.1.1.cmml"><mi id="Sx2.SSx1.p1.5.m5.1.1.2" xref="Sx2.SSx1.p1.5.m5.1.1.2.cmml">π</mi><mo id="Sx2.SSx1.p1.5.m5.1.1.3" xref="Sx2.SSx1.p1.5.m5.1.1.3.cmml">⟂</mo></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p1.5.m5.1b"><apply id="Sx2.SSx1.p1.5.m5.1.1.cmml" xref="Sx2.SSx1.p1.5.m5.1.1"><csymbol cd="ambiguous" id="Sx2.SSx1.p1.5.m5.1.1.1.cmml" xref="Sx2.SSx1.p1.5.m5.1.1">subscript</csymbol><ci id="Sx2.SSx1.p1.5.m5.1.1.2.cmml" xref="Sx2.SSx1.p1.5.m5.1.1.2">𝜋</ci><csymbol cd="latexml" id="Sx2.SSx1.p1.5.m5.1.1.3.cmml" xref="Sx2.SSx1.p1.5.m5.1.1.3">perpendicular-to</csymbol></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p1.5.m5.1c">\pi_{\perp}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p1.5.m5.1d">italic_π start_POSTSUBSCRIPT ⟂ end_POSTSUBSCRIPT</annotation></semantics></math>’) occurs at 255 nm due to optical selection rules <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib43" title="">43</a>]</cite> and the M<sub class="ltx_sub" id="Sx2.SSx1.p1.9.2"><span class="ltx_text ltx_font_italic" id="Sx2.SSx1.p1.9.2.1">11</span></sub> transition is suppressed because of the depolarization effect <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib44" title="">44</a>]</cite>. The helical twist of anisotropic excitonic dipoles and electromagnetic coupling between them, which essentially correspond to the physical picture of helically coupled electrical dipoles in microscopic chiral molecules <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib45" title="">45</a>]</cite>, produce reciprocal CD response (CD<sub class="ltx_sub" id="Sx2.SSx1.p1.9.3">iso</sub>); see Fig. <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F1" title="Figure 1 ‣ Programmable heterostructure architecture ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">1</span></a>c. The CD<sub class="ltx_sub" id="Sx2.SSx1.p1.9.4">iso</sub> response is of intrinsic excitonic nature, isotropic, and independent of sample orientation. The incorporation of PCMs and other isotropic materials in the heterostructure can control the electromagnetic coupling between dipoles to dynamically tune and optimize CD<sub class="ltx_sub" id="Sx2.SSx1.p1.9.5">iso</sub> response.</p> </div> <figure class="ltx_figure" id="Sx2.F1"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="577" id="Sx2.F1.g1" src="x1.png" width="830"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 1: </span><span class="ltx_text ltx_font_bold" id="Sx2.F1.5.1">Programmable heterostructure architecture and chiroptical responses</span>. (a) Illustration of programmable chiroptical heterostructure containing anisotropic aligned CNTs and isotropic PCMs and dielectrics. (b) Linear-polarization-dependent absorption spectra of an aligned CNT film prepared using the SAVF process. The red (blue) line for parallel (perpendicular) polarization. (c) Isotorpic reciprocal CD<sub class="ltx_sub" id="Sx2.F1.6.2">iso</sub> response in the heterostructure originating from the helical coupling of anisotropic 1D excitons in aligned CNTs. (d) Nonreciprocal LDLB response in the heterostructure originating from the interference of linear anisotropy, which displays opposite handednesses from the front and back sides of the same sample.</figcaption> </figure> <div class="ltx_para" id="Sx2.SSx1.p2"> <p class="ltx_p" id="Sx2.SSx1.p2.19">In addition, the other contributor to observed CD response originates from the interference of linear dichroism (LD) and linear birefringence (LB) of aligned CNTs. The LDLB-induced CD response is expressed as 0.5(LD<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.1.m1.1"><semantics id="Sx2.SSx1.p2.1.m1.1a"><msup id="Sx2.SSx1.p2.1.m1.1.1" xref="Sx2.SSx1.p2.1.m1.1.1.cmml"><mi id="Sx2.SSx1.p2.1.m1.1.1a" xref="Sx2.SSx1.p2.1.m1.1.1.cmml"></mi><msup id="Sx2.SSx1.p2.1.m1.1.1.1" xref="Sx2.SSx1.p2.1.m1.1.1.1.cmml"><mi id="Sx2.SSx1.p2.1.m1.1.1.1a" xref="Sx2.SSx1.p2.1.m1.1.1.1.cmml"></mi><mo id="Sx2.SSx1.p2.1.m1.1.1.1.1" xref="Sx2.SSx1.p2.1.m1.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.1.m1.1b"><apply id="Sx2.SSx1.p2.1.m1.1.1.cmml" xref="Sx2.SSx1.p2.1.m1.1.1"><apply id="Sx2.SSx1.p2.1.m1.1.1.1.cmml" xref="Sx2.SSx1.p2.1.m1.1.1.1"><ci id="Sx2.SSx1.p2.1.m1.1.1.1.1.cmml" xref="Sx2.SSx1.p2.1.m1.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.1.m1.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.1.m1.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>LB <math alttext="-" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.2.m2.1"><semantics id="Sx2.SSx1.p2.2.m2.1a"><mo id="Sx2.SSx1.p2.2.m2.1.1" xref="Sx2.SSx1.p2.2.m2.1.1.cmml">−</mo><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.2.m2.1b"><minus id="Sx2.SSx1.p2.2.m2.1.1.cmml" xref="Sx2.SSx1.p2.2.m2.1.1"></minus></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.2.m2.1c">-</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.2.m2.1d">-</annotation></semantics></math> LDLB<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.3.m3.1"><semantics id="Sx2.SSx1.p2.3.m3.1a"><msup id="Sx2.SSx1.p2.3.m3.1.1" xref="Sx2.SSx1.p2.3.m3.1.1.cmml"><mi id="Sx2.SSx1.p2.3.m3.1.1a" xref="Sx2.SSx1.p2.3.m3.1.1.cmml"></mi><msup id="Sx2.SSx1.p2.3.m3.1.1.1" xref="Sx2.SSx1.p2.3.m3.1.1.1.cmml"><mi id="Sx2.SSx1.p2.3.m3.1.1.1a" xref="Sx2.SSx1.p2.3.m3.1.1.1.cmml"></mi><mo id="Sx2.SSx1.p2.3.m3.1.1.1.1" xref="Sx2.SSx1.p2.3.m3.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.3.m3.1b"><apply id="Sx2.SSx1.p2.3.m3.1.1.cmml" xref="Sx2.SSx1.p2.3.m3.1.1"><apply id="Sx2.SSx1.p2.3.m3.1.1.1.cmml" xref="Sx2.SSx1.p2.3.m3.1.1.1"><ci id="Sx2.SSx1.p2.3.m3.1.1.1.1.cmml" xref="Sx2.SSx1.p2.3.m3.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.3.m3.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.3.m3.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>), where LD and LB are measured in arbitrarily defined <math alttext="x" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.4.m4.1"><semantics id="Sx2.SSx1.p2.4.m4.1a"><mi id="Sx2.SSx1.p2.4.m4.1.1" xref="Sx2.SSx1.p2.4.m4.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.4.m4.1b"><ci id="Sx2.SSx1.p2.4.m4.1.1.cmml" xref="Sx2.SSx1.p2.4.m4.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.4.m4.1c">x</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.4.m4.1d">italic_x</annotation></semantics></math>-<math alttext="y" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.5.m5.1"><semantics id="Sx2.SSx1.p2.5.m5.1a"><mi id="Sx2.SSx1.p2.5.m5.1.1" xref="Sx2.SSx1.p2.5.m5.1.1.cmml">y</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.5.m5.1b"><ci id="Sx2.SSx1.p2.5.m5.1.1.cmml" xref="Sx2.SSx1.p2.5.m5.1.1">𝑦</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.5.m5.1c">y</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.5.m5.1d">italic_y</annotation></semantics></math> axes and LD<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.6.m6.1"><semantics id="Sx2.SSx1.p2.6.m6.1a"><msup id="Sx2.SSx1.p2.6.m6.1.1" xref="Sx2.SSx1.p2.6.m6.1.1.cmml"><mi id="Sx2.SSx1.p2.6.m6.1.1a" xref="Sx2.SSx1.p2.6.m6.1.1.cmml"></mi><msup id="Sx2.SSx1.p2.6.m6.1.1.1" xref="Sx2.SSx1.p2.6.m6.1.1.1.cmml"><mi id="Sx2.SSx1.p2.6.m6.1.1.1a" xref="Sx2.SSx1.p2.6.m6.1.1.1.cmml"></mi><mo id="Sx2.SSx1.p2.6.m6.1.1.1.1" xref="Sx2.SSx1.p2.6.m6.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.6.m6.1b"><apply id="Sx2.SSx1.p2.6.m6.1.1.cmml" xref="Sx2.SSx1.p2.6.m6.1.1"><apply id="Sx2.SSx1.p2.6.m6.1.1.1.cmml" xref="Sx2.SSx1.p2.6.m6.1.1.1"><ci id="Sx2.SSx1.p2.6.m6.1.1.1.1.cmml" xref="Sx2.SSx1.p2.6.m6.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.6.m6.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.6.m6.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math> and LB<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.7.m7.1"><semantics id="Sx2.SSx1.p2.7.m7.1a"><msup id="Sx2.SSx1.p2.7.m7.1.1" xref="Sx2.SSx1.p2.7.m7.1.1.cmml"><mi id="Sx2.SSx1.p2.7.m7.1.1a" xref="Sx2.SSx1.p2.7.m7.1.1.cmml"></mi><msup id="Sx2.SSx1.p2.7.m7.1.1.1" xref="Sx2.SSx1.p2.7.m7.1.1.1.cmml"><mi id="Sx2.SSx1.p2.7.m7.1.1.1a" xref="Sx2.SSx1.p2.7.m7.1.1.1.cmml"></mi><mo id="Sx2.SSx1.p2.7.m7.1.1.1.1" xref="Sx2.SSx1.p2.7.m7.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.7.m7.1b"><apply id="Sx2.SSx1.p2.7.m7.1.1.cmml" xref="Sx2.SSx1.p2.7.m7.1.1"><apply id="Sx2.SSx1.p2.7.m7.1.1.1.cmml" xref="Sx2.SSx1.p2.7.m7.1.1.1"><ci id="Sx2.SSx1.p2.7.m7.1.1.1.1.cmml" xref="Sx2.SSx1.p2.7.m7.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.7.m7.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.7.m7.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math> are measured along the bisectors of <math alttext="x" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.8.m8.1"><semantics id="Sx2.SSx1.p2.8.m8.1a"><mi id="Sx2.SSx1.p2.8.m8.1.1" xref="Sx2.SSx1.p2.8.m8.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.8.m8.1b"><ci id="Sx2.SSx1.p2.8.m8.1.1.cmml" xref="Sx2.SSx1.p2.8.m8.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.8.m8.1c">x</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.8.m8.1d">italic_x</annotation></semantics></math>-<math alttext="y" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.9.m9.1"><semantics id="Sx2.SSx1.p2.9.m9.1a"><mi id="Sx2.SSx1.p2.9.m9.1.1" xref="Sx2.SSx1.p2.9.m9.1.1.cmml">y</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.9.m9.1b"><ci id="Sx2.SSx1.p2.9.m9.1.1.cmml" xref="Sx2.SSx1.p2.9.m9.1.1">𝑦</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.9.m9.1c">y</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.9.m9.1d">italic_y</annotation></semantics></math> axes (i.e., with a <math alttext="+45^{\circ}" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.10.m10.1"><semantics id="Sx2.SSx1.p2.10.m10.1a"><mrow id="Sx2.SSx1.p2.10.m10.1.1" xref="Sx2.SSx1.p2.10.m10.1.1.cmml"><mo id="Sx2.SSx1.p2.10.m10.1.1a" xref="Sx2.SSx1.p2.10.m10.1.1.cmml">+</mo><msup id="Sx2.SSx1.p2.10.m10.1.1.2" xref="Sx2.SSx1.p2.10.m10.1.1.2.cmml"><mn id="Sx2.SSx1.p2.10.m10.1.1.2.2" xref="Sx2.SSx1.p2.10.m10.1.1.2.2.cmml">45</mn><mo id="Sx2.SSx1.p2.10.m10.1.1.2.3" xref="Sx2.SSx1.p2.10.m10.1.1.2.3.cmml">∘</mo></msup></mrow><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.10.m10.1b"><apply id="Sx2.SSx1.p2.10.m10.1.1.cmml" xref="Sx2.SSx1.p2.10.m10.1.1"><plus id="Sx2.SSx1.p2.10.m10.1.1.1.cmml" xref="Sx2.SSx1.p2.10.m10.1.1"></plus><apply id="Sx2.SSx1.p2.10.m10.1.1.2.cmml" xref="Sx2.SSx1.p2.10.m10.1.1.2"><csymbol cd="ambiguous" id="Sx2.SSx1.p2.10.m10.1.1.2.1.cmml" xref="Sx2.SSx1.p2.10.m10.1.1.2">superscript</csymbol><cn id="Sx2.SSx1.p2.10.m10.1.1.2.2.cmml" type="integer" xref="Sx2.SSx1.p2.10.m10.1.1.2.2">45</cn><compose id="Sx2.SSx1.p2.10.m10.1.1.2.3.cmml" xref="Sx2.SSx1.p2.10.m10.1.1.2.3"></compose></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.10.m10.1c">+45^{\circ}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.10.m10.1d">+ 45 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT</annotation></semantics></math> rotation). Note that the LDLB response is not from excitons, independent of instrumental faults, and not an artifact <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib14" title="">14</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib15" title="">15</a>]</cite>. 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When looking from the front or back side of the plane or flipping the sample, aligned CNTs become mirrored with LD and LB unaltered and LD<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.17.m17.1"><semantics id="Sx2.SSx1.p2.17.m17.1a"><msup id="Sx2.SSx1.p2.17.m17.1.1" xref="Sx2.SSx1.p2.17.m17.1.1.cmml"><mi id="Sx2.SSx1.p2.17.m17.1.1a" xref="Sx2.SSx1.p2.17.m17.1.1.cmml"></mi><msup id="Sx2.SSx1.p2.17.m17.1.1.1" xref="Sx2.SSx1.p2.17.m17.1.1.1.cmml"><mi id="Sx2.SSx1.p2.17.m17.1.1.1a" xref="Sx2.SSx1.p2.17.m17.1.1.1.cmml"></mi><mo id="Sx2.SSx1.p2.17.m17.1.1.1.1" xref="Sx2.SSx1.p2.17.m17.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.17.m17.1b"><apply id="Sx2.SSx1.p2.17.m17.1.1.cmml" xref="Sx2.SSx1.p2.17.m17.1.1"><apply id="Sx2.SSx1.p2.17.m17.1.1.1.cmml" xref="Sx2.SSx1.p2.17.m17.1.1.1"><ci id="Sx2.SSx1.p2.17.m17.1.1.1.1.cmml" xref="Sx2.SSx1.p2.17.m17.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.17.m17.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.17.m17.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math> and LB<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx2.SSx1.p2.18.m18.1"><semantics id="Sx2.SSx1.p2.18.m18.1a"><msup id="Sx2.SSx1.p2.18.m18.1.1" xref="Sx2.SSx1.p2.18.m18.1.1.cmml"><mi id="Sx2.SSx1.p2.18.m18.1.1a" xref="Sx2.SSx1.p2.18.m18.1.1.cmml"></mi><msup id="Sx2.SSx1.p2.18.m18.1.1.1" xref="Sx2.SSx1.p2.18.m18.1.1.1.cmml"><mi id="Sx2.SSx1.p2.18.m18.1.1.1a" xref="Sx2.SSx1.p2.18.m18.1.1.1.cmml"></mi><mo id="Sx2.SSx1.p2.18.m18.1.1.1.1" xref="Sx2.SSx1.p2.18.m18.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx2.SSx1.p2.18.m18.1b"><apply id="Sx2.SSx1.p2.18.m18.1.1.cmml" xref="Sx2.SSx1.p2.18.m18.1.1"><apply id="Sx2.SSx1.p2.18.m18.1.1.1.cmml" xref="Sx2.SSx1.p2.18.m18.1.1.1"><ci id="Sx2.SSx1.p2.18.m18.1.1.1.1.cmml" xref="Sx2.SSx1.p2.18.m18.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx1.p2.18.m18.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx1.p2.18.m18.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math> signs flipped. Hence, the sign of the LDLB response is also flipped and called nonreciprocal CD <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib14" title="">14</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib15" title="">15</a>]</cite>. If the LDLB response is much larger than isotropic CD<sub class="ltx_sub" id="Sx2.SSx1.p2.19.1">iso</sub>, the measured CD spectra can display opposite signs when measuring from opposite sample sides; see Fig. <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F1" title="Figure 1 ‣ Programmable heterostructure architecture ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">1</span></a>d. The LDLB response is non-zero only when the main axes of LD and LB are not aligned with each other otherwise two terms in the LDLB expression are always canceled. However, the optical axes of maximum attenuation for LD and phase delay for LB of CNTs are both along the CNT axis and minimum ones are both perpendicular to the CNT axis, meaning LD and LB quantities are aligned. This suggests the LDLB response be zero in CNT-only architectures. The incorporation of PCMs and other isotropic materials in the heterostructure can induce and control multiple reflections between layers. Because LD (LB) is related to the imaginary (real) part of the CNT refractive index, the multiple reflections inside the same heterostructure can have different influences on LD and LB and their main axes are decoupled and different from the CNT axis. Hence, the heterostructure not only can generate non-zero LDLB responses but can dynamically tune and optimize LDLB responses.</p> </div> </section> <section class="ltx_subsection" id="Sx2.SSx2"> <h3 class="ltx_title ltx_title_subsection">Simulation framework</h3> <div class="ltx_para" id="Sx2.SSx2.p1"> <p class="ltx_p" id="Sx2.SSx2.p1.6">Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F2" title="Figure 2 ‣ Simulation framework ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">2</span></a>a illustrates the simulation framework we developed to design the heterostructure to achieve prominent dynamic tunability of both CD<sub class="ltx_sub" id="Sx2.SSx2.p1.6.1">iso</sub> and LDLB responses. We developed a general <math alttext="4\times 4" class="ltx_Math" display="inline" id="Sx2.SSx2.p1.2.m2.1"><semantics id="Sx2.SSx2.p1.2.m2.1a"><mrow id="Sx2.SSx2.p1.2.m2.1.1" xref="Sx2.SSx2.p1.2.m2.1.1.cmml"><mn id="Sx2.SSx2.p1.2.m2.1.1.2" xref="Sx2.SSx2.p1.2.m2.1.1.2.cmml">4</mn><mo id="Sx2.SSx2.p1.2.m2.1.1.1" lspace="0.222em" rspace="0.222em" xref="Sx2.SSx2.p1.2.m2.1.1.1.cmml">×</mo><mn id="Sx2.SSx2.p1.2.m2.1.1.3" xref="Sx2.SSx2.p1.2.m2.1.1.3.cmml">4</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p1.2.m2.1b"><apply id="Sx2.SSx2.p1.2.m2.1.1.cmml" xref="Sx2.SSx2.p1.2.m2.1.1"><times id="Sx2.SSx2.p1.2.m2.1.1.1.cmml" xref="Sx2.SSx2.p1.2.m2.1.1.1"></times><cn id="Sx2.SSx2.p1.2.m2.1.1.2.cmml" type="integer" xref="Sx2.SSx2.p1.2.m2.1.1.2">4</cn><cn id="Sx2.SSx2.p1.2.m2.1.1.3.cmml" type="integer" xref="Sx2.SSx2.p1.2.m2.1.1.3">4</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p1.2.m2.1c">4\times 4</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p1.2.m2.1d">4 × 4</annotation></semantics></math> transfer matrix method (TMM) to obtain all transmission and reflection coefficients under different linear and circular polarizations; see Methods and Supplementary Fig. 2 for more details. We calculated these coefficients under four configurations of sample rotation and flipping to obtain CD<sub class="ltx_sub" id="Sx2.SSx2.p1.6.2">iso</sub> and LDLB responses; see Methods and Supplementary Fig. 3 for more details. Since all fundamental operations in TMM are matrix multiplications, we implemented the TMM framework using the <span class="ltx_text ltx_font_typewriter" id="Sx2.SSx2.p1.6.3">PyTorch</span> framework so that all calculations were GPU-accelerated in parallel. The TMM input included the dielectric functions of anisotropic and isotropic materials and a set of heterostructure parameters <math alttext="s" class="ltx_Math" display="inline" id="Sx2.SSx2.p1.4.m4.1"><semantics id="Sx2.SSx2.p1.4.m4.1a"><mi id="Sx2.SSx2.p1.4.m4.1.1" xref="Sx2.SSx2.p1.4.m4.1.1.cmml">s</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p1.4.m4.1b"><ci id="Sx2.SSx2.p1.4.m4.1.1.cmml" xref="Sx2.SSx2.p1.4.m4.1.1">𝑠</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p1.4.m4.1c">s</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p1.4.m4.1d">italic_s</annotation></semantics></math>, such as the choice of materials, layer thicknesses, and rotation angles between aligned CNTs. Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F2" title="Figure 2 ‣ Simulation framework ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">2</span></a>b and <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F2" title="Figure 2 ‣ Simulation framework ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">2</span></a>c display our experimentally determined complex-valued dielectric functions of aligned CNT films through multi-curve fittings and sputtered GST films under amorphous and crystalline phases through spectroscopic ellipsometry; see Methods and Supplementary Fig. 4 for more details. We focused on the spectra range covering the <math alttext="M_{11}" class="ltx_Math" display="inline" id="Sx2.SSx2.p1.5.m5.1"><semantics id="Sx2.SSx2.p1.5.m5.1a"><msub id="Sx2.SSx2.p1.5.m5.1.1" xref="Sx2.SSx2.p1.5.m5.1.1.cmml"><mi id="Sx2.SSx2.p1.5.m5.1.1.2" xref="Sx2.SSx2.p1.5.m5.1.1.2.cmml">M</mi><mn id="Sx2.SSx2.p1.5.m5.1.1.3" xref="Sx2.SSx2.p1.5.m5.1.1.3.cmml">11</mn></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p1.5.m5.1b"><apply id="Sx2.SSx2.p1.5.m5.1.1.cmml" xref="Sx2.SSx2.p1.5.m5.1.1"><csymbol cd="ambiguous" id="Sx2.SSx2.p1.5.m5.1.1.1.cmml" xref="Sx2.SSx2.p1.5.m5.1.1">subscript</csymbol><ci id="Sx2.SSx2.p1.5.m5.1.1.2.cmml" xref="Sx2.SSx2.p1.5.m5.1.1.2">𝑀</ci><cn id="Sx2.SSx2.p1.5.m5.1.1.3.cmml" type="integer" xref="Sx2.SSx2.p1.5.m5.1.1.3">11</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p1.5.m5.1c">M_{11}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p1.5.m5.1d">italic_M start_POSTSUBSCRIPT 11 end_POSTSUBSCRIPT</annotation></semantics></math> transition of CNTs because of the relatively low optical loss of GST at least in one phase in this range and the limitation of the spectrometer measurement range (shaded green areas in Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F2" title="Figure 2 ‣ Simulation framework ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">2</span></a>b and <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F2" title="Figure 2 ‣ Simulation framework ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">2</span></a>c). Note that although we focused on the non-volatile GST material for programming the heterostructure, the candidate materials can be broadly expanded to other electro-optic materials, such as electro-optic LiNbO<sub class="ltx_sub" id="Sx2.SSx2.p1.6.4">3</sub> and organic materials.</p> </div> <figure class="ltx_figure" id="Sx2.F2"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_square" height="769" id="Sx2.F2.g1" src="x2.png" width="830"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 2: </span><span class="ltx_text ltx_font_bold" id="Sx2.F2.11.1">Simulation framework based on machine learning frameworks</span>. (a) Flowchart of designing the chiroptical heterostructure to achieve prominent dynamic tunability ranges of CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.F2.5.m1.1"><semantics id="Sx2.F2.5.m1.1b"><msub id="Sx2.F2.5.m1.1.1" xref="Sx2.F2.5.m1.1.1.cmml"><mi id="Sx2.F2.5.m1.1.1b" xref="Sx2.F2.5.m1.1.1.cmml"></mi><mtext id="Sx2.F2.5.m1.1.1.1" xref="Sx2.F2.5.m1.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.F2.5.m1.1c"><apply id="Sx2.F2.5.m1.1.1.cmml" xref="Sx2.F2.5.m1.1.1"><ci id="Sx2.F2.5.m1.1.1.1a.cmml" xref="Sx2.F2.5.m1.1.1.1"><mtext id="Sx2.F2.5.m1.1.1.1.cmml" mathsize="70%" xref="Sx2.F2.5.m1.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F2.5.m1.1d">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.F2.5.m1.1e">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> or LDLB (<math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.F2.6.m2.1"><semantics id="Sx2.F2.6.m2.1b"><mi id="Sx2.F2.6.m2.1.1" mathvariant="normal" xref="Sx2.F2.6.m2.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.F2.6.m2.1c"><ci id="Sx2.F2.6.m2.1.1.cmml" xref="Sx2.F2.6.m2.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F2.6.m2.1d">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.F2.6.m2.1e">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.F2.7.m3.1"><semantics id="Sx2.F2.7.m3.1b"><msub id="Sx2.F2.7.m3.1.1" xref="Sx2.F2.7.m3.1.1.cmml"><mi id="Sx2.F2.7.m3.1.1b" xref="Sx2.F2.7.m3.1.1.cmml"></mi><mtext id="Sx2.F2.7.m3.1.1.1" xref="Sx2.F2.7.m3.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.F2.7.m3.1c"><apply id="Sx2.F2.7.m3.1.1.cmml" xref="Sx2.F2.7.m3.1.1"><ci id="Sx2.F2.7.m3.1.1.1a.cmml" xref="Sx2.F2.7.m3.1.1.1"><mtext id="Sx2.F2.7.m3.1.1.1.cmml" mathsize="70%" xref="Sx2.F2.7.m3.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F2.7.m3.1d">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.F2.7.m3.1e">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> or <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.F2.8.m4.1"><semantics id="Sx2.F2.8.m4.1b"><mi id="Sx2.F2.8.m4.1.1" mathvariant="normal" xref="Sx2.F2.8.m4.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.F2.8.m4.1c"><ci id="Sx2.F2.8.m4.1.1.cmml" xref="Sx2.F2.8.m4.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F2.8.m4.1d">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.F2.8.m4.1e">roman_Δ</annotation></semantics></math>LDLB) through differentiable programming enabled by the stochastic gradient descent (SGD) algorithm through the backpropagation algorithm in <span class="ltx_text ltx_font_typewriter" id="Sx2.F2.12.2">PyTorch</span> and derivative-free Bayesian optimization algorithm. The framework takes input from experimentally determined complex-valued dielectric functions of (b) an anisotropic aligned CNT film and (c) a sputtered isotropic GST film. In (b), the red (blue) solid line is the real part of the dielectric function of the aligned CNT film along (perpendicular to) the CNT axis. In (c), the red (blue) solid line is the real part of the dielectric function of the GST film under the crystalline (amorphous) phase. The dashed lines are imaginary parts in both (b) and (c).</figcaption> </figure> <div class="ltx_para" id="Sx2.SSx2.p2"> <p class="ltx_p" id="Sx2.SSx2.p2.18">To design the heterostructure to achieve optimal tunable ranges of CD<sub class="ltx_sub" id="Sx2.SSx2.p2.18.1">iso</sub> and LDLB responses, a randomly initiated structure <math alttext="s_{0}" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.2.m2.1"><semantics id="Sx2.SSx2.p2.2.m2.1a"><msub id="Sx2.SSx2.p2.2.m2.1.1" xref="Sx2.SSx2.p2.2.m2.1.1.cmml"><mi id="Sx2.SSx2.p2.2.m2.1.1.2" xref="Sx2.SSx2.p2.2.m2.1.1.2.cmml">s</mi><mn id="Sx2.SSx2.p2.2.m2.1.1.3" xref="Sx2.SSx2.p2.2.m2.1.1.3.cmml">0</mn></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.2.m2.1b"><apply id="Sx2.SSx2.p2.2.m2.1.1.cmml" xref="Sx2.SSx2.p2.2.m2.1.1"><csymbol cd="ambiguous" id="Sx2.SSx2.p2.2.m2.1.1.1.cmml" xref="Sx2.SSx2.p2.2.m2.1.1">subscript</csymbol><ci id="Sx2.SSx2.p2.2.m2.1.1.2.cmml" xref="Sx2.SSx2.p2.2.m2.1.1.2">𝑠</ci><cn id="Sx2.SSx2.p2.2.m2.1.1.3.cmml" type="integer" xref="Sx2.SSx2.p2.2.m2.1.1.3">0</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.2.m2.1c">s_{0}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.2.m2.1d">italic_s start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT</annotation></semantics></math> was input into the TMM to calculate CD<sub class="ltx_sub" id="Sx2.SSx2.p2.18.2">iso</sub> and LDLB responses when the dielectric functions of amorphous and crystalline GST were used. The difference of CD<sub class="ltx_sub" id="Sx2.SSx2.p2.18.3">iso</sub> (LDLB) spectra in the wavelength range of interest under two states of GST, denoted as <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.5.m5.1"><semantics id="Sx2.SSx2.p2.5.m5.1a"><mi id="Sx2.SSx2.p2.5.m5.1.1" mathvariant="normal" xref="Sx2.SSx2.p2.5.m5.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.5.m5.1b"><ci id="Sx2.SSx2.p2.5.m5.1.1.cmml" xref="Sx2.SSx2.p2.5.m5.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.5.m5.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.5.m5.1d">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.6.m6.1"><semantics id="Sx2.SSx2.p2.6.m6.1a"><msub id="Sx2.SSx2.p2.6.m6.1.1" xref="Sx2.SSx2.p2.6.m6.1.1.cmml"><mi id="Sx2.SSx2.p2.6.m6.1.1a" xref="Sx2.SSx2.p2.6.m6.1.1.cmml"></mi><mtext id="Sx2.SSx2.p2.6.m6.1.1.1" xref="Sx2.SSx2.p2.6.m6.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.6.m6.1b"><apply id="Sx2.SSx2.p2.6.m6.1.1.cmml" xref="Sx2.SSx2.p2.6.m6.1.1"><ci id="Sx2.SSx2.p2.6.m6.1.1.1a.cmml" xref="Sx2.SSx2.p2.6.m6.1.1.1"><mtext id="Sx2.SSx2.p2.6.m6.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx2.p2.6.m6.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.6.m6.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.6.m6.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> (<math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.7.m7.1"><semantics id="Sx2.SSx2.p2.7.m7.1a"><mi id="Sx2.SSx2.p2.7.m7.1.1" mathvariant="normal" xref="Sx2.SSx2.p2.7.m7.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.7.m7.1b"><ci id="Sx2.SSx2.p2.7.m7.1.1.cmml" xref="Sx2.SSx2.p2.7.m7.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.7.m7.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.7.m7.1d">roman_Δ</annotation></semantics></math>LDLB), was used to define optimization target functions. In principle, any other physical quantities calculated from transmission and reflection coefficients can become target functions, such as the dissymmetry <math alttext="g" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.8.m8.1"><semantics id="Sx2.SSx2.p2.8.m8.1a"><mi id="Sx2.SSx2.p2.8.m8.1.1" xref="Sx2.SSx2.p2.8.m8.1.1.cmml">g</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.8.m8.1b"><ci id="Sx2.SSx2.p2.8.m8.1.1.cmml" xref="Sx2.SSx2.p2.8.m8.1.1">𝑔</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.8.m8.1c">g</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.8.m8.1d">italic_g</annotation></semantics></math> factor defined as the ratio of CD<sub class="ltx_sub" id="Sx2.SSx2.p2.18.4">iso</sub> over the attenuation under unpolarized light. We developed two different categories of optimization algorithms. The first one is based on the stochastic gradient descent algorithm implemented using <span class="ltx_text ltx_font_typewriter" id="Sx2.SSx2.p2.18.5">PyTorch</span>-supported backpropagation algorithm. Since the backpropagation algorithm aims to minimize a target loss function, the loss function was defined as the most negative absolute value of <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.10.m10.1"><semantics id="Sx2.SSx2.p2.10.m10.1a"><mi id="Sx2.SSx2.p2.10.m10.1.1" mathvariant="normal" xref="Sx2.SSx2.p2.10.m10.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.10.m10.1b"><ci id="Sx2.SSx2.p2.10.m10.1.1.cmml" xref="Sx2.SSx2.p2.10.m10.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.10.m10.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.10.m10.1d">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.11.m11.1"><semantics id="Sx2.SSx2.p2.11.m11.1a"><msub id="Sx2.SSx2.p2.11.m11.1.1" xref="Sx2.SSx2.p2.11.m11.1.1.cmml"><mi id="Sx2.SSx2.p2.11.m11.1.1a" xref="Sx2.SSx2.p2.11.m11.1.1.cmml"></mi><mtext id="Sx2.SSx2.p2.11.m11.1.1.1" xref="Sx2.SSx2.p2.11.m11.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.11.m11.1b"><apply id="Sx2.SSx2.p2.11.m11.1.1.cmml" xref="Sx2.SSx2.p2.11.m11.1.1"><ci id="Sx2.SSx2.p2.11.m11.1.1.1a.cmml" xref="Sx2.SSx2.p2.11.m11.1.1.1"><mtext id="Sx2.SSx2.p2.11.m11.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx2.p2.11.m11.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.11.m11.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.11.m11.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> or <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.12.m12.1"><semantics id="Sx2.SSx2.p2.12.m12.1a"><mi id="Sx2.SSx2.p2.12.m12.1.1" mathvariant="normal" xref="Sx2.SSx2.p2.12.m12.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.12.m12.1b"><ci id="Sx2.SSx2.p2.12.m12.1.1.cmml" xref="Sx2.SSx2.p2.12.m12.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.12.m12.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.12.m12.1d">roman_Δ</annotation></semantics></math>LDLB spectra. Based on the gradient calculated from the backpropagation algorithm, the heterostructure parameters were updated. Hence, in <math alttext="i" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.13.m13.1"><semantics id="Sx2.SSx2.p2.13.m13.1a"><mi id="Sx2.SSx2.p2.13.m13.1.1" xref="Sx2.SSx2.p2.13.m13.1.1.cmml">i</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.13.m13.1b"><ci id="Sx2.SSx2.p2.13.m13.1.1.cmml" xref="Sx2.SSx2.p2.13.m13.1.1">𝑖</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.13.m13.1c">i</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.13.m13.1d">italic_i</annotation></semantics></math>-th iteration, the set of heterostructure parameters <math alttext="s_{i}" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.14.m14.1"><semantics id="Sx2.SSx2.p2.14.m14.1a"><msub id="Sx2.SSx2.p2.14.m14.1.1" xref="Sx2.SSx2.p2.14.m14.1.1.cmml"><mi id="Sx2.SSx2.p2.14.m14.1.1.2" xref="Sx2.SSx2.p2.14.m14.1.1.2.cmml">s</mi><mi id="Sx2.SSx2.p2.14.m14.1.1.3" xref="Sx2.SSx2.p2.14.m14.1.1.3.cmml">i</mi></msub><annotation-xml encoding="MathML-Content" 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id="Sx2.SSx2.p2.15.m15.1c">s_{i+1}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.15.m15.1d">italic_s start_POSTSUBSCRIPT italic_i + 1 end_POSTSUBSCRIPT</annotation></semantics></math> to decrease the loss function, which was equivalent to increase <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.16.m16.1"><semantics id="Sx2.SSx2.p2.16.m16.1a"><mi id="Sx2.SSx2.p2.16.m16.1.1" mathvariant="normal" xref="Sx2.SSx2.p2.16.m16.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.16.m16.1b"><ci id="Sx2.SSx2.p2.16.m16.1.1.cmml" xref="Sx2.SSx2.p2.16.m16.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.16.m16.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.16.m16.1d">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.17.m17.1"><semantics id="Sx2.SSx2.p2.17.m17.1a"><msub id="Sx2.SSx2.p2.17.m17.1.1" xref="Sx2.SSx2.p2.17.m17.1.1.cmml"><mi id="Sx2.SSx2.p2.17.m17.1.1a" xref="Sx2.SSx2.p2.17.m17.1.1.cmml"></mi><mtext id="Sx2.SSx2.p2.17.m17.1.1.1" xref="Sx2.SSx2.p2.17.m17.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.17.m17.1b"><apply id="Sx2.SSx2.p2.17.m17.1.1.cmml" xref="Sx2.SSx2.p2.17.m17.1.1"><ci id="Sx2.SSx2.p2.17.m17.1.1.1a.cmml" xref="Sx2.SSx2.p2.17.m17.1.1.1"><mtext id="Sx2.SSx2.p2.17.m17.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx2.p2.17.m17.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.17.m17.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.17.m17.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> or <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx2.p2.18.m18.1"><semantics id="Sx2.SSx2.p2.18.m18.1a"><mi id="Sx2.SSx2.p2.18.m18.1.1" mathvariant="normal" xref="Sx2.SSx2.p2.18.m18.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p2.18.m18.1b"><ci id="Sx2.SSx2.p2.18.m18.1.1.cmml" xref="Sx2.SSx2.p2.18.m18.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p2.18.m18.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p2.18.m18.1d">roman_Δ</annotation></semantics></math>LDLB. The optimal heterostructure was obtained after multiple iterations.</p> </div> <div class="ltx_para" id="Sx2.SSx2.p3"> <p class="ltx_p" id="Sx2.SSx2.p3.6">In addition to the gradient-based algorithm, we also demonstrated the feasibility of derivative-free algorithms to design the heterostructure. Note that although our developed TMM solver using <span class="ltx_text ltx_font_typewriter" id="Sx2.SSx2.p3.6.1">PyTorch</span> is differentiable, the derivative-free algorithm can be broadly applicable even when gradients are not available in TMM implementations. Specifically, we utilized the Bayesian optimization algorithm. In contrast to the gradient-based algorithm, the target of the Bayesian optimization algorithm is to maximize the reward function. Hence, we defined the largest absolute value of <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx2.p3.1.m1.1"><semantics id="Sx2.SSx2.p3.1.m1.1a"><mi id="Sx2.SSx2.p3.1.m1.1.1" mathvariant="normal" xref="Sx2.SSx2.p3.1.m1.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p3.1.m1.1b"><ci id="Sx2.SSx2.p3.1.m1.1.1.cmml" xref="Sx2.SSx2.p3.1.m1.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p3.1.m1.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p3.1.m1.1d">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx2.p3.2.m2.1"><semantics id="Sx2.SSx2.p3.2.m2.1a"><msub id="Sx2.SSx2.p3.2.m2.1.1" xref="Sx2.SSx2.p3.2.m2.1.1.cmml"><mi id="Sx2.SSx2.p3.2.m2.1.1a" xref="Sx2.SSx2.p3.2.m2.1.1.cmml"></mi><mtext id="Sx2.SSx2.p3.2.m2.1.1.1" xref="Sx2.SSx2.p3.2.m2.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p3.2.m2.1b"><apply id="Sx2.SSx2.p3.2.m2.1.1.cmml" xref="Sx2.SSx2.p3.2.m2.1.1"><ci id="Sx2.SSx2.p3.2.m2.1.1.1a.cmml" xref="Sx2.SSx2.p3.2.m2.1.1.1"><mtext id="Sx2.SSx2.p3.2.m2.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx2.p3.2.m2.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p3.2.m2.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p3.2.m2.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> or <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx2.p3.3.m3.1"><semantics id="Sx2.SSx2.p3.3.m3.1a"><mi id="Sx2.SSx2.p3.3.m3.1.1" mathvariant="normal" xref="Sx2.SSx2.p3.3.m3.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p3.3.m3.1b"><ci id="Sx2.SSx2.p3.3.m3.1.1.cmml" xref="Sx2.SSx2.p3.3.m3.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p3.3.m3.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p3.3.m3.1d">roman_Δ</annotation></semantics></math>LDLB spectra as the reward function. In each iteration, based on prior sets of structural parameters and reward functions, the algorithm determined the Bayesian posterior probability and a new set of structural parameters through sampling. After multiple iterations, the heterostructures that display <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx2.p3.4.m4.1"><semantics id="Sx2.SSx2.p3.4.m4.1a"><mi id="Sx2.SSx2.p3.4.m4.1.1" mathvariant="normal" xref="Sx2.SSx2.p3.4.m4.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p3.4.m4.1b"><ci id="Sx2.SSx2.p3.4.m4.1.1.cmml" xref="Sx2.SSx2.p3.4.m4.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p3.4.m4.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p3.4.m4.1d">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx2.p3.5.m5.1"><semantics id="Sx2.SSx2.p3.5.m5.1a"><msub id="Sx2.SSx2.p3.5.m5.1.1" xref="Sx2.SSx2.p3.5.m5.1.1.cmml"><mi id="Sx2.SSx2.p3.5.m5.1.1a" xref="Sx2.SSx2.p3.5.m5.1.1.cmml"></mi><mtext id="Sx2.SSx2.p3.5.m5.1.1.1" xref="Sx2.SSx2.p3.5.m5.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p3.5.m5.1b"><apply id="Sx2.SSx2.p3.5.m5.1.1.cmml" xref="Sx2.SSx2.p3.5.m5.1.1"><ci id="Sx2.SSx2.p3.5.m5.1.1.1a.cmml" xref="Sx2.SSx2.p3.5.m5.1.1.1"><mtext id="Sx2.SSx2.p3.5.m5.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx2.p3.5.m5.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p3.5.m5.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p3.5.m5.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> or <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx2.p3.6.m6.1"><semantics id="Sx2.SSx2.p3.6.m6.1a"><mi id="Sx2.SSx2.p3.6.m6.1.1" mathvariant="normal" xref="Sx2.SSx2.p3.6.m6.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx2.p3.6.m6.1b"><ci id="Sx2.SSx2.p3.6.m6.1.1.cmml" xref="Sx2.SSx2.p3.6.m6.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx2.p3.6.m6.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx2.p3.6.m6.1d">roman_Δ</annotation></semantics></math>LDLB were highly probably sampled.</p> </div> </section> <section class="ltx_subsection" id="Sx2.SSx3"> <h3 class="ltx_title ltx_title_subsection">Experimental demonstration</h3> <div class="ltx_para" id="Sx2.SSx3.p1"> <p class="ltx_p" id="Sx2.SSx3.p1.10">Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F3" title="Figure 3 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">3</span></a>a illustrates a specific heterostructure consisting of two layers of twisted aligned CNTs, two silicon oxide (SiO<sub class="ltx_sub" id="Sx2.SSx3.p1.10.1"><span class="ltx_text ltx_font_italic" id="Sx2.SSx3.p1.10.1.1">2</span></sub>) layers, and one GST layer between SiO<sub class="ltx_sub" id="Sx2.SSx3.p1.10.2"><span class="ltx_text ltx_font_italic" id="Sx2.SSx3.p1.10.2.1">2</span></sub> layers to demonstrate the optimization using the simulation framework and experimental validation. Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F3" title="Figure 3 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">3</span></a>b and <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F3" title="Figure 3 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">3</span></a>c display training curves using the differentiable backpropagation algorithm and derivative-free Bayesian optimization algorithm, respectively, for optimizing <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx3.p1.3.m3.1"><semantics id="Sx2.SSx3.p1.3.m3.1a"><mi id="Sx2.SSx3.p1.3.m3.1.1" mathvariant="normal" xref="Sx2.SSx3.p1.3.m3.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p1.3.m3.1b"><ci id="Sx2.SSx3.p1.3.m3.1.1.cmml" xref="Sx2.SSx3.p1.3.m3.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p1.3.m3.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p1.3.m3.1d">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx3.p1.4.m4.1"><semantics id="Sx2.SSx3.p1.4.m4.1a"><msub id="Sx2.SSx3.p1.4.m4.1.1" xref="Sx2.SSx3.p1.4.m4.1.1.cmml"><mi id="Sx2.SSx3.p1.4.m4.1.1a" xref="Sx2.SSx3.p1.4.m4.1.1.cmml"></mi><mtext id="Sx2.SSx3.p1.4.m4.1.1.1" xref="Sx2.SSx3.p1.4.m4.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p1.4.m4.1b"><apply id="Sx2.SSx3.p1.4.m4.1.1.cmml" xref="Sx2.SSx3.p1.4.m4.1.1"><ci id="Sx2.SSx3.p1.4.m4.1.1.1a.cmml" xref="Sx2.SSx3.p1.4.m4.1.1.1"><mtext id="Sx2.SSx3.p1.4.m4.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx3.p1.4.m4.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p1.4.m4.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p1.4.m4.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> and the <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx3.p1.5.m5.1"><semantics id="Sx2.SSx3.p1.5.m5.1a"><mi id="Sx2.SSx3.p1.5.m5.1.1" mathvariant="normal" xref="Sx2.SSx3.p1.5.m5.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p1.5.m5.1b"><ci id="Sx2.SSx3.p1.5.m5.1.1.cmml" xref="Sx2.SSx3.p1.5.m5.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p1.5.m5.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p1.5.m5.1d">roman_Δ</annotation></semantics></math>LDLB; see Methods for more details. The twisted angle between aligned CNTs and thicknesses of SiO<sub class="ltx_sub" id="Sx2.SSx3.p1.10.3"><span class="ltx_text ltx_font_italic" id="Sx2.SSx3.p1.10.3.1">2</span></sub> and GST layers were structural parameters to be optimized. The aligned CNT thickness was assumed to be a constant and benchmarked by comparing the ultraviolet attenuation with a standard sample; see Methods for more details. For Bayesian optimization, Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F3" title="Figure 3 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">3</span></a>c shows the accumulated average of <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx3.p1.7.m7.1"><semantics id="Sx2.SSx3.p1.7.m7.1a"><mi id="Sx2.SSx3.p1.7.m7.1.1" mathvariant="normal" xref="Sx2.SSx3.p1.7.m7.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p1.7.m7.1b"><ci id="Sx2.SSx3.p1.7.m7.1.1.cmml" xref="Sx2.SSx3.p1.7.m7.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p1.7.m7.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p1.7.m7.1d">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx3.p1.8.m8.1"><semantics id="Sx2.SSx3.p1.8.m8.1a"><msub id="Sx2.SSx3.p1.8.m8.1.1" xref="Sx2.SSx3.p1.8.m8.1.1.cmml"><mi id="Sx2.SSx3.p1.8.m8.1.1a" xref="Sx2.SSx3.p1.8.m8.1.1.cmml"></mi><mtext id="Sx2.SSx3.p1.8.m8.1.1.1" xref="Sx2.SSx3.p1.8.m8.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p1.8.m8.1b"><apply id="Sx2.SSx3.p1.8.m8.1.1.cmml" xref="Sx2.SSx3.p1.8.m8.1.1"><ci id="Sx2.SSx3.p1.8.m8.1.1.1a.cmml" xref="Sx2.SSx3.p1.8.m8.1.1.1"><mtext id="Sx2.SSx3.p1.8.m8.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx3.p1.8.m8.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p1.8.m8.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p1.8.m8.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> and <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx3.p1.9.m9.1"><semantics id="Sx2.SSx3.p1.9.m9.1a"><mi id="Sx2.SSx3.p1.9.m9.1.1" mathvariant="normal" xref="Sx2.SSx3.p1.9.m9.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p1.9.m9.1b"><ci id="Sx2.SSx3.p1.9.m9.1.1.cmml" xref="Sx2.SSx3.p1.9.m9.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p1.9.m9.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p1.9.m9.1d">roman_Δ</annotation></semantics></math>LDLB. In comparison, the average values from the Bayesian optimization are lower than those from the backpropagation algorithm because of relatively wide parameter ranges. If parameter ranges were set narrower, the Bayesian optimization produced similar optimization values to the backpropagation algorithm; see Supplementary Fig. 5a. The obtained twisted angle between two aligned CNT layers was 45<sup class="ltx_sup" id="Sx2.SSx3.p1.10.4"><span class="ltx_text ltx_font_italic" id="Sx2.SSx3.p1.10.4.1">∘</span></sup> in both algorithms (Supplementary Fig. 5b and Fig. 5c), which agrees with the optimized angle in CNT-only twisted stack <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib17" title="">17</a>]</cite>.</p> </div> <figure class="ltx_figure" id="Sx2.F3"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_landscape" height="499" id="Sx2.F3.g1" src="x3.png" width="830"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 3: </span><span class="ltx_text ltx_font_bold" id="Sx2.F3.16.1">Simulation and experimental implementation of a programmable heterostructure with two layers of aligned CNT films</span>. (a) Illustration of the specific heterostructure containing two layers of twisted aligned CNT films. Training curves of <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.F3.8.m1.1"><semantics id="Sx2.F3.8.m1.1b"><mi id="Sx2.F3.8.m1.1.1" mathvariant="normal" xref="Sx2.F3.8.m1.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.F3.8.m1.1c"><ci id="Sx2.F3.8.m1.1.1.cmml" xref="Sx2.F3.8.m1.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F3.8.m1.1d">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.F3.8.m1.1e">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.F3.9.m2.1"><semantics id="Sx2.F3.9.m2.1b"><msub id="Sx2.F3.9.m2.1.1" xref="Sx2.F3.9.m2.1.1.cmml"><mi id="Sx2.F3.9.m2.1.1b" xref="Sx2.F3.9.m2.1.1.cmml"></mi><mtext id="Sx2.F3.9.m2.1.1.1" xref="Sx2.F3.9.m2.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.F3.9.m2.1c"><apply id="Sx2.F3.9.m2.1.1.cmml" xref="Sx2.F3.9.m2.1.1"><ci id="Sx2.F3.9.m2.1.1.1a.cmml" xref="Sx2.F3.9.m2.1.1.1"><mtext id="Sx2.F3.9.m2.1.1.1.cmml" mathsize="70%" xref="Sx2.F3.9.m2.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F3.9.m2.1d">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.F3.9.m2.1e">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> (red lines in (b) or dots in (c)) and <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.F3.10.m3.1"><semantics id="Sx2.F3.10.m3.1b"><mi id="Sx2.F3.10.m3.1.1" mathvariant="normal" xref="Sx2.F3.10.m3.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.F3.10.m3.1c"><ci id="Sx2.F3.10.m3.1.1.cmml" xref="Sx2.F3.10.m3.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F3.10.m3.1d">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.F3.10.m3.1e">roman_Δ</annotation></semantics></math>LDLB (blue lines in (b) or dots in (c)) using (b) differentiable programming and (c) derivative-free Bayesian optimization, respectively. Red (blue) dashed lines in (c) indicate optimized values for <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.F3.11.m4.1"><semantics id="Sx2.F3.11.m4.1b"><mi id="Sx2.F3.11.m4.1.1" mathvariant="normal" xref="Sx2.F3.11.m4.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.F3.11.m4.1c"><ci id="Sx2.F3.11.m4.1.1.cmml" xref="Sx2.F3.11.m4.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F3.11.m4.1d">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.F3.11.m4.1e">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.F3.12.m5.1"><semantics id="Sx2.F3.12.m5.1b"><msub id="Sx2.F3.12.m5.1.1" xref="Sx2.F3.12.m5.1.1.cmml"><mi id="Sx2.F3.12.m5.1.1b" xref="Sx2.F3.12.m5.1.1.cmml"></mi><mtext id="Sx2.F3.12.m5.1.1.1" xref="Sx2.F3.12.m5.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.F3.12.m5.1c"><apply id="Sx2.F3.12.m5.1.1.cmml" xref="Sx2.F3.12.m5.1.1"><ci id="Sx2.F3.12.m5.1.1.1a.cmml" xref="Sx2.F3.12.m5.1.1.1"><mtext id="Sx2.F3.12.m5.1.1.1.cmml" mathsize="70%" xref="Sx2.F3.12.m5.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F3.12.m5.1d">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.F3.12.m5.1e">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> and <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.F3.13.m6.1"><semantics id="Sx2.F3.13.m6.1b"><mi id="Sx2.F3.13.m6.1.1" mathvariant="normal" xref="Sx2.F3.13.m6.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.F3.13.m6.1c"><ci id="Sx2.F3.13.m6.1.1.cmml" xref="Sx2.F3.13.m6.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F3.13.m6.1d">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.F3.13.m6.1e">roman_Δ</annotation></semantics></math>LDLB from (b). Measured (solid lines) and simulation (dashed lines) spectra of (d) CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.F3.14.m7.1"><semantics id="Sx2.F3.14.m7.1b"><msub id="Sx2.F3.14.m7.1.1" xref="Sx2.F3.14.m7.1.1.cmml"><mi id="Sx2.F3.14.m7.1.1b" xref="Sx2.F3.14.m7.1.1.cmml"></mi><mtext id="Sx2.F3.14.m7.1.1.1" xref="Sx2.F3.14.m7.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.F3.14.m7.1c"><apply id="Sx2.F3.14.m7.1.1.cmml" xref="Sx2.F3.14.m7.1.1"><ci id="Sx2.F3.14.m7.1.1.1a.cmml" xref="Sx2.F3.14.m7.1.1.1"><mtext id="Sx2.F3.14.m7.1.1.1.cmml" mathsize="70%" xref="Sx2.F3.14.m7.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F3.14.m7.1d">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.F3.14.m7.1e">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> and (e) LDLB responses under GST crystalline (red lines) and amorphous (blue lines) phases, respectively. (f) Observed CD spectra measured from the front (solid lines) and back (dashed lines) sides of the same heterostructure under GST crystalline (red lines) and amorphous (blue lines) phases. The gray shaded area indicates the polarity reversal range. </figcaption> </figure> <div class="ltx_para" id="Sx2.SSx3.p2"> <p class="ltx_p" id="Sx2.SSx3.p2.8">We fabricated optimized heterostructures by transferring SAVF-prepared aligned CNT films and depositing GST and SiO<sub class="ltx_sub" id="Sx2.SSx3.p2.8.1"><span class="ltx_text ltx_font_italic" id="Sx2.SSx3.p2.8.1.1">2</span></sub> films using sputtering on fused silica substrates, which are transparent in the measurement spectra range (200 nm – 900 nm); see Methods for more details. Similar to the simulation framework, we performed four CD measurements using a standard CD spectrometer with a compatible 3D-printed sample holder under four configurations of sample rotation and flipping to obtain CD<sub class="ltx_sub" id="Sx2.SSx3.p2.8.2">iso</sub> and LDLB responses; see Methods for more details. The as-deposited GST film was in the amorphous phase and was converted into the crystalline phase by heating the sample; see Methods, Supplementary Fig. 6, and Supplementary Video 1 for more details. Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F3" title="Figure 3 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">3</span></a>d and <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F3" title="Figure 3 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">3</span></a>e show measured CD<sub class="ltx_sub" id="Sx2.SSx3.p2.8.3">iso</sub> and LDLB spectra (solid lines) when the GST film was under amorphous and crystalline phases, which agreed with the simulation spectra (dashed lines) using the developed simulation framework. The maximum obtained <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx3.p2.4.m4.1"><semantics id="Sx2.SSx3.p2.4.m4.1a"><mi id="Sx2.SSx3.p2.4.m4.1.1" mathvariant="normal" xref="Sx2.SSx3.p2.4.m4.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p2.4.m4.1b"><ci id="Sx2.SSx3.p2.4.m4.1.1.cmml" xref="Sx2.SSx3.p2.4.m4.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p2.4.m4.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p2.4.m4.1d">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx3.p2.5.m5.1"><semantics id="Sx2.SSx3.p2.5.m5.1a"><msub id="Sx2.SSx3.p2.5.m5.1.1" xref="Sx2.SSx3.p2.5.m5.1.1.cmml"><mi id="Sx2.SSx3.p2.5.m5.1.1a" xref="Sx2.SSx3.p2.5.m5.1.1.cmml"></mi><mtext id="Sx2.SSx3.p2.5.m5.1.1.1" xref="Sx2.SSx3.p2.5.m5.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p2.5.m5.1b"><apply id="Sx2.SSx3.p2.5.m5.1.1.cmml" xref="Sx2.SSx3.p2.5.m5.1.1"><ci id="Sx2.SSx3.p2.5.m5.1.1.1a.cmml" xref="Sx2.SSx3.p2.5.m5.1.1.1"><mtext id="Sx2.SSx3.p2.5.m5.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx3.p2.5.m5.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p2.5.m5.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p2.5.m5.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> was 123 mdeg at 750 nm wavelength and the maximum obtained <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx3.p2.6.m6.1"><semantics id="Sx2.SSx3.p2.6.m6.1a"><mi id="Sx2.SSx3.p2.6.m6.1.1" mathvariant="normal" xref="Sx2.SSx3.p2.6.m6.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p2.6.m6.1b"><ci id="Sx2.SSx3.p2.6.m6.1.1.cmml" xref="Sx2.SSx3.p2.6.m6.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p2.6.m6.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p2.6.m6.1d">roman_Δ</annotation></semantics></math>LDLB was 60 mdeg at 737 nm wavelength. Broadband CD<sub class="ltx_sub" id="Sx2.SSx3.p2.8.4">iso</sub> and LDLB spectra under two GST phases are shown in Supplementary Fig. 7a and 7b. As shown in Supplementary Fig. 7c, the measured average absorption spectra of LCP and RCP light of the heterostructure under two GST phases (solid lines) also showed agreement with simulations (dashed lines). Further, we designed and optimized the heterostructure for the tunable range of <math alttext="g" class="ltx_Math" display="inline" id="Sx2.SSx3.p2.8.m8.1"><semantics id="Sx2.SSx3.p2.8.m8.1a"><mi id="Sx2.SSx3.p2.8.m8.1.1" xref="Sx2.SSx3.p2.8.m8.1.1.cmml">g</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p2.8.m8.1b"><ci id="Sx2.SSx3.p2.8.m8.1.1.cmml" xref="Sx2.SSx3.p2.8.m8.1.1">𝑔</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p2.8.m8.1c">g</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p2.8.m8.1d">italic_g</annotation></semantics></math> factor using the backpropagation algorithm and experimentally measured spectra, which also agreed with simulation spectra (Supplementary Fig. 8). This demonstrates the broad applicability of the simulation framework and experimental implementation of the heterostructure.</p> </div> <div class="ltx_para" id="Sx2.SSx3.p3"> <p class="ltx_p" id="Sx2.SSx3.p3.8">In particular, prominent LDLB responses were observed in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F3" title="Figure 3 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">3</span></a>e. For the same heterostructure, Fig. <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F3" title="Figure 3 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">3</span></a>f and Supplementary Fig. 9 display measured CD spectra (CD<sub class="ltx_sub" id="Sx2.SSx3.p3.8.1">obs</sub>) when the front and back sides of the heterostructure faced the direction of incident light; see Methods for more details. We observed a clear sign or polarity reversal of CD<sub class="ltx_sub" id="Sx2.SSx3.p3.8.2">obs</sub> in a broadband wavelength range of <math alttext="424-721" class="ltx_Math" display="inline" id="Sx2.SSx3.p3.3.m3.1"><semantics id="Sx2.SSx3.p3.3.m3.1a"><mrow id="Sx2.SSx3.p3.3.m3.1.1" xref="Sx2.SSx3.p3.3.m3.1.1.cmml"><mn id="Sx2.SSx3.p3.3.m3.1.1.2" xref="Sx2.SSx3.p3.3.m3.1.1.2.cmml">424</mn><mo id="Sx2.SSx3.p3.3.m3.1.1.1" xref="Sx2.SSx3.p3.3.m3.1.1.1.cmml">−</mo><mn id="Sx2.SSx3.p3.3.m3.1.1.3" xref="Sx2.SSx3.p3.3.m3.1.1.3.cmml">721</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p3.3.m3.1b"><apply id="Sx2.SSx3.p3.3.m3.1.1.cmml" xref="Sx2.SSx3.p3.3.m3.1.1"><minus id="Sx2.SSx3.p3.3.m3.1.1.1.cmml" xref="Sx2.SSx3.p3.3.m3.1.1.1"></minus><cn id="Sx2.SSx3.p3.3.m3.1.1.2.cmml" type="integer" xref="Sx2.SSx3.p3.3.m3.1.1.2">424</cn><cn id="Sx2.SSx3.p3.3.m3.1.1.3.cmml" type="integer" xref="Sx2.SSx3.p3.3.m3.1.1.3">721</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p3.3.m3.1c">424-721</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p3.3.m3.1d">424 - 721</annotation></semantics></math> nm for the GST amorphous phase and a wavelength range of <math alttext="421-735" class="ltx_Math" display="inline" id="Sx2.SSx3.p3.4.m4.1"><semantics id="Sx2.SSx3.p3.4.m4.1a"><mrow id="Sx2.SSx3.p3.4.m4.1.1" xref="Sx2.SSx3.p3.4.m4.1.1.cmml"><mn id="Sx2.SSx3.p3.4.m4.1.1.2" xref="Sx2.SSx3.p3.4.m4.1.1.2.cmml">421</mn><mo id="Sx2.SSx3.p3.4.m4.1.1.1" xref="Sx2.SSx3.p3.4.m4.1.1.1.cmml">−</mo><mn id="Sx2.SSx3.p3.4.m4.1.1.3" xref="Sx2.SSx3.p3.4.m4.1.1.3.cmml">735</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p3.4.m4.1b"><apply id="Sx2.SSx3.p3.4.m4.1.1.cmml" xref="Sx2.SSx3.p3.4.m4.1.1"><minus id="Sx2.SSx3.p3.4.m4.1.1.1.cmml" xref="Sx2.SSx3.p3.4.m4.1.1.1"></minus><cn id="Sx2.SSx3.p3.4.m4.1.1.2.cmml" type="integer" xref="Sx2.SSx3.p3.4.m4.1.1.2">421</cn><cn id="Sx2.SSx3.p3.4.m4.1.1.3.cmml" type="integer" xref="Sx2.SSx3.p3.4.m4.1.1.3">735</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p3.4.m4.1c">421-735</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p3.4.m4.1d">421 - 735</annotation></semantics></math> nm for the crystalline phase. As mentioned before, the LDLB response originates from the difference between intensity attenuation and phase delay extrema due to the interference of multiple reflections in the heterostructure. To confirm this, we further employed the developed simulation framework to calculate linear-polarization-dependent transmitted intensity and the phase delay between transmitted light and input light at a specific wavelength, as illustrated in Supplementary Fig. 10a. The zero degree was defined when the orientation of the first aligned CNT layer and the polarization direction were the same. Supplementary Fig. 10b and 10c display the calculated normalized attenuation and phase delay as a function of polarization angle at 630 nm for two GST phases, showing clear shifts of extrema positions. 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Note these values are also different from the orientation of second-layer aligned CNTs, which is <math alttext="45^{\circ}" class="ltx_Math" display="inline" id="Sx2.SSx3.p3.8.m8.1"><semantics id="Sx2.SSx3.p3.8.m8.1a"><msup id="Sx2.SSx3.p3.8.m8.1.1" xref="Sx2.SSx3.p3.8.m8.1.1.cmml"><mn id="Sx2.SSx3.p3.8.m8.1.1.2" xref="Sx2.SSx3.p3.8.m8.1.1.2.cmml">45</mn><mo id="Sx2.SSx3.p3.8.m8.1.1.3" xref="Sx2.SSx3.p3.8.m8.1.1.3.cmml">∘</mo></msup><annotation-xml encoding="MathML-Content" id="Sx2.SSx3.p3.8.m8.1b"><apply id="Sx2.SSx3.p3.8.m8.1.1.cmml" xref="Sx2.SSx3.p3.8.m8.1.1"><csymbol cd="ambiguous" id="Sx2.SSx3.p3.8.m8.1.1.1.cmml" xref="Sx2.SSx3.p3.8.m8.1.1">superscript</csymbol><cn id="Sx2.SSx3.p3.8.m8.1.1.2.cmml" type="integer" xref="Sx2.SSx3.p3.8.m8.1.1.2">45</cn><compose id="Sx2.SSx3.p3.8.m8.1.1.3.cmml" xref="Sx2.SSx3.p3.8.m8.1.1.3"></compose></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx3.p3.8.m8.1c">45^{\circ}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx3.p3.8.m8.1d">45 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT</annotation></semantics></math> under the coordination system defined in Supplementary Fig. 10a. We also experimentally measured attenuation at 630 nm of the heterostructure as a function of polarization angle, confirming the shift, as shown in Supplementary Fig. 10d.</p> </div> <figure class="ltx_figure" id="Sx2.F4"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_square" height="706" id="Sx2.F4.g1" src="x4.png" width="747"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 4: </span><span class="ltx_text ltx_font_bold" id="Sx2.F4.16.1">Layer scalability of chiroptical responses in the programmable heterostructure</span>. (a) Illustration of heterostructures containing multiple CNTs-SiO<sub class="ltx_sub" id="Sx2.F4.17.2"><span class="ltx_text ltx_font_italic" id="Sx2.F4.17.2.1">2</span></sub>-GST-SiO<sub class="ltx_sub" id="Sx2.F4.18.3"><span class="ltx_text ltx_font_italic" id="Sx2.F4.18.3.1">2</span></sub> units. (b) Experimentally measured (solid lines) and simulation (dashed lines) CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.F4.9.m3.1"><semantics id="Sx2.F4.9.m3.1b"><msub id="Sx2.F4.9.m3.1.1" xref="Sx2.F4.9.m3.1.1.cmml"><mi id="Sx2.F4.9.m3.1.1b" xref="Sx2.F4.9.m3.1.1.cmml"></mi><mtext id="Sx2.F4.9.m3.1.1.1" xref="Sx2.F4.9.m3.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.F4.9.m3.1c"><apply id="Sx2.F4.9.m3.1.1.cmml" xref="Sx2.F4.9.m3.1.1"><ci id="Sx2.F4.9.m3.1.1.1a.cmml" xref="Sx2.F4.9.m3.1.1.1"><mtext id="Sx2.F4.9.m3.1.1.1.cmml" mathsize="70%" xref="Sx2.F4.9.m3.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F4.9.m3.1d">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.F4.9.m3.1e">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> spectra under GST amorphous (blue lines) and crystalline (red lines) phases, respectively. (c) <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.F4.10.m4.1"><semantics id="Sx2.F4.10.m4.1b"><mi id="Sx2.F4.10.m4.1.1" mathvariant="normal" xref="Sx2.F4.10.m4.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.F4.10.m4.1c"><ci id="Sx2.F4.10.m4.1.1.cmml" xref="Sx2.F4.10.m4.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F4.10.m4.1d">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.F4.10.m4.1e">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.F4.11.m5.1"><semantics id="Sx2.F4.11.m5.1b"><msub id="Sx2.F4.11.m5.1.1" xref="Sx2.F4.11.m5.1.1.cmml"><mi id="Sx2.F4.11.m5.1.1b" xref="Sx2.F4.11.m5.1.1.cmml"></mi><mtext id="Sx2.F4.11.m5.1.1.1" xref="Sx2.F4.11.m5.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.F4.11.m5.1c"><apply id="Sx2.F4.11.m5.1.1.cmml" xref="Sx2.F4.11.m5.1.1"><ci id="Sx2.F4.11.m5.1.1.1a.cmml" xref="Sx2.F4.11.m5.1.1.1"><mtext id="Sx2.F4.11.m5.1.1.1.cmml" mathsize="70%" xref="Sx2.F4.11.m5.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F4.11.m5.1d">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.F4.11.m5.1e">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> and (d) <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.F4.12.m6.1"><semantics id="Sx2.F4.12.m6.1b"><mi id="Sx2.F4.12.m6.1.1" mathvariant="normal" xref="Sx2.F4.12.m6.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.F4.12.m6.1c"><ci id="Sx2.F4.12.m6.1.1.cmml" xref="Sx2.F4.12.m6.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F4.12.m6.1d">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.F4.12.m6.1e">roman_Δ</annotation></semantics></math>LDLB spectra for heterostructures containing four (blue lines), five (green lines), and six layers (red lines) of twisted aligned CNT films.</figcaption> </figure> </section> <section class="ltx_subsection" id="Sx2.SSx4"> <h3 class="ltx_title ltx_title_subsection">Layer scalability</h3> <div class="ltx_para" id="Sx2.SSx4.p1"> <p class="ltx_p" id="Sx2.SSx4.p1.15">Further, we demonstrated that both the simulation framework and experimental implementation are scalable with respect to the number of layers in the heterostructure. Specifically, we repeated CNTs-SiO<sub class="ltx_sub" id="Sx2.SSx4.p1.15.1"><span class="ltx_text ltx_font_italic" id="Sx2.SSx4.p1.15.1.1">2</span></sub>-GST-SiO<sub class="ltx_sub" id="Sx2.SSx4.p1.15.2"><span class="ltx_text ltx_font_italic" id="Sx2.SSx4.p1.15.2.1">2</span></sub> configuration in the heterostructure to increase the layer number, as illustrated in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F4" title="Figure 4 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">4</span></a>a. We followed the same fabrication processes including the transfer of aligned CNT films and the sputtering deposition of other films; see Methods for more details. Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F4" title="Figure 4 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">4</span></a>b shows experimentally measured CD<sub class="ltx_sub" id="Sx2.SSx4.p1.15.3">iso</sub> spectra under two GST phases (solid lines), which agree with simulation CD<sub class="ltx_sub" id="Sx2.SSx4.p1.15.4">iso</sub> spectra (dashed lines). The maximum <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.5.m5.1"><semantics id="Sx2.SSx4.p1.5.m5.1a"><mi id="Sx2.SSx4.p1.5.m5.1.1" mathvariant="normal" xref="Sx2.SSx4.p1.5.m5.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.5.m5.1b"><ci id="Sx2.SSx4.p1.5.m5.1.1.cmml" xref="Sx2.SSx4.p1.5.m5.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.5.m5.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.5.m5.1d">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.6.m6.1"><semantics id="Sx2.SSx4.p1.6.m6.1a"><msub id="Sx2.SSx4.p1.6.m6.1.1" xref="Sx2.SSx4.p1.6.m6.1.1.cmml"><mi id="Sx2.SSx4.p1.6.m6.1.1a" xref="Sx2.SSx4.p1.6.m6.1.1.cmml"></mi><mtext id="Sx2.SSx4.p1.6.m6.1.1.1" xref="Sx2.SSx4.p1.6.m6.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.6.m6.1b"><apply id="Sx2.SSx4.p1.6.m6.1.1.cmml" xref="Sx2.SSx4.p1.6.m6.1.1"><ci id="Sx2.SSx4.p1.6.m6.1.1.1a.cmml" xref="Sx2.SSx4.p1.6.m6.1.1.1"><mtext id="Sx2.SSx4.p1.6.m6.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx4.p1.6.m6.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.6.m6.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.6.m6.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> was 363 mdeg at 752 nm wavelength, which is nearly three times as large as that of the heterostructure with two aligned CNT films in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F3" title="Figure 3 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">3</span></a>d. In addition, we designed heterostructures containing four, five, and six layers of twisted aligned CNT films for optimizing <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.7.m7.1"><semantics id="Sx2.SSx4.p1.7.m7.1a"><mi id="Sx2.SSx4.p1.7.m7.1.1" mathvariant="normal" xref="Sx2.SSx4.p1.7.m7.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.7.m7.1b"><ci id="Sx2.SSx4.p1.7.m7.1.1.cmml" xref="Sx2.SSx4.p1.7.m7.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.7.m7.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.7.m7.1d">roman_Δ</annotation></semantics></math>CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.8.m8.1"><semantics id="Sx2.SSx4.p1.8.m8.1a"><msub id="Sx2.SSx4.p1.8.m8.1.1" xref="Sx2.SSx4.p1.8.m8.1.1.cmml"><mi id="Sx2.SSx4.p1.8.m8.1.1a" xref="Sx2.SSx4.p1.8.m8.1.1.cmml"></mi><mtext id="Sx2.SSx4.p1.8.m8.1.1.1" xref="Sx2.SSx4.p1.8.m8.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.8.m8.1b"><apply id="Sx2.SSx4.p1.8.m8.1.1.cmml" xref="Sx2.SSx4.p1.8.m8.1.1"><ci id="Sx2.SSx4.p1.8.m8.1.1.1a.cmml" xref="Sx2.SSx4.p1.8.m8.1.1.1"><mtext id="Sx2.SSx4.p1.8.m8.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx4.p1.8.m8.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.8.m8.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.8.m8.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> and <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.9.m9.1"><semantics id="Sx2.SSx4.p1.9.m9.1a"><mi id="Sx2.SSx4.p1.9.m9.1.1" mathvariant="normal" xref="Sx2.SSx4.p1.9.m9.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.9.m9.1b"><ci id="Sx2.SSx4.p1.9.m9.1.1.cmml" xref="Sx2.SSx4.p1.9.m9.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.9.m9.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.9.m9.1d">roman_Δ</annotation></semantics></math>LDLB. Note that the total number of layers in the heterostructure containing six aligned CNT films is 21. Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F4" title="Figure 4 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">4</span></a>c and <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F4" title="Figure 4 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">4</span></a>d show their corresponding spectra. The obtained maximum <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.10.m10.1"><semantics id="Sx2.SSx4.p1.10.m10.1a"><mi id="Sx2.SSx4.p1.10.m10.1.1" mathvariant="normal" xref="Sx2.SSx4.p1.10.m10.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.10.m10.1b"><ci id="Sx2.SSx4.p1.10.m10.1.1.cmml" xref="Sx2.SSx4.p1.10.m10.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.10.m10.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.10.m10.1d">roman_Δ</annotation></semantics></math> CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.11.m11.1"><semantics id="Sx2.SSx4.p1.11.m11.1a"><msub id="Sx2.SSx4.p1.11.m11.1.1" xref="Sx2.SSx4.p1.11.m11.1.1.cmml"><mi id="Sx2.SSx4.p1.11.m11.1.1a" xref="Sx2.SSx4.p1.11.m11.1.1.cmml"></mi><mtext id="Sx2.SSx4.p1.11.m11.1.1.1" xref="Sx2.SSx4.p1.11.m11.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.11.m11.1b"><apply id="Sx2.SSx4.p1.11.m11.1.1.cmml" xref="Sx2.SSx4.p1.11.m11.1.1"><ci id="Sx2.SSx4.p1.11.m11.1.1.1a.cmml" xref="Sx2.SSx4.p1.11.m11.1.1.1"><mtext id="Sx2.SSx4.p1.11.m11.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx4.p1.11.m11.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.11.m11.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.11.m11.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> and <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.12.m12.1"><semantics id="Sx2.SSx4.p1.12.m12.1a"><mi id="Sx2.SSx4.p1.12.m12.1.1" mathvariant="normal" xref="Sx2.SSx4.p1.12.m12.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.12.m12.1b"><ci id="Sx2.SSx4.p1.12.m12.1.1.cmml" xref="Sx2.SSx4.p1.12.m12.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.12.m12.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.12.m12.1d">roman_Δ</annotation></semantics></math>LDLB for the six-CNT-layer heterostructure were 7.8 deg and 6.8 deg, respectively. The <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.13.m13.1"><semantics id="Sx2.SSx4.p1.13.m13.1a"><mi id="Sx2.SSx4.p1.13.m13.1.1" mathvariant="normal" xref="Sx2.SSx4.p1.13.m13.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.13.m13.1b"><ci id="Sx2.SSx4.p1.13.m13.1.1.cmml" xref="Sx2.SSx4.p1.13.m13.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.13.m13.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.13.m13.1d">roman_Δ</annotation></semantics></math> CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.14.m14.1"><semantics id="Sx2.SSx4.p1.14.m14.1a"><msub id="Sx2.SSx4.p1.14.m14.1.1" xref="Sx2.SSx4.p1.14.m14.1.1.cmml"><mi id="Sx2.SSx4.p1.14.m14.1.1a" xref="Sx2.SSx4.p1.14.m14.1.1.cmml"></mi><mtext id="Sx2.SSx4.p1.14.m14.1.1.1" xref="Sx2.SSx4.p1.14.m14.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.14.m14.1b"><apply id="Sx2.SSx4.p1.14.m14.1.1.cmml" xref="Sx2.SSx4.p1.14.m14.1.1"><ci id="Sx2.SSx4.p1.14.m14.1.1.1a.cmml" xref="Sx2.SSx4.p1.14.m14.1.1.1"><mtext id="Sx2.SSx4.p1.14.m14.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx4.p1.14.m14.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.14.m14.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.14.m14.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> and <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx2.SSx4.p1.15.m15.1"><semantics id="Sx2.SSx4.p1.15.m15.1a"><mi id="Sx2.SSx4.p1.15.m15.1.1" mathvariant="normal" xref="Sx2.SSx4.p1.15.m15.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx2.SSx4.p1.15.m15.1b"><ci id="Sx2.SSx4.p1.15.m15.1.1.cmml" xref="Sx2.SSx4.p1.15.m15.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx4.p1.15.m15.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx4.p1.15.m15.1d">roman_Δ</annotation></semantics></math>LDLB spectra under two GST phases are shown in Supplementary Fig. 11 and Fig. 12.</p> </div> </section> <section class="ltx_subsection" id="Sx2.SSx5"> <h3 class="ltx_title ltx_title_subsection">Electrical tunability</h3> <figure class="ltx_figure" id="Sx2.F5"><img alt="Refer to caption" class="ltx_graphics ltx_centering ltx_img_square" height="815" id="Sx2.F5.g1" src="x5.png" width="830"/> <figcaption class="ltx_caption ltx_centering"><span class="ltx_tag ltx_tag_figure">Figure 5: </span><span class="ltx_text ltx_font_bold" id="Sx2.F5.5.1">Electrical tunability of chiroptical responses in the heterostructure.</span>. (a) Illustration of <em class="ltx_emph ltx_font_italic" id="Sx2.F5.6.2">in-situ</em> programming of the heterostructure in the CD spectrometer. (b) Experimentally measured (solid lines) and simulation (dashed lines) CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.F5.2.m1.1"><semantics id="Sx2.F5.2.m1.1b"><msub id="Sx2.F5.2.m1.1.1" xref="Sx2.F5.2.m1.1.1.cmml"><mi id="Sx2.F5.2.m1.1.1b" xref="Sx2.F5.2.m1.1.1.cmml"></mi><mtext id="Sx2.F5.2.m1.1.1.1" xref="Sx2.F5.2.m1.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.F5.2.m1.1c"><apply id="Sx2.F5.2.m1.1.1.cmml" xref="Sx2.F5.2.m1.1.1"><ci id="Sx2.F5.2.m1.1.1.1a.cmml" xref="Sx2.F5.2.m1.1.1.1"><mtext id="Sx2.F5.2.m1.1.1.1.cmml" mathsize="70%" xref="Sx2.F5.2.m1.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.F5.2.m1.1d">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.F5.2.m1.1e">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> spectra under GST amorphous (blue lines) and crystalline (red lines) phases, respectively. (c) Spatial temperature distribution of a scaled-down heterostructure.</figcaption> </figure> <div class="ltx_para" id="Sx2.SSx5.p1"> <p class="ltx_p" id="Sx2.SSx5.p1.5">In addition to contributing to chiroptical responses through twisted stacks, the high thermal conductivity, low heat capacity, and reliable and high current carrying capacity of CNTs <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib18" title="">18</a>]</cite> along the tube axis make aligned CNT films a promising candidate for an efficient Joule heating electrode for programming GST phases. Hence, the aligned CNT film in the heterostructure can play dual roles as both chiroptical and electrode materials. Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F5" title="Figure 5 ‣ Electrical tunability ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">5</span></a>a illustrates <em class="ltx_emph ltx_font_italic" id="Sx2.SSx5.p1.5.1">in-situ</em> programming of the heterostructure in the CD spectrometer. Two electrodes and wires were in contact with the top layer of the aligned CNT film, with the current flowing along the alignment direction. The sample was loaded into the developed 3D-printed sample holder compatible with the spectrometer. We first measured CD spectra under four sample configurations, then applied voltages across the sample through a sourcemeter, and measured CD spectra again under four sample configurations. Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F5" title="Figure 5 ‣ Electrical tunability ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">5</span></a>b displayed measured CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx2.SSx5.p1.1.m1.1"><semantics id="Sx2.SSx5.p1.1.m1.1a"><msub id="Sx2.SSx5.p1.1.m1.1.1" xref="Sx2.SSx5.p1.1.m1.1.1.cmml"><mi id="Sx2.SSx5.p1.1.m1.1.1a" xref="Sx2.SSx5.p1.1.m1.1.1.cmml"></mi><mtext id="Sx2.SSx5.p1.1.m1.1.1.1" xref="Sx2.SSx5.p1.1.m1.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx2.SSx5.p1.1.m1.1b"><apply id="Sx2.SSx5.p1.1.m1.1.1.cmml" xref="Sx2.SSx5.p1.1.m1.1.1"><ci id="Sx2.SSx5.p1.1.m1.1.1.1a.cmml" xref="Sx2.SSx5.p1.1.m1.1.1.1"><mtext id="Sx2.SSx5.p1.1.m1.1.1.1.cmml" mathsize="70%" xref="Sx2.SSx5.p1.1.m1.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx5.p1.1.m1.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx5.p1.1.m1.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> spectra (solid lines), which agreed with simulation spectra (dashed lines) as well. The applied voltage and current for converting the GST film from amorphous to crystalline phases were <math alttext="\sim 80\," class="ltx_Math" display="inline" id="Sx2.SSx5.p1.2.m2.1"><semantics id="Sx2.SSx5.p1.2.m2.1a"><mrow id="Sx2.SSx5.p1.2.m2.1.1" xref="Sx2.SSx5.p1.2.m2.1.1.cmml"><mi id="Sx2.SSx5.p1.2.m2.1.1.2" xref="Sx2.SSx5.p1.2.m2.1.1.2.cmml"></mi><mo id="Sx2.SSx5.p1.2.m2.1.1.1" xref="Sx2.SSx5.p1.2.m2.1.1.1.cmml">∼</mo><mn id="Sx2.SSx5.p1.2.m2.1.1.3" xref="Sx2.SSx5.p1.2.m2.1.1.3.cmml">80</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx2.SSx5.p1.2.m2.1b"><apply id="Sx2.SSx5.p1.2.m2.1.1.cmml" xref="Sx2.SSx5.p1.2.m2.1.1"><csymbol cd="latexml" id="Sx2.SSx5.p1.2.m2.1.1.1.cmml" xref="Sx2.SSx5.p1.2.m2.1.1.1">similar-to</csymbol><csymbol cd="latexml" id="Sx2.SSx5.p1.2.m2.1.1.2.cmml" xref="Sx2.SSx5.p1.2.m2.1.1.2">absent</csymbol><cn id="Sx2.SSx5.p1.2.m2.1.1.3.cmml" type="integer" xref="Sx2.SSx5.p1.2.m2.1.1.3">80</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx5.p1.2.m2.1c">\sim 80\,</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx5.p1.2.m2.1d">∼ 80</annotation></semantics></math>V and <math alttext="\sim 13.6\," class="ltx_Math" display="inline" id="Sx2.SSx5.p1.3.m3.1"><semantics id="Sx2.SSx5.p1.3.m3.1a"><mrow id="Sx2.SSx5.p1.3.m3.1.1" xref="Sx2.SSx5.p1.3.m3.1.1.cmml"><mi id="Sx2.SSx5.p1.3.m3.1.1.2" xref="Sx2.SSx5.p1.3.m3.1.1.2.cmml"></mi><mo id="Sx2.SSx5.p1.3.m3.1.1.1" xref="Sx2.SSx5.p1.3.m3.1.1.1.cmml">∼</mo><mn id="Sx2.SSx5.p1.3.m3.1.1.3" xref="Sx2.SSx5.p1.3.m3.1.1.3.cmml">13.6</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx2.SSx5.p1.3.m3.1b"><apply id="Sx2.SSx5.p1.3.m3.1.1.cmml" xref="Sx2.SSx5.p1.3.m3.1.1"><csymbol cd="latexml" id="Sx2.SSx5.p1.3.m3.1.1.1.cmml" xref="Sx2.SSx5.p1.3.m3.1.1.1">similar-to</csymbol><csymbol cd="latexml" id="Sx2.SSx5.p1.3.m3.1.1.2.cmml" xref="Sx2.SSx5.p1.3.m3.1.1.2">absent</csymbol><cn id="Sx2.SSx5.p1.3.m3.1.1.3.cmml" type="float" xref="Sx2.SSx5.p1.3.m3.1.1.3">13.6</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx5.p1.3.m3.1c">\sim 13.6\,</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx5.p1.3.m3.1d">∼ 13.6</annotation></semantics></math>mA, respectively. We further performed multiphysics simulations using the COMSOL Multiphysics software to estimate the temperature profile; see Methods for more details. Figure <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F5" title="Figure 5 ‣ Electrical tunability ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">5</span></a>c shows a spatial distribution of temperature in the heterostructure with scaled-down lateral dimension and delivered electrical energy from the top aligned CNT film. The achieved temperature inside the GST film can be <math alttext="\sim 320^{\circ}" class="ltx_Math" display="inline" id="Sx2.SSx5.p1.4.m4.1"><semantics id="Sx2.SSx5.p1.4.m4.1a"><mrow id="Sx2.SSx5.p1.4.m4.1.1" xref="Sx2.SSx5.p1.4.m4.1.1.cmml"><mi id="Sx2.SSx5.p1.4.m4.1.1.2" xref="Sx2.SSx5.p1.4.m4.1.1.2.cmml"></mi><mo id="Sx2.SSx5.p1.4.m4.1.1.1" xref="Sx2.SSx5.p1.4.m4.1.1.1.cmml">∼</mo><msup id="Sx2.SSx5.p1.4.m4.1.1.3" xref="Sx2.SSx5.p1.4.m4.1.1.3.cmml"><mn id="Sx2.SSx5.p1.4.m4.1.1.3.2" xref="Sx2.SSx5.p1.4.m4.1.1.3.2.cmml">320</mn><mo id="Sx2.SSx5.p1.4.m4.1.1.3.3" xref="Sx2.SSx5.p1.4.m4.1.1.3.3.cmml">∘</mo></msup></mrow><annotation-xml encoding="MathML-Content" id="Sx2.SSx5.p1.4.m4.1b"><apply id="Sx2.SSx5.p1.4.m4.1.1.cmml" xref="Sx2.SSx5.p1.4.m4.1.1"><csymbol cd="latexml" id="Sx2.SSx5.p1.4.m4.1.1.1.cmml" xref="Sx2.SSx5.p1.4.m4.1.1.1">similar-to</csymbol><csymbol cd="latexml" id="Sx2.SSx5.p1.4.m4.1.1.2.cmml" xref="Sx2.SSx5.p1.4.m4.1.1.2">absent</csymbol><apply id="Sx2.SSx5.p1.4.m4.1.1.3.cmml" xref="Sx2.SSx5.p1.4.m4.1.1.3"><csymbol cd="ambiguous" id="Sx2.SSx5.p1.4.m4.1.1.3.1.cmml" xref="Sx2.SSx5.p1.4.m4.1.1.3">superscript</csymbol><cn id="Sx2.SSx5.p1.4.m4.1.1.3.2.cmml" type="integer" xref="Sx2.SSx5.p1.4.m4.1.1.3.2">320</cn><compose id="Sx2.SSx5.p1.4.m4.1.1.3.3.cmml" xref="Sx2.SSx5.p1.4.m4.1.1.3.3"></compose></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx5.p1.4.m4.1c">\sim 320^{\circ}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx5.p1.4.m4.1d">∼ 320 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT</annotation></semantics></math>C, which is much larger than the GST transition temperature from amorphous to crystalline phase (<math alttext="\sim 250^{\circ}" class="ltx_Math" display="inline" id="Sx2.SSx5.p1.5.m5.1"><semantics id="Sx2.SSx5.p1.5.m5.1a"><mrow id="Sx2.SSx5.p1.5.m5.1.1" xref="Sx2.SSx5.p1.5.m5.1.1.cmml"><mi id="Sx2.SSx5.p1.5.m5.1.1.2" xref="Sx2.SSx5.p1.5.m5.1.1.2.cmml"></mi><mo id="Sx2.SSx5.p1.5.m5.1.1.1" xref="Sx2.SSx5.p1.5.m5.1.1.1.cmml">∼</mo><msup id="Sx2.SSx5.p1.5.m5.1.1.3" xref="Sx2.SSx5.p1.5.m5.1.1.3.cmml"><mn id="Sx2.SSx5.p1.5.m5.1.1.3.2" xref="Sx2.SSx5.p1.5.m5.1.1.3.2.cmml">250</mn><mo id="Sx2.SSx5.p1.5.m5.1.1.3.3" xref="Sx2.SSx5.p1.5.m5.1.1.3.3.cmml">∘</mo></msup></mrow><annotation-xml encoding="MathML-Content" id="Sx2.SSx5.p1.5.m5.1b"><apply id="Sx2.SSx5.p1.5.m5.1.1.cmml" xref="Sx2.SSx5.p1.5.m5.1.1"><csymbol cd="latexml" id="Sx2.SSx5.p1.5.m5.1.1.1.cmml" xref="Sx2.SSx5.p1.5.m5.1.1.1">similar-to</csymbol><csymbol cd="latexml" id="Sx2.SSx5.p1.5.m5.1.1.2.cmml" xref="Sx2.SSx5.p1.5.m5.1.1.2">absent</csymbol><apply id="Sx2.SSx5.p1.5.m5.1.1.3.cmml" xref="Sx2.SSx5.p1.5.m5.1.1.3"><csymbol cd="ambiguous" id="Sx2.SSx5.p1.5.m5.1.1.3.1.cmml" xref="Sx2.SSx5.p1.5.m5.1.1.3">superscript</csymbol><cn id="Sx2.SSx5.p1.5.m5.1.1.3.2.cmml" type="integer" xref="Sx2.SSx5.p1.5.m5.1.1.3.2">250</cn><compose id="Sx2.SSx5.p1.5.m5.1.1.3.3.cmml" xref="Sx2.SSx5.p1.5.m5.1.1.3.3"></compose></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx2.SSx5.p1.5.m5.1c">\sim 250^{\circ}</annotation><annotation encoding="application/x-llamapun" id="Sx2.SSx5.p1.5.m5.1d">∼ 250 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT</annotation></semantics></math>C), confirming the phase transition of GST film.</p> </div> </section> </section> <section class="ltx_section" id="Sx3"> <h2 class="ltx_title ltx_title_section">Discussion</h2> <div class="ltx_para" id="Sx3.p1"> <p class="ltx_p" id="Sx3.p1.1">We have developed a full stack of a versatile experimental platform of programmable chiroptical heterostructure of twisted aligned CNTs and PCMs and corresponding design software infrastructure based on machine learning frameworks including differentiable programming and derivative-free Bayesian optimization. The heterostructure is scalable not only in lateral dimensions to a wafer scale but also in the vertical thickness dimension to a large number of stack layers. We have demonstrated the design and implementation of heterostructures to dynamically program both reciprocal and nonreciprocal CD responses, leading to the discovery of novel phenomena and the development of high-performance devices. Further, aligned CNT films are multifunctional and also serve as electrodes for heating and reconfiguring PCMs. Although the required switching power is large due to the wafer-scale size of the heterostructure, the creation of microscopic nanophotonic planar structures of the heterostructure can substantially reduce switching power, allow reliable multilevel switching, improve cyclability, enable further control of light-matter interaction, and enrich device functionalities. Further, the demonstrated 1D CNT and GST materials in the heterostructure can be expanded to a large library of 1D nanomaterials and electro-optic materials.</p> </div> </section> <section class="ltx_section" id="Sx4"> <h2 class="ltx_title ltx_title_section">Methods</h2> <div class="ltx_para ltx_noindent" id="Sx4.p1"> <p class="ltx_p" id="Sx4.p1.3"><span class="ltx_text ltx_font_bold" id="Sx4.p1.3.1">Shaking-assisted vacuum filtration (SAVF)</span> – The CNT powder used was purchased from Carbon Solutions, Inc. (product number P2, with a purity <math alttext=">" class="ltx_Math" display="inline" id="Sx4.p1.1.m1.1"><semantics id="Sx4.p1.1.m1.1a"><mo id="Sx4.p1.1.m1.1.1" xref="Sx4.p1.1.m1.1.1.cmml">></mo><annotation-xml encoding="MathML-Content" id="Sx4.p1.1.m1.1b"><gt id="Sx4.p1.1.m1.1.1.cmml" xref="Sx4.p1.1.m1.1.1"></gt></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p1.1.m1.1c">></annotation><annotation encoding="application/x-llamapun" id="Sx4.p1.1.m1.1d">></annotation></semantics></math>90 wt%) and synthesized using the arc-discharge method. To prepare aqueous dispersions, 8 mg of CNT powder was mixed with 20 mL of an aqueous <math alttext="0.5\%" class="ltx_Math" display="inline" id="Sx4.p1.2.m2.1"><semantics id="Sx4.p1.2.m2.1a"><mrow id="Sx4.p1.2.m2.1.1" xref="Sx4.p1.2.m2.1.1.cmml"><mn id="Sx4.p1.2.m2.1.1.2" xref="Sx4.p1.2.m2.1.1.2.cmml">0.5</mn><mo id="Sx4.p1.2.m2.1.1.1" xref="Sx4.p1.2.m2.1.1.1.cmml">%</mo></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p1.2.m2.1b"><apply id="Sx4.p1.2.m2.1.1.cmml" xref="Sx4.p1.2.m2.1.1"><csymbol cd="latexml" id="Sx4.p1.2.m2.1.1.1.cmml" xref="Sx4.p1.2.m2.1.1.1">percent</csymbol><cn id="Sx4.p1.2.m2.1.1.2.cmml" type="float" xref="Sx4.p1.2.m2.1.1.2">0.5</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p1.2.m2.1c">0.5\%</annotation><annotation encoding="application/x-llamapun" id="Sx4.p1.2.m2.1d">0.5 %</annotation></semantics></math> w/w sodium deoxycholate solution, and then was sonicated using an ultrasonic tip horn sonicator (QSonica Q125) for 45 minutes at an output power of 21 W. Afterward, the sonicated suspension was purified by ultracentrifugation at <math alttext="247,104\times g" class="ltx_Math" display="inline" id="Sx4.p1.3.m3.2"><semantics id="Sx4.p1.3.m3.2a"><mrow id="Sx4.p1.3.m3.2.2.1" xref="Sx4.p1.3.m3.2.2.2.cmml"><mn id="Sx4.p1.3.m3.1.1" xref="Sx4.p1.3.m3.1.1.cmml">247</mn><mo id="Sx4.p1.3.m3.2.2.1.2" xref="Sx4.p1.3.m3.2.2.2.cmml">,</mo><mrow id="Sx4.p1.3.m3.2.2.1.1" xref="Sx4.p1.3.m3.2.2.1.1.cmml"><mn id="Sx4.p1.3.m3.2.2.1.1.2" xref="Sx4.p1.3.m3.2.2.1.1.2.cmml">104</mn><mo id="Sx4.p1.3.m3.2.2.1.1.1" lspace="0.222em" rspace="0.222em" xref="Sx4.p1.3.m3.2.2.1.1.1.cmml">×</mo><mi id="Sx4.p1.3.m3.2.2.1.1.3" xref="Sx4.p1.3.m3.2.2.1.1.3.cmml">g</mi></mrow></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p1.3.m3.2b"><list id="Sx4.p1.3.m3.2.2.2.cmml" xref="Sx4.p1.3.m3.2.2.1"><cn id="Sx4.p1.3.m3.1.1.cmml" type="integer" xref="Sx4.p1.3.m3.1.1">247</cn><apply id="Sx4.p1.3.m3.2.2.1.1.cmml" xref="Sx4.p1.3.m3.2.2.1.1"><times id="Sx4.p1.3.m3.2.2.1.1.1.cmml" xref="Sx4.p1.3.m3.2.2.1.1.1"></times><cn id="Sx4.p1.3.m3.2.2.1.1.2.cmml" type="integer" xref="Sx4.p1.3.m3.2.2.1.1.2">104</cn><ci id="Sx4.p1.3.m3.2.2.1.1.3.cmml" xref="Sx4.p1.3.m3.2.2.1.1.3">𝑔</ci></apply></list></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p1.3.m3.2c">247,104\times g</annotation><annotation encoding="application/x-llamapun" id="Sx4.p1.3.m3.2d">247 , 104 × italic_g</annotation></semantics></math> for two hours to remove large bundles. The supernatant was collected and diluted 27 times before undergoing vacuum filtration using a 1-inch filtration system (MilliporeSigma) with 100-nm-pore-size filter membranes (Whatman Nuclepore Track-Etched polycarbonate hydrophilic membranes, MilliporeSigma). The whole filtration system was placed on a linear shaker (Scilogex SCI-L180-Pro LCD digital linear shaker) as illustrated in Supplementary Fig. 1. Instead of a conventional cylindrical funnel, a funnel with a square-shaped cross-section was fabricated using a 3D printer (Elegoo Saturn 3D Printer). The lateral dimension of the square was 1 cm. Hence, the linear shaking direction was found to be the alignment direction of obtained aligned CNT films. The linear shaker shook the filtration system at 200 RPM during the first 15 minutes of the filtration process. Afterward, the standard filtration process continued without shaking. Close to the end of filtration, the vacuum pump was turned on to fix the alignment structure on the membrane. More details can be found in Ref. <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib46" title="">46</a>]</cite>. Supplementary Fig. 1 shows a photo and scanning electron microscopy image of the obtained film, confirming a good alignment along the shaking direction. The obtained film can be transferred onto the desired substrate for characterization and heterostructure fabrication using a wet transfer method. Specifically, a small droplet of water was first placed on the target substrate. The CNT film on the polycarbonate filter membrane was placed with the CNT side in contact with the wet substrate and the polycarbonate side on top. Once the water between the CNT film and the substrate evaporated, the top polycarbonate layer was removed by immersing the sample in a chloroform solution. The sample was finally cleaned with isopropanol.</p> </div> <div class="ltx_para ltx_noindent" id="Sx4.p2"> <p class="ltx_p" id="Sx4.p2.22"><span class="ltx_text ltx_font_bold" id="Sx4.p2.22.1">TMM calculations</span> – A <math alttext="4\times 4" class="ltx_Math" display="inline" id="Sx4.p2.1.m1.1"><semantics id="Sx4.p2.1.m1.1a"><mrow id="Sx4.p2.1.m1.1.1" xref="Sx4.p2.1.m1.1.1.cmml"><mn id="Sx4.p2.1.m1.1.1.2" xref="Sx4.p2.1.m1.1.1.2.cmml">4</mn><mo id="Sx4.p2.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="Sx4.p2.1.m1.1.1.1.cmml">×</mo><mn id="Sx4.p2.1.m1.1.1.3" xref="Sx4.p2.1.m1.1.1.3.cmml">4</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.1.m1.1b"><apply id="Sx4.p2.1.m1.1.1.cmml" xref="Sx4.p2.1.m1.1.1"><times id="Sx4.p2.1.m1.1.1.1.cmml" xref="Sx4.p2.1.m1.1.1.1"></times><cn id="Sx4.p2.1.m1.1.1.2.cmml" type="integer" xref="Sx4.p2.1.m1.1.1.2">4</cn><cn id="Sx4.p2.1.m1.1.1.3.cmml" type="integer" xref="Sx4.p2.1.m1.1.1.3">4</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.1.m1.1c">4\times 4</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.1.m1.1d">4 × 4</annotation></semantics></math> transfer matrix method was developed to calculate chiroptical responses of the heterostructure containing anisotropic non-magnetic materials under normal incidence. The details can be found in Ref. <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib47" title="">47</a>]</cite> and our prior work <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib17" title="">17</a>]</cite>. Briefly, as illustrated in Supplementary Fig. 2, a layer of an isotropic material was modeled with a scalar dielectric function <math alttext="\varepsilon" class="ltx_Math" display="inline" id="Sx4.p2.2.m2.1"><semantics id="Sx4.p2.2.m2.1a"><mi id="Sx4.p2.2.m2.1.1" xref="Sx4.p2.2.m2.1.1.cmml">ε</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.2.m2.1b"><ci id="Sx4.p2.2.m2.1.1.cmml" xref="Sx4.p2.2.m2.1.1">𝜀</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.2.m2.1c">\varepsilon</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.2.m2.1d">italic_ε</annotation></semantics></math> and a thickness <math alttext="t" class="ltx_Math" display="inline" id="Sx4.p2.3.m3.1"><semantics id="Sx4.p2.3.m3.1a"><mi id="Sx4.p2.3.m3.1.1" xref="Sx4.p2.3.m3.1.1.cmml">t</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.3.m3.1b"><ci id="Sx4.p2.3.m3.1.1.cmml" xref="Sx4.p2.3.m3.1.1">𝑡</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.3.m3.1c">t</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.3.m3.1d">italic_t</annotation></semantics></math>. A layer of anisotropic material was modeled with a <math alttext="2\times 2" class="ltx_Math" display="inline" id="Sx4.p2.4.m4.1"><semantics id="Sx4.p2.4.m4.1a"><mrow id="Sx4.p2.4.m4.1.1" xref="Sx4.p2.4.m4.1.1.cmml"><mn id="Sx4.p2.4.m4.1.1.2" xref="Sx4.p2.4.m4.1.1.2.cmml">2</mn><mo id="Sx4.p2.4.m4.1.1.1" lspace="0.222em" rspace="0.222em" xref="Sx4.p2.4.m4.1.1.1.cmml">×</mo><mn id="Sx4.p2.4.m4.1.1.3" xref="Sx4.p2.4.m4.1.1.3.cmml">2</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.4.m4.1b"><apply id="Sx4.p2.4.m4.1.1.cmml" xref="Sx4.p2.4.m4.1.1"><times id="Sx4.p2.4.m4.1.1.1.cmml" xref="Sx4.p2.4.m4.1.1.1"></times><cn id="Sx4.p2.4.m4.1.1.2.cmml" type="integer" xref="Sx4.p2.4.m4.1.1.2">2</cn><cn id="Sx4.p2.4.m4.1.1.3.cmml" type="integer" xref="Sx4.p2.4.m4.1.1.3">2</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.4.m4.1c">2\times 2</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.4.m4.1d">2 × 2</annotation></semantics></math> dielectric function tensor <math alttext="\boldsymbol{\varepsilon}" class="ltx_Math" display="inline" id="Sx4.p2.5.m5.1"><semantics id="Sx4.p2.5.m5.1a"><mi id="Sx4.p2.5.m5.1.1" xref="Sx4.p2.5.m5.1.1.cmml">𝜺</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.5.m5.1b"><ci id="Sx4.p2.5.m5.1.1.cmml" xref="Sx4.p2.5.m5.1.1">𝜺</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.5.m5.1c">\boldsymbol{\varepsilon}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.5.m5.1d">bold_italic_ε</annotation></semantics></math>, a twist angle <math alttext="\theta" class="ltx_Math" display="inline" id="Sx4.p2.6.m6.1"><semantics id="Sx4.p2.6.m6.1a"><mi id="Sx4.p2.6.m6.1.1" xref="Sx4.p2.6.m6.1.1.cmml">θ</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.6.m6.1b"><ci id="Sx4.p2.6.m6.1.1.cmml" xref="Sx4.p2.6.m6.1.1">𝜃</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.6.m6.1c">\theta</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.6.m6.1d">italic_θ</annotation></semantics></math>, and a thickness. Specifically, for an anisotropic material with orthogonal principal axes, such as the directions parallel and perpendicular to CNT alignment, there are four eigenmodes, which are <math alttext="s" class="ltx_Math" display="inline" id="Sx4.p2.7.m7.1"><semantics id="Sx4.p2.7.m7.1a"><mi id="Sx4.p2.7.m7.1.1" xref="Sx4.p2.7.m7.1.1.cmml">s</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.7.m7.1b"><ci id="Sx4.p2.7.m7.1.1.cmml" xref="Sx4.p2.7.m7.1.1">𝑠</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.7.m7.1c">s</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.7.m7.1d">italic_s</annotation></semantics></math>-wave forward, <math alttext="s" class="ltx_Math" display="inline" id="Sx4.p2.8.m8.1"><semantics id="Sx4.p2.8.m8.1a"><mi id="Sx4.p2.8.m8.1.1" xref="Sx4.p2.8.m8.1.1.cmml">s</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.8.m8.1b"><ci id="Sx4.p2.8.m8.1.1.cmml" xref="Sx4.p2.8.m8.1.1">𝑠</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.8.m8.1c">s</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.8.m8.1d">italic_s</annotation></semantics></math>-wave backward, <math alttext="p" class="ltx_Math" display="inline" id="Sx4.p2.9.m9.1"><semantics id="Sx4.p2.9.m9.1a"><mi id="Sx4.p2.9.m9.1.1" xref="Sx4.p2.9.m9.1.1.cmml">p</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.9.m9.1b"><ci id="Sx4.p2.9.m9.1.1.cmml" xref="Sx4.p2.9.m9.1.1">𝑝</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.9.m9.1c">p</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.9.m9.1d">italic_p</annotation></semantics></math>-wave forward, and <math alttext="p" class="ltx_Math" display="inline" id="Sx4.p2.10.m10.1"><semantics id="Sx4.p2.10.m10.1a"><mi id="Sx4.p2.10.m10.1.1" xref="Sx4.p2.10.m10.1.1.cmml">p</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.10.m10.1b"><ci id="Sx4.p2.10.m10.1.1.cmml" xref="Sx4.p2.10.m10.1.1">𝑝</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.10.m10.1c">p</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.10.m10.1d">italic_p</annotation></semantics></math>-wave backward modes, respectively. In the definition of the coordinate systems, waves propagate along the <math alttext="z" class="ltx_Math" display="inline" id="Sx4.p2.11.m11.1"><semantics id="Sx4.p2.11.m11.1a"><mi id="Sx4.p2.11.m11.1.1" xref="Sx4.p2.11.m11.1.1.cmml">z</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.11.m11.1b"><ci id="Sx4.p2.11.m11.1.1.cmml" xref="Sx4.p2.11.m11.1.1">𝑧</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.11.m11.1c">z</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.11.m11.1d">italic_z</annotation></semantics></math>-axis and <math alttext="x" class="ltx_Math" display="inline" id="Sx4.p2.12.m12.1"><semantics id="Sx4.p2.12.m12.1a"><mi id="Sx4.p2.12.m12.1.1" xref="Sx4.p2.12.m12.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.12.m12.1b"><ci id="Sx4.p2.12.m12.1.1.cmml" xref="Sx4.p2.12.m12.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.12.m12.1c">x</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.12.m12.1d">italic_x</annotation></semantics></math> and <math alttext="y" class="ltx_Math" display="inline" id="Sx4.p2.13.m13.1"><semantics id="Sx4.p2.13.m13.1a"><mi id="Sx4.p2.13.m13.1.1" xref="Sx4.p2.13.m13.1.1.cmml">y</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.13.m13.1b"><ci id="Sx4.p2.13.m13.1.1.cmml" xref="Sx4.p2.13.m13.1.1">𝑦</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.13.m13.1c">y</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.13.m13.1d">italic_y</annotation></semantics></math> axes are in the heterostructure plane. <math alttext="\hat{\textbf{x}}" class="ltx_Math" display="inline" id="Sx4.p2.14.m14.1"><semantics id="Sx4.p2.14.m14.1a"><mover accent="true" id="Sx4.p2.14.m14.1.1" xref="Sx4.p2.14.m14.1.1.cmml"><mtext class="ltx_mathvariant_bold" id="Sx4.p2.14.m14.1.1.2" xref="Sx4.p2.14.m14.1.1.2a.cmml">x</mtext><mo id="Sx4.p2.14.m14.1.1.1" xref="Sx4.p2.14.m14.1.1.1.cmml">^</mo></mover><annotation-xml encoding="MathML-Content" id="Sx4.p2.14.m14.1b"><apply id="Sx4.p2.14.m14.1.1.cmml" xref="Sx4.p2.14.m14.1.1"><ci id="Sx4.p2.14.m14.1.1.1.cmml" xref="Sx4.p2.14.m14.1.1.1">^</ci><ci id="Sx4.p2.14.m14.1.1.2a.cmml" xref="Sx4.p2.14.m14.1.1.2"><mtext class="ltx_mathvariant_bold" id="Sx4.p2.14.m14.1.1.2.cmml" xref="Sx4.p2.14.m14.1.1.2">x</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.14.m14.1c">\hat{\textbf{x}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.14.m14.1d">over^ start_ARG x end_ARG</annotation></semantics></math>, <math alttext="\hat{\textbf{y}}" class="ltx_Math" display="inline" id="Sx4.p2.15.m15.1"><semantics id="Sx4.p2.15.m15.1a"><mover accent="true" id="Sx4.p2.15.m15.1.1" xref="Sx4.p2.15.m15.1.1.cmml"><mtext class="ltx_mathvariant_bold" id="Sx4.p2.15.m15.1.1.2" xref="Sx4.p2.15.m15.1.1.2a.cmml">y</mtext><mo id="Sx4.p2.15.m15.1.1.1" xref="Sx4.p2.15.m15.1.1.1.cmml">^</mo></mover><annotation-xml encoding="MathML-Content" id="Sx4.p2.15.m15.1b"><apply id="Sx4.p2.15.m15.1.1.cmml" xref="Sx4.p2.15.m15.1.1"><ci id="Sx4.p2.15.m15.1.1.1.cmml" xref="Sx4.p2.15.m15.1.1.1">^</ci><ci id="Sx4.p2.15.m15.1.1.2a.cmml" xref="Sx4.p2.15.m15.1.1.2"><mtext class="ltx_mathvariant_bold" id="Sx4.p2.15.m15.1.1.2.cmml" xref="Sx4.p2.15.m15.1.1.2">y</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.15.m15.1c">\hat{\textbf{y}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.15.m15.1d">over^ start_ARG y end_ARG</annotation></semantics></math>, and <math alttext="\hat{\textbf{z}}" class="ltx_Math" display="inline" id="Sx4.p2.16.m16.1"><semantics id="Sx4.p2.16.m16.1a"><mover accent="true" id="Sx4.p2.16.m16.1.1" xref="Sx4.p2.16.m16.1.1.cmml"><mtext class="ltx_mathvariant_bold" id="Sx4.p2.16.m16.1.1.2" xref="Sx4.p2.16.m16.1.1.2a.cmml">z</mtext><mo id="Sx4.p2.16.m16.1.1.1" xref="Sx4.p2.16.m16.1.1.1.cmml">^</mo></mover><annotation-xml encoding="MathML-Content" id="Sx4.p2.16.m16.1b"><apply id="Sx4.p2.16.m16.1.1.cmml" xref="Sx4.p2.16.m16.1.1"><ci id="Sx4.p2.16.m16.1.1.1.cmml" xref="Sx4.p2.16.m16.1.1.1">^</ci><ci id="Sx4.p2.16.m16.1.1.2a.cmml" xref="Sx4.p2.16.m16.1.1.2"><mtext class="ltx_mathvariant_bold" id="Sx4.p2.16.m16.1.1.2.cmml" xref="Sx4.p2.16.m16.1.1.2">z</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.16.m16.1c">\hat{\textbf{z}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.16.m16.1d">over^ start_ARG z end_ARG</annotation></semantics></math> are defined as unit vectors along <math alttext="x" class="ltx_Math" display="inline" id="Sx4.p2.17.m17.1"><semantics id="Sx4.p2.17.m17.1a"><mi id="Sx4.p2.17.m17.1.1" xref="Sx4.p2.17.m17.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.17.m17.1b"><ci id="Sx4.p2.17.m17.1.1.cmml" xref="Sx4.p2.17.m17.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.17.m17.1c">x</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.17.m17.1d">italic_x</annotation></semantics></math>-, <math alttext="y" class="ltx_Math" display="inline" id="Sx4.p2.18.m18.1"><semantics id="Sx4.p2.18.m18.1a"><mi id="Sx4.p2.18.m18.1.1" xref="Sx4.p2.18.m18.1.1.cmml">y</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.18.m18.1b"><ci id="Sx4.p2.18.m18.1.1.cmml" xref="Sx4.p2.18.m18.1.1">𝑦</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.18.m18.1c">y</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.18.m18.1d">italic_y</annotation></semantics></math>-, and <math alttext="z" class="ltx_Math" display="inline" id="Sx4.p2.19.m19.1"><semantics id="Sx4.p2.19.m19.1a"><mi id="Sx4.p2.19.m19.1.1" xref="Sx4.p2.19.m19.1.1.cmml">z</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.19.m19.1b"><ci id="Sx4.p2.19.m19.1.1.cmml" xref="Sx4.p2.19.m19.1.1">𝑧</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.19.m19.1c">z</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.19.m19.1d">italic_z</annotation></semantics></math>-axes, respectively. The transmitted field <math alttext="(E_{t,s},E_{t,p})" class="ltx_Math" display="inline" id="Sx4.p2.20.m20.6"><semantics id="Sx4.p2.20.m20.6a"><mrow id="Sx4.p2.20.m20.6.6.2" xref="Sx4.p2.20.m20.6.6.3.cmml"><mo id="Sx4.p2.20.m20.6.6.2.3" stretchy="false" xref="Sx4.p2.20.m20.6.6.3.cmml">(</mo><msub id="Sx4.p2.20.m20.5.5.1.1" xref="Sx4.p2.20.m20.5.5.1.1.cmml"><mi id="Sx4.p2.20.m20.5.5.1.1.2" xref="Sx4.p2.20.m20.5.5.1.1.2.cmml">E</mi><mrow id="Sx4.p2.20.m20.2.2.2.4" xref="Sx4.p2.20.m20.2.2.2.3.cmml"><mi id="Sx4.p2.20.m20.1.1.1.1" xref="Sx4.p2.20.m20.1.1.1.1.cmml">t</mi><mo id="Sx4.p2.20.m20.2.2.2.4.1" xref="Sx4.p2.20.m20.2.2.2.3.cmml">,</mo><mi id="Sx4.p2.20.m20.2.2.2.2" xref="Sx4.p2.20.m20.2.2.2.2.cmml">s</mi></mrow></msub><mo id="Sx4.p2.20.m20.6.6.2.4" xref="Sx4.p2.20.m20.6.6.3.cmml">,</mo><msub id="Sx4.p2.20.m20.6.6.2.2" xref="Sx4.p2.20.m20.6.6.2.2.cmml"><mi id="Sx4.p2.20.m20.6.6.2.2.2" xref="Sx4.p2.20.m20.6.6.2.2.2.cmml">E</mi><mrow id="Sx4.p2.20.m20.4.4.2.4" xref="Sx4.p2.20.m20.4.4.2.3.cmml"><mi id="Sx4.p2.20.m20.3.3.1.1" xref="Sx4.p2.20.m20.3.3.1.1.cmml">t</mi><mo id="Sx4.p2.20.m20.4.4.2.4.1" xref="Sx4.p2.20.m20.4.4.2.3.cmml">,</mo><mi id="Sx4.p2.20.m20.4.4.2.2" xref="Sx4.p2.20.m20.4.4.2.2.cmml">p</mi></mrow></msub><mo id="Sx4.p2.20.m20.6.6.2.5" stretchy="false" xref="Sx4.p2.20.m20.6.6.3.cmml">)</mo></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.20.m20.6b"><interval closure="open" id="Sx4.p2.20.m20.6.6.3.cmml" xref="Sx4.p2.20.m20.6.6.2"><apply id="Sx4.p2.20.m20.5.5.1.1.cmml" xref="Sx4.p2.20.m20.5.5.1.1"><csymbol cd="ambiguous" id="Sx4.p2.20.m20.5.5.1.1.1.cmml" xref="Sx4.p2.20.m20.5.5.1.1">subscript</csymbol><ci id="Sx4.p2.20.m20.5.5.1.1.2.cmml" xref="Sx4.p2.20.m20.5.5.1.1.2">𝐸</ci><list id="Sx4.p2.20.m20.2.2.2.3.cmml" xref="Sx4.p2.20.m20.2.2.2.4"><ci id="Sx4.p2.20.m20.1.1.1.1.cmml" xref="Sx4.p2.20.m20.1.1.1.1">𝑡</ci><ci id="Sx4.p2.20.m20.2.2.2.2.cmml" xref="Sx4.p2.20.m20.2.2.2.2">𝑠</ci></list></apply><apply id="Sx4.p2.20.m20.6.6.2.2.cmml" xref="Sx4.p2.20.m20.6.6.2.2"><csymbol cd="ambiguous" id="Sx4.p2.20.m20.6.6.2.2.1.cmml" xref="Sx4.p2.20.m20.6.6.2.2">subscript</csymbol><ci id="Sx4.p2.20.m20.6.6.2.2.2.cmml" xref="Sx4.p2.20.m20.6.6.2.2.2">𝐸</ci><list id="Sx4.p2.20.m20.4.4.2.3.cmml" xref="Sx4.p2.20.m20.4.4.2.4"><ci id="Sx4.p2.20.m20.3.3.1.1.cmml" xref="Sx4.p2.20.m20.3.3.1.1">𝑡</ci><ci id="Sx4.p2.20.m20.4.4.2.2.cmml" xref="Sx4.p2.20.m20.4.4.2.2">𝑝</ci></list></apply></interval></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.20.m20.6c">(E_{t,s},E_{t,p})</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.20.m20.6d">( italic_E start_POSTSUBSCRIPT italic_t , italic_s end_POSTSUBSCRIPT , italic_E start_POSTSUBSCRIPT italic_t , italic_p end_POSTSUBSCRIPT )</annotation></semantics></math>, reflected field <math alttext="(E_{r,s},E_{r,p})" class="ltx_Math" display="inline" id="Sx4.p2.21.m21.6"><semantics id="Sx4.p2.21.m21.6a"><mrow id="Sx4.p2.21.m21.6.6.2" xref="Sx4.p2.21.m21.6.6.3.cmml"><mo id="Sx4.p2.21.m21.6.6.2.3" stretchy="false" xref="Sx4.p2.21.m21.6.6.3.cmml">(</mo><msub id="Sx4.p2.21.m21.5.5.1.1" xref="Sx4.p2.21.m21.5.5.1.1.cmml"><mi id="Sx4.p2.21.m21.5.5.1.1.2" xref="Sx4.p2.21.m21.5.5.1.1.2.cmml">E</mi><mrow id="Sx4.p2.21.m21.2.2.2.4" xref="Sx4.p2.21.m21.2.2.2.3.cmml"><mi id="Sx4.p2.21.m21.1.1.1.1" xref="Sx4.p2.21.m21.1.1.1.1.cmml">r</mi><mo id="Sx4.p2.21.m21.2.2.2.4.1" xref="Sx4.p2.21.m21.2.2.2.3.cmml">,</mo><mi id="Sx4.p2.21.m21.2.2.2.2" xref="Sx4.p2.21.m21.2.2.2.2.cmml">s</mi></mrow></msub><mo id="Sx4.p2.21.m21.6.6.2.4" xref="Sx4.p2.21.m21.6.6.3.cmml">,</mo><msub id="Sx4.p2.21.m21.6.6.2.2" xref="Sx4.p2.21.m21.6.6.2.2.cmml"><mi id="Sx4.p2.21.m21.6.6.2.2.2" xref="Sx4.p2.21.m21.6.6.2.2.2.cmml">E</mi><mrow id="Sx4.p2.21.m21.4.4.2.4" xref="Sx4.p2.21.m21.4.4.2.3.cmml"><mi id="Sx4.p2.21.m21.3.3.1.1" xref="Sx4.p2.21.m21.3.3.1.1.cmml">r</mi><mo id="Sx4.p2.21.m21.4.4.2.4.1" xref="Sx4.p2.21.m21.4.4.2.3.cmml">,</mo><mi id="Sx4.p2.21.m21.4.4.2.2" xref="Sx4.p2.21.m21.4.4.2.2.cmml">p</mi></mrow></msub><mo id="Sx4.p2.21.m21.6.6.2.5" stretchy="false" xref="Sx4.p2.21.m21.6.6.3.cmml">)</mo></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.21.m21.6b"><interval closure="open" id="Sx4.p2.21.m21.6.6.3.cmml" xref="Sx4.p2.21.m21.6.6.2"><apply id="Sx4.p2.21.m21.5.5.1.1.cmml" xref="Sx4.p2.21.m21.5.5.1.1"><csymbol cd="ambiguous" id="Sx4.p2.21.m21.5.5.1.1.1.cmml" xref="Sx4.p2.21.m21.5.5.1.1">subscript</csymbol><ci id="Sx4.p2.21.m21.5.5.1.1.2.cmml" xref="Sx4.p2.21.m21.5.5.1.1.2">𝐸</ci><list id="Sx4.p2.21.m21.2.2.2.3.cmml" xref="Sx4.p2.21.m21.2.2.2.4"><ci id="Sx4.p2.21.m21.1.1.1.1.cmml" xref="Sx4.p2.21.m21.1.1.1.1">𝑟</ci><ci id="Sx4.p2.21.m21.2.2.2.2.cmml" xref="Sx4.p2.21.m21.2.2.2.2">𝑠</ci></list></apply><apply id="Sx4.p2.21.m21.6.6.2.2.cmml" xref="Sx4.p2.21.m21.6.6.2.2"><csymbol cd="ambiguous" id="Sx4.p2.21.m21.6.6.2.2.1.cmml" xref="Sx4.p2.21.m21.6.6.2.2">subscript</csymbol><ci id="Sx4.p2.21.m21.6.6.2.2.2.cmml" xref="Sx4.p2.21.m21.6.6.2.2.2">𝐸</ci><list id="Sx4.p2.21.m21.4.4.2.3.cmml" xref="Sx4.p2.21.m21.4.4.2.4"><ci id="Sx4.p2.21.m21.3.3.1.1.cmml" xref="Sx4.p2.21.m21.3.3.1.1">𝑟</ci><ci id="Sx4.p2.21.m21.4.4.2.2.cmml" xref="Sx4.p2.21.m21.4.4.2.2">𝑝</ci></list></apply></interval></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.21.m21.6c">(E_{r,s},E_{r,p})</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.21.m21.6d">( italic_E start_POSTSUBSCRIPT italic_r , italic_s end_POSTSUBSCRIPT , italic_E start_POSTSUBSCRIPT italic_r , italic_p end_POSTSUBSCRIPT )</annotation></semantics></math>, and the incident field <math alttext="(E_{i,s},E_{i,p})" class="ltx_Math" display="inline" id="Sx4.p2.22.m22.6"><semantics id="Sx4.p2.22.m22.6a"><mrow id="Sx4.p2.22.m22.6.6.2" xref="Sx4.p2.22.m22.6.6.3.cmml"><mo id="Sx4.p2.22.m22.6.6.2.3" stretchy="false" xref="Sx4.p2.22.m22.6.6.3.cmml">(</mo><msub id="Sx4.p2.22.m22.5.5.1.1" xref="Sx4.p2.22.m22.5.5.1.1.cmml"><mi id="Sx4.p2.22.m22.5.5.1.1.2" xref="Sx4.p2.22.m22.5.5.1.1.2.cmml">E</mi><mrow id="Sx4.p2.22.m22.2.2.2.4" xref="Sx4.p2.22.m22.2.2.2.3.cmml"><mi id="Sx4.p2.22.m22.1.1.1.1" xref="Sx4.p2.22.m22.1.1.1.1.cmml">i</mi><mo id="Sx4.p2.22.m22.2.2.2.4.1" xref="Sx4.p2.22.m22.2.2.2.3.cmml">,</mo><mi id="Sx4.p2.22.m22.2.2.2.2" xref="Sx4.p2.22.m22.2.2.2.2.cmml">s</mi></mrow></msub><mo id="Sx4.p2.22.m22.6.6.2.4" xref="Sx4.p2.22.m22.6.6.3.cmml">,</mo><msub id="Sx4.p2.22.m22.6.6.2.2" xref="Sx4.p2.22.m22.6.6.2.2.cmml"><mi id="Sx4.p2.22.m22.6.6.2.2.2" xref="Sx4.p2.22.m22.6.6.2.2.2.cmml">E</mi><mrow id="Sx4.p2.22.m22.4.4.2.4" xref="Sx4.p2.22.m22.4.4.2.3.cmml"><mi id="Sx4.p2.22.m22.3.3.1.1" xref="Sx4.p2.22.m22.3.3.1.1.cmml">i</mi><mo id="Sx4.p2.22.m22.4.4.2.4.1" xref="Sx4.p2.22.m22.4.4.2.3.cmml">,</mo><mi id="Sx4.p2.22.m22.4.4.2.2" xref="Sx4.p2.22.m22.4.4.2.2.cmml">p</mi></mrow></msub><mo id="Sx4.p2.22.m22.6.6.2.5" stretchy="false" xref="Sx4.p2.22.m22.6.6.3.cmml">)</mo></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.22.m22.6b"><interval closure="open" id="Sx4.p2.22.m22.6.6.3.cmml" xref="Sx4.p2.22.m22.6.6.2"><apply id="Sx4.p2.22.m22.5.5.1.1.cmml" xref="Sx4.p2.22.m22.5.5.1.1"><csymbol cd="ambiguous" id="Sx4.p2.22.m22.5.5.1.1.1.cmml" xref="Sx4.p2.22.m22.5.5.1.1">subscript</csymbol><ci id="Sx4.p2.22.m22.5.5.1.1.2.cmml" xref="Sx4.p2.22.m22.5.5.1.1.2">𝐸</ci><list id="Sx4.p2.22.m22.2.2.2.3.cmml" xref="Sx4.p2.22.m22.2.2.2.4"><ci id="Sx4.p2.22.m22.1.1.1.1.cmml" xref="Sx4.p2.22.m22.1.1.1.1">𝑖</ci><ci id="Sx4.p2.22.m22.2.2.2.2.cmml" xref="Sx4.p2.22.m22.2.2.2.2">𝑠</ci></list></apply><apply id="Sx4.p2.22.m22.6.6.2.2.cmml" xref="Sx4.p2.22.m22.6.6.2.2"><csymbol cd="ambiguous" id="Sx4.p2.22.m22.6.6.2.2.1.cmml" xref="Sx4.p2.22.m22.6.6.2.2">subscript</csymbol><ci id="Sx4.p2.22.m22.6.6.2.2.2.cmml" xref="Sx4.p2.22.m22.6.6.2.2.2">𝐸</ci><list id="Sx4.p2.22.m22.4.4.2.3.cmml" xref="Sx4.p2.22.m22.4.4.2.4"><ci id="Sx4.p2.22.m22.3.3.1.1.cmml" xref="Sx4.p2.22.m22.3.3.1.1">𝑖</ci><ci id="Sx4.p2.22.m22.4.4.2.2.cmml" xref="Sx4.p2.22.m22.4.4.2.2">𝑝</ci></list></apply></interval></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.22.m22.6c">(E_{i,s},E_{i,p})</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.22.m22.6d">( italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT , italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT )</annotation></semantics></math> can be related through</p> <table class="ltx_equation ltx_eqn_table" id="Sx4.E1"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="\left(\begin{array}[]{c}E_{t,s}\\ 0\\ E_{t,p}\\ 0\end{array}\right)=Q\left(\begin{array}[]{c}E_{i,s}\\ E_{r,s}\\ E_{i,p}\\ E_{r,p}\end{array}\right)=\left(\begin{array}[]{cccc}Q_{11}&Q_{12}&Q_{13}&Q_{1% 4}\\ Q_{21}&Q_{22}&Q_{23}&Q_{24}\\ Q_{31}&Q_{32}&Q_{33}&Q_{34}\\ Q_{41}&Q_{42}&Q_{43}&Q_{44}\\ \end{array}\right)\left(\begin{array}[]{c}E_{i,s}\\ E_{r,s}\\ E_{i,p}\\ E_{r,p}\end{array}\right)," class="ltx_Math" display="block" id="Sx4.E1.m1.22"><semantics id="Sx4.E1.m1.22a"><mrow id="Sx4.E1.m1.22.22.1" xref="Sx4.E1.m1.22.22.1.1.cmml"><mrow id="Sx4.E1.m1.22.22.1.1" xref="Sx4.E1.m1.22.22.1.1.cmml"><mrow id="Sx4.E1.m1.22.22.1.1.2.2" xref="Sx4.E1.m1.4.4.cmml"><mo id="Sx4.E1.m1.22.22.1.1.2.2.1" xref="Sx4.E1.m1.4.4.cmml">(</mo><mtable displaystyle="true" id="Sx4.E1.m1.4.4" rowspacing="0pt" xref="Sx4.E1.m1.4.4.cmml"><mtr id="Sx4.E1.m1.4.4a" xref="Sx4.E1.m1.4.4.cmml"><mtd id="Sx4.E1.m1.4.4b" xref="Sx4.E1.m1.4.4.cmml"><msub id="Sx4.E1.m1.2.2.2.2.2" xref="Sx4.E1.m1.2.2.2.2.2.cmml"><mi id="Sx4.E1.m1.2.2.2.2.2.4" xref="Sx4.E1.m1.2.2.2.2.2.4.cmml">E</mi><mrow id="Sx4.E1.m1.2.2.2.2.2.2.2.4" xref="Sx4.E1.m1.2.2.2.2.2.2.2.3.cmml"><mi id="Sx4.E1.m1.1.1.1.1.1.1.1.1" xref="Sx4.E1.m1.1.1.1.1.1.1.1.1.cmml">t</mi><mo id="Sx4.E1.m1.2.2.2.2.2.2.2.4.1" xref="Sx4.E1.m1.2.2.2.2.2.2.2.3.cmml">,</mo><mi id="Sx4.E1.m1.2.2.2.2.2.2.2.2" xref="Sx4.E1.m1.2.2.2.2.2.2.2.2.cmml">s</mi></mrow></msub></mtd></mtr><mtr id="Sx4.E1.m1.4.4c" xref="Sx4.E1.m1.4.4.cmml"><mtd id="Sx4.E1.m1.4.4d" xref="Sx4.E1.m1.4.4.cmml"><mn id="Sx4.E1.m1.4.4.5.1.1" xref="Sx4.E1.m1.4.4.5.1.1.cmml">0</mn></mtd></mtr><mtr id="Sx4.E1.m1.4.4e" xref="Sx4.E1.m1.4.4.cmml"><mtd id="Sx4.E1.m1.4.4f" xref="Sx4.E1.m1.4.4.cmml"><msub id="Sx4.E1.m1.4.4.4.2.2" xref="Sx4.E1.m1.4.4.4.2.2.cmml"><mi id="Sx4.E1.m1.4.4.4.2.2.4" xref="Sx4.E1.m1.4.4.4.2.2.4.cmml">E</mi><mrow id="Sx4.E1.m1.4.4.4.2.2.2.2.4" xref="Sx4.E1.m1.4.4.4.2.2.2.2.3.cmml"><mi id="Sx4.E1.m1.3.3.3.1.1.1.1.1" xref="Sx4.E1.m1.3.3.3.1.1.1.1.1.cmml">t</mi><mo id="Sx4.E1.m1.4.4.4.2.2.2.2.4.1" xref="Sx4.E1.m1.4.4.4.2.2.2.2.3.cmml">,</mo><mi id="Sx4.E1.m1.4.4.4.2.2.2.2.2" xref="Sx4.E1.m1.4.4.4.2.2.2.2.2.cmml">p</mi></mrow></msub></mtd></mtr><mtr id="Sx4.E1.m1.4.4g" xref="Sx4.E1.m1.4.4.cmml"><mtd id="Sx4.E1.m1.4.4h" xref="Sx4.E1.m1.4.4.cmml"><mn id="Sx4.E1.m1.4.4.6.1.1" xref="Sx4.E1.m1.4.4.6.1.1.cmml">0</mn></mtd></mtr></mtable><mo id="Sx4.E1.m1.22.22.1.1.2.2.2" xref="Sx4.E1.m1.4.4.cmml">)</mo></mrow><mo id="Sx4.E1.m1.22.22.1.1.3" xref="Sx4.E1.m1.22.22.1.1.3.cmml">=</mo><mrow id="Sx4.E1.m1.22.22.1.1.4" xref="Sx4.E1.m1.22.22.1.1.4.cmml"><mi id="Sx4.E1.m1.22.22.1.1.4.2" xref="Sx4.E1.m1.22.22.1.1.4.2.cmml">Q</mi><mo id="Sx4.E1.m1.22.22.1.1.4.1" xref="Sx4.E1.m1.22.22.1.1.4.1.cmml">⁢</mo><mrow id="Sx4.E1.m1.22.22.1.1.4.3.2" xref="Sx4.E1.m1.12.12.cmml"><mo id="Sx4.E1.m1.22.22.1.1.4.3.2.1" xref="Sx4.E1.m1.12.12.cmml">(</mo><mtable displaystyle="true" id="Sx4.E1.m1.12.12" rowspacing="0pt" xref="Sx4.E1.m1.12.12.cmml"><mtr id="Sx4.E1.m1.12.12a" xref="Sx4.E1.m1.12.12.cmml"><mtd id="Sx4.E1.m1.12.12b" xref="Sx4.E1.m1.12.12.cmml"><msub id="Sx4.E1.m1.6.6.2.2.2" xref="Sx4.E1.m1.6.6.2.2.2.cmml"><mi id="Sx4.E1.m1.6.6.2.2.2.4" 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xref="Sx4.E1.m1.21.21.3.1.1">subscript</csymbol><ci id="Sx4.E1.m1.21.21.3.1.1.2.cmml" xref="Sx4.E1.m1.21.21.3.1.1.2">𝑄</ci><cn id="Sx4.E1.m1.21.21.3.1.1.3.cmml" type="integer" xref="Sx4.E1.m1.21.21.3.1.1.3">31</cn></apply><apply id="Sx4.E1.m1.21.21.3.2.1.cmml" xref="Sx4.E1.m1.21.21.3.2.1"><csymbol cd="ambiguous" id="Sx4.E1.m1.21.21.3.2.1.1.cmml" xref="Sx4.E1.m1.21.21.3.2.1">subscript</csymbol><ci id="Sx4.E1.m1.21.21.3.2.1.2.cmml" xref="Sx4.E1.m1.21.21.3.2.1.2">𝑄</ci><cn id="Sx4.E1.m1.21.21.3.2.1.3.cmml" type="integer" xref="Sx4.E1.m1.21.21.3.2.1.3">32</cn></apply><apply id="Sx4.E1.m1.21.21.3.3.1.cmml" xref="Sx4.E1.m1.21.21.3.3.1"><csymbol cd="ambiguous" id="Sx4.E1.m1.21.21.3.3.1.1.cmml" xref="Sx4.E1.m1.21.21.3.3.1">subscript</csymbol><ci id="Sx4.E1.m1.21.21.3.3.1.2.cmml" xref="Sx4.E1.m1.21.21.3.3.1.2">𝑄</ci><cn id="Sx4.E1.m1.21.21.3.3.1.3.cmml" type="integer" xref="Sx4.E1.m1.21.21.3.3.1.3">33</cn></apply><apply id="Sx4.E1.m1.21.21.3.4.1.cmml" xref="Sx4.E1.m1.21.21.3.4.1"><csymbol cd="ambiguous" id="Sx4.E1.m1.21.21.3.4.1.1.cmml" xref="Sx4.E1.m1.21.21.3.4.1">subscript</csymbol><ci id="Sx4.E1.m1.21.21.3.4.1.2.cmml" xref="Sx4.E1.m1.21.21.3.4.1.2">𝑄</ci><cn id="Sx4.E1.m1.21.21.3.4.1.3.cmml" type="integer" xref="Sx4.E1.m1.21.21.3.4.1.3">34</cn></apply></matrixrow><matrixrow id="Sx4.E1.m1.21.21d.cmml" xref="Sx4.E1.m1.22.22.1.1.6.2.2"><apply id="Sx4.E1.m1.21.21.4.1.1.cmml" xref="Sx4.E1.m1.21.21.4.1.1"><csymbol cd="ambiguous" id="Sx4.E1.m1.21.21.4.1.1.1.cmml" xref="Sx4.E1.m1.21.21.4.1.1">subscript</csymbol><ci id="Sx4.E1.m1.21.21.4.1.1.2.cmml" xref="Sx4.E1.m1.21.21.4.1.1.2">𝑄</ci><cn id="Sx4.E1.m1.21.21.4.1.1.3.cmml" type="integer" xref="Sx4.E1.m1.21.21.4.1.1.3">41</cn></apply><apply id="Sx4.E1.m1.21.21.4.2.1.cmml" xref="Sx4.E1.m1.21.21.4.2.1"><csymbol cd="ambiguous" id="Sx4.E1.m1.21.21.4.2.1.1.cmml" xref="Sx4.E1.m1.21.21.4.2.1">subscript</csymbol><ci id="Sx4.E1.m1.21.21.4.2.1.2.cmml" xref="Sx4.E1.m1.21.21.4.2.1.2">𝑄</ci><cn id="Sx4.E1.m1.21.21.4.2.1.3.cmml" type="integer" xref="Sx4.E1.m1.21.21.4.2.1.3">42</cn></apply><apply id="Sx4.E1.m1.21.21.4.3.1.cmml" xref="Sx4.E1.m1.21.21.4.3.1"><csymbol cd="ambiguous" id="Sx4.E1.m1.21.21.4.3.1.1.cmml" xref="Sx4.E1.m1.21.21.4.3.1">subscript</csymbol><ci id="Sx4.E1.m1.21.21.4.3.1.2.cmml" xref="Sx4.E1.m1.21.21.4.3.1.2">𝑄</ci><cn id="Sx4.E1.m1.21.21.4.3.1.3.cmml" type="integer" xref="Sx4.E1.m1.21.21.4.3.1.3">43</cn></apply><apply id="Sx4.E1.m1.21.21.4.4.1.cmml" xref="Sx4.E1.m1.21.21.4.4.1"><csymbol cd="ambiguous" id="Sx4.E1.m1.21.21.4.4.1.1.cmml" xref="Sx4.E1.m1.21.21.4.4.1">subscript</csymbol><ci id="Sx4.E1.m1.21.21.4.4.1.2.cmml" xref="Sx4.E1.m1.21.21.4.4.1.2">𝑄</ci><cn id="Sx4.E1.m1.21.21.4.4.1.3.cmml" type="integer" xref="Sx4.E1.m1.21.21.4.4.1.3">44</cn></apply></matrixrow></matrix><matrix id="Sx4.E1.m1.20.20.cmml" xref="Sx4.E1.m1.22.22.1.1.6.3.2"><matrixrow id="Sx4.E1.m1.20.20a.cmml" xref="Sx4.E1.m1.22.22.1.1.6.3.2"><apply id="Sx4.E1.m1.14.14.2.2.2.cmml" xref="Sx4.E1.m1.14.14.2.2.2"><csymbol cd="ambiguous" id="Sx4.E1.m1.14.14.2.2.2.3.cmml" xref="Sx4.E1.m1.14.14.2.2.2">subscript</csymbol><ci id="Sx4.E1.m1.14.14.2.2.2.4.cmml" xref="Sx4.E1.m1.14.14.2.2.2.4">𝐸</ci><list id="Sx4.E1.m1.14.14.2.2.2.2.2.3.cmml" xref="Sx4.E1.m1.14.14.2.2.2.2.2.4"><ci id="Sx4.E1.m1.13.13.1.1.1.1.1.1.cmml" xref="Sx4.E1.m1.13.13.1.1.1.1.1.1">𝑖</ci><ci id="Sx4.E1.m1.14.14.2.2.2.2.2.2.cmml" xref="Sx4.E1.m1.14.14.2.2.2.2.2.2">𝑠</ci></list></apply></matrixrow><matrixrow id="Sx4.E1.m1.20.20b.cmml" xref="Sx4.E1.m1.22.22.1.1.6.3.2"><apply id="Sx4.E1.m1.16.16.4.2.2.cmml" xref="Sx4.E1.m1.16.16.4.2.2"><csymbol cd="ambiguous" id="Sx4.E1.m1.16.16.4.2.2.3.cmml" xref="Sx4.E1.m1.16.16.4.2.2">subscript</csymbol><ci id="Sx4.E1.m1.16.16.4.2.2.4.cmml" xref="Sx4.E1.m1.16.16.4.2.2.4">𝐸</ci><list id="Sx4.E1.m1.16.16.4.2.2.2.2.3.cmml" xref="Sx4.E1.m1.16.16.4.2.2.2.2.4"><ci id="Sx4.E1.m1.15.15.3.1.1.1.1.1.cmml" xref="Sx4.E1.m1.15.15.3.1.1.1.1.1">𝑟</ci><ci id="Sx4.E1.m1.16.16.4.2.2.2.2.2.cmml" xref="Sx4.E1.m1.16.16.4.2.2.2.2.2">𝑠</ci></list></apply></matrixrow><matrixrow id="Sx4.E1.m1.20.20c.cmml" xref="Sx4.E1.m1.22.22.1.1.6.3.2"><apply id="Sx4.E1.m1.18.18.6.2.2.cmml" xref="Sx4.E1.m1.18.18.6.2.2"><csymbol cd="ambiguous" id="Sx4.E1.m1.18.18.6.2.2.3.cmml" xref="Sx4.E1.m1.18.18.6.2.2">subscript</csymbol><ci id="Sx4.E1.m1.18.18.6.2.2.4.cmml" xref="Sx4.E1.m1.18.18.6.2.2.4">𝐸</ci><list id="Sx4.E1.m1.18.18.6.2.2.2.2.3.cmml" xref="Sx4.E1.m1.18.18.6.2.2.2.2.4"><ci id="Sx4.E1.m1.17.17.5.1.1.1.1.1.cmml" xref="Sx4.E1.m1.17.17.5.1.1.1.1.1">𝑖</ci><ci id="Sx4.E1.m1.18.18.6.2.2.2.2.2.cmml" xref="Sx4.E1.m1.18.18.6.2.2.2.2.2">𝑝</ci></list></apply></matrixrow><matrixrow id="Sx4.E1.m1.20.20d.cmml" xref="Sx4.E1.m1.22.22.1.1.6.3.2"><apply id="Sx4.E1.m1.20.20.8.2.2.cmml" xref="Sx4.E1.m1.20.20.8.2.2"><csymbol cd="ambiguous" id="Sx4.E1.m1.20.20.8.2.2.3.cmml" xref="Sx4.E1.m1.20.20.8.2.2">subscript</csymbol><ci id="Sx4.E1.m1.20.20.8.2.2.4.cmml" xref="Sx4.E1.m1.20.20.8.2.2.4">𝐸</ci><list id="Sx4.E1.m1.20.20.8.2.2.2.2.3.cmml" xref="Sx4.E1.m1.20.20.8.2.2.2.2.4"><ci id="Sx4.E1.m1.19.19.7.1.1.1.1.1.cmml" xref="Sx4.E1.m1.19.19.7.1.1.1.1.1">𝑟</ci><ci id="Sx4.E1.m1.20.20.8.2.2.2.2.2.cmml" xref="Sx4.E1.m1.20.20.8.2.2.2.2.2">𝑝</ci></list></apply></matrixrow></matrix></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.E1.m1.22c">\left(\begin{array}[]{c}E_{t,s}\\ 0\\ E_{t,p}\\ 0\end{array}\right)=Q\left(\begin{array}[]{c}E_{i,s}\\ E_{r,s}\\ E_{i,p}\\ E_{r,p}\end{array}\right)=\left(\begin{array}[]{cccc}Q_{11}&Q_{12}&Q_{13}&Q_{1% 4}\\ Q_{21}&Q_{22}&Q_{23}&Q_{24}\\ Q_{31}&Q_{32}&Q_{33}&Q_{34}\\ Q_{41}&Q_{42}&Q_{43}&Q_{44}\\ \end{array}\right)\left(\begin{array}[]{c}E_{i,s}\\ E_{r,s}\\ E_{i,p}\\ E_{r,p}\end{array}\right),</annotation><annotation encoding="application/x-llamapun" id="Sx4.E1.m1.22d">( start_ARRAY start_ROW start_CELL italic_E start_POSTSUBSCRIPT italic_t , italic_s end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL 0 end_CELL end_ROW start_ROW start_CELL italic_E start_POSTSUBSCRIPT italic_t , italic_p end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL 0 end_CELL end_ROW end_ARRAY ) = italic_Q ( start_ARRAY start_ROW start_CELL italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_E start_POSTSUBSCRIPT italic_r , italic_s end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_E start_POSTSUBSCRIPT italic_r , italic_p end_POSTSUBSCRIPT end_CELL end_ROW end_ARRAY ) = ( start_ARRAY start_ROW start_CELL italic_Q start_POSTSUBSCRIPT 11 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 13 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 14 end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_Q start_POSTSUBSCRIPT 21 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_Q start_POSTSUBSCRIPT 31 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 32 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 33 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 34 end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_Q start_POSTSUBSCRIPT 41 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 43 end_POSTSUBSCRIPT end_CELL start_CELL italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT end_CELL end_ROW end_ARRAY ) ( start_ARRAY start_ROW start_CELL italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_E start_POSTSUBSCRIPT italic_r , italic_s end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_E start_POSTSUBSCRIPT italic_r , italic_p end_POSTSUBSCRIPT end_CELL end_ROW end_ARRAY ) ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(1)</span></td> </tr></tbody> </table> <p class="ltx_p" id="Sx4.p2.26">where <math alttext="Q" class="ltx_Math" display="inline" id="Sx4.p2.23.m1.1"><semantics id="Sx4.p2.23.m1.1a"><mi id="Sx4.p2.23.m1.1.1" xref="Sx4.p2.23.m1.1.1.cmml">Q</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.23.m1.1b"><ci id="Sx4.p2.23.m1.1.1.cmml" xref="Sx4.p2.23.m1.1.1">𝑄</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.23.m1.1c">Q</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.23.m1.1d">italic_Q</annotation></semantics></math> can be written as a product of a series of <math alttext="D" class="ltx_Math" display="inline" id="Sx4.p2.24.m2.1"><semantics id="Sx4.p2.24.m2.1a"><mi id="Sx4.p2.24.m2.1.1" xref="Sx4.p2.24.m2.1.1.cmml">D</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.24.m2.1b"><ci id="Sx4.p2.24.m2.1.1.cmml" xref="Sx4.p2.24.m2.1.1">𝐷</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.24.m2.1c">D</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.24.m2.1d">italic_D</annotation></semantics></math> and <math alttext="P" class="ltx_Math" display="inline" id="Sx4.p2.25.m3.1"><semantics id="Sx4.p2.25.m3.1a"><mi id="Sx4.p2.25.m3.1.1" xref="Sx4.p2.25.m3.1.1.cmml">P</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.25.m3.1b"><ci id="Sx4.p2.25.m3.1.1.cmml" xref="Sx4.p2.25.m3.1.1">𝑃</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.25.m3.1c">P</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.25.m3.1d">italic_P</annotation></semantics></math> matrices. Specifically, for a stack with <math alttext="N" class="ltx_Math" display="inline" id="Sx4.p2.26.m4.1"><semantics id="Sx4.p2.26.m4.1a"><mi id="Sx4.p2.26.m4.1.1" xref="Sx4.p2.26.m4.1.1.cmml">N</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.26.m4.1b"><ci id="Sx4.p2.26.m4.1.1.cmml" xref="Sx4.p2.26.m4.1.1">𝑁</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.26.m4.1c">N</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.26.m4.1d">italic_N</annotation></semantics></math> layers,</p> <table class="ltx_equation ltx_eqn_table" id="Sx4.E2"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="Q=D_{N+1}^{-1}D_{N}P_{N}D_{N}^{-1}D_{N-1}P_{N-1}D_{N-1}^{-1}\cdot\cdot\cdot D_% {1}P_{1}D_{1}^{-1}D_{0}" class="ltx_Math" display="block" id="Sx4.E2.m1.1"><semantics id="Sx4.E2.m1.1a"><mrow id="Sx4.E2.m1.1.1" xref="Sx4.E2.m1.1.1.cmml"><mi id="Sx4.E2.m1.1.1.2" xref="Sx4.E2.m1.1.1.2.cmml">Q</mi><mo id="Sx4.E2.m1.1.1.1" xref="Sx4.E2.m1.1.1.1.cmml">=</mo><mrow id="Sx4.E2.m1.1.1.3" xref="Sx4.E2.m1.1.1.3.cmml"><msubsup id="Sx4.E2.m1.1.1.3.2" xref="Sx4.E2.m1.1.1.3.2.cmml"><mi id="Sx4.E2.m1.1.1.3.2.2.2" xref="Sx4.E2.m1.1.1.3.2.2.2.cmml">D</mi><mrow id="Sx4.E2.m1.1.1.3.2.2.3" xref="Sx4.E2.m1.1.1.3.2.2.3.cmml"><mi id="Sx4.E2.m1.1.1.3.2.2.3.2" xref="Sx4.E2.m1.1.1.3.2.2.3.2.cmml">N</mi><mo id="Sx4.E2.m1.1.1.3.2.2.3.1" xref="Sx4.E2.m1.1.1.3.2.2.3.1.cmml">+</mo><mn id="Sx4.E2.m1.1.1.3.2.2.3.3" xref="Sx4.E2.m1.1.1.3.2.2.3.3.cmml">1</mn></mrow><mrow id="Sx4.E2.m1.1.1.3.2.3" xref="Sx4.E2.m1.1.1.3.2.3.cmml"><mo id="Sx4.E2.m1.1.1.3.2.3a" xref="Sx4.E2.m1.1.1.3.2.3.cmml">−</mo><mn id="Sx4.E2.m1.1.1.3.2.3.2" xref="Sx4.E2.m1.1.1.3.2.3.2.cmml">1</mn></mrow></msubsup><mo id="Sx4.E2.m1.1.1.3.1" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><msub id="Sx4.E2.m1.1.1.3.3" xref="Sx4.E2.m1.1.1.3.3.cmml"><mi id="Sx4.E2.m1.1.1.3.3.2" xref="Sx4.E2.m1.1.1.3.3.2.cmml">D</mi><mi id="Sx4.E2.m1.1.1.3.3.3" xref="Sx4.E2.m1.1.1.3.3.3.cmml">N</mi></msub><mo id="Sx4.E2.m1.1.1.3.1a" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><msub id="Sx4.E2.m1.1.1.3.4" xref="Sx4.E2.m1.1.1.3.4.cmml"><mi id="Sx4.E2.m1.1.1.3.4.2" xref="Sx4.E2.m1.1.1.3.4.2.cmml">P</mi><mi id="Sx4.E2.m1.1.1.3.4.3" xref="Sx4.E2.m1.1.1.3.4.3.cmml">N</mi></msub><mo id="Sx4.E2.m1.1.1.3.1b" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><msubsup id="Sx4.E2.m1.1.1.3.5" xref="Sx4.E2.m1.1.1.3.5.cmml"><mi id="Sx4.E2.m1.1.1.3.5.2.2" xref="Sx4.E2.m1.1.1.3.5.2.2.cmml">D</mi><mi id="Sx4.E2.m1.1.1.3.5.2.3" xref="Sx4.E2.m1.1.1.3.5.2.3.cmml">N</mi><mrow id="Sx4.E2.m1.1.1.3.5.3" xref="Sx4.E2.m1.1.1.3.5.3.cmml"><mo id="Sx4.E2.m1.1.1.3.5.3a" xref="Sx4.E2.m1.1.1.3.5.3.cmml">−</mo><mn id="Sx4.E2.m1.1.1.3.5.3.2" xref="Sx4.E2.m1.1.1.3.5.3.2.cmml">1</mn></mrow></msubsup><mo id="Sx4.E2.m1.1.1.3.1c" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><msub id="Sx4.E2.m1.1.1.3.6" xref="Sx4.E2.m1.1.1.3.6.cmml"><mi id="Sx4.E2.m1.1.1.3.6.2" xref="Sx4.E2.m1.1.1.3.6.2.cmml">D</mi><mrow id="Sx4.E2.m1.1.1.3.6.3" xref="Sx4.E2.m1.1.1.3.6.3.cmml"><mi id="Sx4.E2.m1.1.1.3.6.3.2" xref="Sx4.E2.m1.1.1.3.6.3.2.cmml">N</mi><mo id="Sx4.E2.m1.1.1.3.6.3.1" xref="Sx4.E2.m1.1.1.3.6.3.1.cmml">−</mo><mn id="Sx4.E2.m1.1.1.3.6.3.3" xref="Sx4.E2.m1.1.1.3.6.3.3.cmml">1</mn></mrow></msub><mo id="Sx4.E2.m1.1.1.3.1d" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><msub id="Sx4.E2.m1.1.1.3.7" xref="Sx4.E2.m1.1.1.3.7.cmml"><mi id="Sx4.E2.m1.1.1.3.7.2" xref="Sx4.E2.m1.1.1.3.7.2.cmml">P</mi><mrow id="Sx4.E2.m1.1.1.3.7.3" xref="Sx4.E2.m1.1.1.3.7.3.cmml"><mi id="Sx4.E2.m1.1.1.3.7.3.2" xref="Sx4.E2.m1.1.1.3.7.3.2.cmml">N</mi><mo id="Sx4.E2.m1.1.1.3.7.3.1" xref="Sx4.E2.m1.1.1.3.7.3.1.cmml">−</mo><mn id="Sx4.E2.m1.1.1.3.7.3.3" xref="Sx4.E2.m1.1.1.3.7.3.3.cmml">1</mn></mrow></msub><mo id="Sx4.E2.m1.1.1.3.1e" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><msubsup id="Sx4.E2.m1.1.1.3.8" xref="Sx4.E2.m1.1.1.3.8.cmml"><mi id="Sx4.E2.m1.1.1.3.8.2.2" xref="Sx4.E2.m1.1.1.3.8.2.2.cmml">D</mi><mrow id="Sx4.E2.m1.1.1.3.8.2.3" xref="Sx4.E2.m1.1.1.3.8.2.3.cmml"><mi id="Sx4.E2.m1.1.1.3.8.2.3.2" xref="Sx4.E2.m1.1.1.3.8.2.3.2.cmml">N</mi><mo id="Sx4.E2.m1.1.1.3.8.2.3.1" xref="Sx4.E2.m1.1.1.3.8.2.3.1.cmml">−</mo><mn id="Sx4.E2.m1.1.1.3.8.2.3.3" xref="Sx4.E2.m1.1.1.3.8.2.3.3.cmml">1</mn></mrow><mrow id="Sx4.E2.m1.1.1.3.8.3" xref="Sx4.E2.m1.1.1.3.8.3.cmml"><mo id="Sx4.E2.m1.1.1.3.8.3a" xref="Sx4.E2.m1.1.1.3.8.3.cmml">−</mo><mn id="Sx4.E2.m1.1.1.3.8.3.2" xref="Sx4.E2.m1.1.1.3.8.3.2.cmml">1</mn></mrow></msubsup><mo id="Sx4.E2.m1.1.1.3.1f" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><mi id="Sx4.E2.m1.1.1.3.9" mathvariant="normal" xref="Sx4.E2.m1.1.1.3.9.cmml">⋯</mi><mo id="Sx4.E2.m1.1.1.3.1g" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><msub id="Sx4.E2.m1.1.1.3.10" xref="Sx4.E2.m1.1.1.3.10.cmml"><mi id="Sx4.E2.m1.1.1.3.10.2" xref="Sx4.E2.m1.1.1.3.10.2.cmml">D</mi><mn id="Sx4.E2.m1.1.1.3.10.3" xref="Sx4.E2.m1.1.1.3.10.3.cmml">1</mn></msub><mo id="Sx4.E2.m1.1.1.3.1h" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><msub id="Sx4.E2.m1.1.1.3.11" xref="Sx4.E2.m1.1.1.3.11.cmml"><mi id="Sx4.E2.m1.1.1.3.11.2" xref="Sx4.E2.m1.1.1.3.11.2.cmml">P</mi><mn id="Sx4.E2.m1.1.1.3.11.3" xref="Sx4.E2.m1.1.1.3.11.3.cmml">1</mn></msub><mo id="Sx4.E2.m1.1.1.3.1i" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><msubsup id="Sx4.E2.m1.1.1.3.12" xref="Sx4.E2.m1.1.1.3.12.cmml"><mi id="Sx4.E2.m1.1.1.3.12.2.2" xref="Sx4.E2.m1.1.1.3.12.2.2.cmml">D</mi><mn id="Sx4.E2.m1.1.1.3.12.2.3" xref="Sx4.E2.m1.1.1.3.12.2.3.cmml">1</mn><mrow id="Sx4.E2.m1.1.1.3.12.3" xref="Sx4.E2.m1.1.1.3.12.3.cmml"><mo id="Sx4.E2.m1.1.1.3.12.3a" xref="Sx4.E2.m1.1.1.3.12.3.cmml">−</mo><mn id="Sx4.E2.m1.1.1.3.12.3.2" xref="Sx4.E2.m1.1.1.3.12.3.2.cmml">1</mn></mrow></msubsup><mo id="Sx4.E2.m1.1.1.3.1j" xref="Sx4.E2.m1.1.1.3.1.cmml">⁢</mo><msub id="Sx4.E2.m1.1.1.3.13" xref="Sx4.E2.m1.1.1.3.13.cmml"><mi id="Sx4.E2.m1.1.1.3.13.2" xref="Sx4.E2.m1.1.1.3.13.2.cmml">D</mi><mn id="Sx4.E2.m1.1.1.3.13.3" xref="Sx4.E2.m1.1.1.3.13.3.cmml">0</mn></msub></mrow></mrow><annotation-xml encoding="MathML-Content" id="Sx4.E2.m1.1b"><apply id="Sx4.E2.m1.1.1.cmml" xref="Sx4.E2.m1.1.1"><eq id="Sx4.E2.m1.1.1.1.cmml" xref="Sx4.E2.m1.1.1.1"></eq><ci id="Sx4.E2.m1.1.1.2.cmml" xref="Sx4.E2.m1.1.1.2">𝑄</ci><apply id="Sx4.E2.m1.1.1.3.cmml" xref="Sx4.E2.m1.1.1.3"><times id="Sx4.E2.m1.1.1.3.1.cmml" xref="Sx4.E2.m1.1.1.3.1"></times><apply id="Sx4.E2.m1.1.1.3.2.cmml" xref="Sx4.E2.m1.1.1.3.2"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.2.1.cmml" xref="Sx4.E2.m1.1.1.3.2">superscript</csymbol><apply id="Sx4.E2.m1.1.1.3.2.2.cmml" xref="Sx4.E2.m1.1.1.3.2"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.2.2.1.cmml" xref="Sx4.E2.m1.1.1.3.2">subscript</csymbol><ci id="Sx4.E2.m1.1.1.3.2.2.2.cmml" xref="Sx4.E2.m1.1.1.3.2.2.2">𝐷</ci><apply id="Sx4.E2.m1.1.1.3.2.2.3.cmml" xref="Sx4.E2.m1.1.1.3.2.2.3"><plus id="Sx4.E2.m1.1.1.3.2.2.3.1.cmml" xref="Sx4.E2.m1.1.1.3.2.2.3.1"></plus><ci id="Sx4.E2.m1.1.1.3.2.2.3.2.cmml" xref="Sx4.E2.m1.1.1.3.2.2.3.2">𝑁</ci><cn id="Sx4.E2.m1.1.1.3.2.2.3.3.cmml" type="integer" xref="Sx4.E2.m1.1.1.3.2.2.3.3">1</cn></apply></apply><apply id="Sx4.E2.m1.1.1.3.2.3.cmml" xref="Sx4.E2.m1.1.1.3.2.3"><minus id="Sx4.E2.m1.1.1.3.2.3.1.cmml" xref="Sx4.E2.m1.1.1.3.2.3"></minus><cn id="Sx4.E2.m1.1.1.3.2.3.2.cmml" type="integer" xref="Sx4.E2.m1.1.1.3.2.3.2">1</cn></apply></apply><apply id="Sx4.E2.m1.1.1.3.3.cmml" xref="Sx4.E2.m1.1.1.3.3"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.3.1.cmml" xref="Sx4.E2.m1.1.1.3.3">subscript</csymbol><ci id="Sx4.E2.m1.1.1.3.3.2.cmml" xref="Sx4.E2.m1.1.1.3.3.2">𝐷</ci><ci id="Sx4.E2.m1.1.1.3.3.3.cmml" xref="Sx4.E2.m1.1.1.3.3.3">𝑁</ci></apply><apply id="Sx4.E2.m1.1.1.3.4.cmml" xref="Sx4.E2.m1.1.1.3.4"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.4.1.cmml" xref="Sx4.E2.m1.1.1.3.4">subscript</csymbol><ci id="Sx4.E2.m1.1.1.3.4.2.cmml" xref="Sx4.E2.m1.1.1.3.4.2">𝑃</ci><ci id="Sx4.E2.m1.1.1.3.4.3.cmml" xref="Sx4.E2.m1.1.1.3.4.3">𝑁</ci></apply><apply id="Sx4.E2.m1.1.1.3.5.cmml" xref="Sx4.E2.m1.1.1.3.5"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.5.1.cmml" xref="Sx4.E2.m1.1.1.3.5">superscript</csymbol><apply id="Sx4.E2.m1.1.1.3.5.2.cmml" xref="Sx4.E2.m1.1.1.3.5"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.5.2.1.cmml" xref="Sx4.E2.m1.1.1.3.5">subscript</csymbol><ci id="Sx4.E2.m1.1.1.3.5.2.2.cmml" xref="Sx4.E2.m1.1.1.3.5.2.2">𝐷</ci><ci id="Sx4.E2.m1.1.1.3.5.2.3.cmml" xref="Sx4.E2.m1.1.1.3.5.2.3">𝑁</ci></apply><apply id="Sx4.E2.m1.1.1.3.5.3.cmml" xref="Sx4.E2.m1.1.1.3.5.3"><minus id="Sx4.E2.m1.1.1.3.5.3.1.cmml" xref="Sx4.E2.m1.1.1.3.5.3"></minus><cn id="Sx4.E2.m1.1.1.3.5.3.2.cmml" type="integer" xref="Sx4.E2.m1.1.1.3.5.3.2">1</cn></apply></apply><apply id="Sx4.E2.m1.1.1.3.6.cmml" xref="Sx4.E2.m1.1.1.3.6"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.6.1.cmml" xref="Sx4.E2.m1.1.1.3.6">subscript</csymbol><ci id="Sx4.E2.m1.1.1.3.6.2.cmml" xref="Sx4.E2.m1.1.1.3.6.2">𝐷</ci><apply id="Sx4.E2.m1.1.1.3.6.3.cmml" xref="Sx4.E2.m1.1.1.3.6.3"><minus id="Sx4.E2.m1.1.1.3.6.3.1.cmml" xref="Sx4.E2.m1.1.1.3.6.3.1"></minus><ci id="Sx4.E2.m1.1.1.3.6.3.2.cmml" xref="Sx4.E2.m1.1.1.3.6.3.2">𝑁</ci><cn id="Sx4.E2.m1.1.1.3.6.3.3.cmml" type="integer" xref="Sx4.E2.m1.1.1.3.6.3.3">1</cn></apply></apply><apply id="Sx4.E2.m1.1.1.3.7.cmml" xref="Sx4.E2.m1.1.1.3.7"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.7.1.cmml" xref="Sx4.E2.m1.1.1.3.7">subscript</csymbol><ci id="Sx4.E2.m1.1.1.3.7.2.cmml" xref="Sx4.E2.m1.1.1.3.7.2">𝑃</ci><apply id="Sx4.E2.m1.1.1.3.7.3.cmml" xref="Sx4.E2.m1.1.1.3.7.3"><minus id="Sx4.E2.m1.1.1.3.7.3.1.cmml" xref="Sx4.E2.m1.1.1.3.7.3.1"></minus><ci id="Sx4.E2.m1.1.1.3.7.3.2.cmml" xref="Sx4.E2.m1.1.1.3.7.3.2">𝑁</ci><cn id="Sx4.E2.m1.1.1.3.7.3.3.cmml" type="integer" xref="Sx4.E2.m1.1.1.3.7.3.3">1</cn></apply></apply><apply id="Sx4.E2.m1.1.1.3.8.cmml" xref="Sx4.E2.m1.1.1.3.8"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.8.1.cmml" xref="Sx4.E2.m1.1.1.3.8">superscript</csymbol><apply id="Sx4.E2.m1.1.1.3.8.2.cmml" xref="Sx4.E2.m1.1.1.3.8"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.8.2.1.cmml" xref="Sx4.E2.m1.1.1.3.8">subscript</csymbol><ci id="Sx4.E2.m1.1.1.3.8.2.2.cmml" xref="Sx4.E2.m1.1.1.3.8.2.2">𝐷</ci><apply id="Sx4.E2.m1.1.1.3.8.2.3.cmml" xref="Sx4.E2.m1.1.1.3.8.2.3"><minus id="Sx4.E2.m1.1.1.3.8.2.3.1.cmml" xref="Sx4.E2.m1.1.1.3.8.2.3.1"></minus><ci id="Sx4.E2.m1.1.1.3.8.2.3.2.cmml" xref="Sx4.E2.m1.1.1.3.8.2.3.2">𝑁</ci><cn id="Sx4.E2.m1.1.1.3.8.2.3.3.cmml" type="integer" xref="Sx4.E2.m1.1.1.3.8.2.3.3">1</cn></apply></apply><apply id="Sx4.E2.m1.1.1.3.8.3.cmml" xref="Sx4.E2.m1.1.1.3.8.3"><minus id="Sx4.E2.m1.1.1.3.8.3.1.cmml" xref="Sx4.E2.m1.1.1.3.8.3"></minus><cn id="Sx4.E2.m1.1.1.3.8.3.2.cmml" type="integer" xref="Sx4.E2.m1.1.1.3.8.3.2">1</cn></apply></apply><ci id="Sx4.E2.m1.1.1.3.9.cmml" xref="Sx4.E2.m1.1.1.3.9">⋯</ci><apply id="Sx4.E2.m1.1.1.3.10.cmml" xref="Sx4.E2.m1.1.1.3.10"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.10.1.cmml" xref="Sx4.E2.m1.1.1.3.10">subscript</csymbol><ci 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id="Sx4.E2.m1.1.1.3.12.3.cmml" xref="Sx4.E2.m1.1.1.3.12.3"><minus id="Sx4.E2.m1.1.1.3.12.3.1.cmml" xref="Sx4.E2.m1.1.1.3.12.3"></minus><cn id="Sx4.E2.m1.1.1.3.12.3.2.cmml" type="integer" xref="Sx4.E2.m1.1.1.3.12.3.2">1</cn></apply></apply><apply id="Sx4.E2.m1.1.1.3.13.cmml" xref="Sx4.E2.m1.1.1.3.13"><csymbol cd="ambiguous" id="Sx4.E2.m1.1.1.3.13.1.cmml" xref="Sx4.E2.m1.1.1.3.13">subscript</csymbol><ci id="Sx4.E2.m1.1.1.3.13.2.cmml" xref="Sx4.E2.m1.1.1.3.13.2">𝐷</ci><cn id="Sx4.E2.m1.1.1.3.13.3.cmml" type="integer" xref="Sx4.E2.m1.1.1.3.13.3">0</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.E2.m1.1c">Q=D_{N+1}^{-1}D_{N}P_{N}D_{N}^{-1}D_{N-1}P_{N-1}D_{N-1}^{-1}\cdot\cdot\cdot D_% {1}P_{1}D_{1}^{-1}D_{0}</annotation><annotation encoding="application/x-llamapun" id="Sx4.E2.m1.1d">italic_Q = italic_D start_POSTSUBSCRIPT italic_N + 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT italic_D start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT italic_P start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT italic_D start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT italic_D start_POSTSUBSCRIPT italic_N - 1 end_POSTSUBSCRIPT italic_P start_POSTSUBSCRIPT italic_N - 1 end_POSTSUBSCRIPT italic_D start_POSTSUBSCRIPT italic_N - 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ⋯ italic_D start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_P start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_D start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT italic_D start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(2)</span></td> </tr></tbody> </table> <p class="ltx_p" id="Sx4.p2.48">with</p> <table class="ltx_equation ltx_eqn_table" id="Sx4.E3"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="{D_{j}}=\left(\begin{array}[]{cccc}\textrm{sin}\theta_{j}&\textrm{sin}\theta_{% j}&\textrm{cos}\theta_{j}&\textrm{cos}\theta_{j}\\ -n_{s_{j}}\textrm{sin}\theta_{j}&n_{s_{j}}\textrm{sin}\theta_{j}&-n_{p_{j}}% \textrm{cos}\theta_{j}&n_{p_{j}}\textrm{cos}\theta_{j}\\ n_{s_{j}}\textrm{cos}\theta_{j}&-n_{s_{j}}\textrm{cos}\theta_{j}&-n_{p_{j}}% \textrm{sin}\theta_{j}&n_{p_{j}}\textrm{sin}\theta_{j}\\ \textrm{cos}\theta_{j}&\textrm{cos}\theta_{j}&-\textrm{sin}\theta_{j}&-\textrm% {sin}\theta_{j}\\ \end{array}\right)" class="ltx_Math" display="block" id="Sx4.E3.m1.1"><semantics id="Sx4.E3.m1.1a"><mrow id="Sx4.E3.m1.1.2" xref="Sx4.E3.m1.1.2.cmml"><msub id="Sx4.E3.m1.1.2.2" xref="Sx4.E3.m1.1.2.2.cmml"><mi id="Sx4.E3.m1.1.2.2.2" xref="Sx4.E3.m1.1.2.2.2.cmml">D</mi><mi id="Sx4.E3.m1.1.2.2.3" xref="Sx4.E3.m1.1.2.2.3.cmml">j</mi></msub><mo id="Sx4.E3.m1.1.2.1" xref="Sx4.E3.m1.1.2.1.cmml">=</mo><mrow id="Sx4.E3.m1.1.2.3.2" xref="Sx4.E3.m1.1.1.cmml"><mo id="Sx4.E3.m1.1.2.3.2.1" xref="Sx4.E3.m1.1.1.cmml">(</mo><mtable columnspacing="5pt" displaystyle="true" id="Sx4.E3.m1.1.1" rowspacing="0pt" xref="Sx4.E3.m1.1.1.cmml"><mtr id="Sx4.E3.m1.1.1a" xref="Sx4.E3.m1.1.1.cmml"><mtd id="Sx4.E3.m1.1.1b" xref="Sx4.E3.m1.1.1.cmml"><mrow id="Sx4.E3.m1.1.1.1.1.1" xref="Sx4.E3.m1.1.1.1.1.1.cmml"><mtext id="Sx4.E3.m1.1.1.1.1.1.2" xref="Sx4.E3.m1.1.1.1.1.1.2a.cmml">sin</mtext><mo id="Sx4.E3.m1.1.1.1.1.1.1" xref="Sx4.E3.m1.1.1.1.1.1.1.cmml">⁢</mo><msub id="Sx4.E3.m1.1.1.1.1.1.3" xref="Sx4.E3.m1.1.1.1.1.1.3.cmml"><mi id="Sx4.E3.m1.1.1.1.1.1.3.2" xref="Sx4.E3.m1.1.1.1.1.1.3.2.cmml">θ</mi><mi id="Sx4.E3.m1.1.1.1.1.1.3.3" xref="Sx4.E3.m1.1.1.1.1.1.3.3.cmml">j</mi></msub></mrow></mtd><mtd id="Sx4.E3.m1.1.1c" xref="Sx4.E3.m1.1.1.cmml"><mrow id="Sx4.E3.m1.1.1.1.2.1" 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id="Sx4.E3.m1.1.1.2.2.1.2.3.2" xref="Sx4.E3.m1.1.1.2.2.1.2.3.2.cmml">s</mi><mi id="Sx4.E3.m1.1.1.2.2.1.2.3.3" xref="Sx4.E3.m1.1.1.2.2.1.2.3.3.cmml">j</mi></msub></msub><mo id="Sx4.E3.m1.1.1.2.2.1.1" xref="Sx4.E3.m1.1.1.2.2.1.1.cmml">⁢</mo><mtext id="Sx4.E3.m1.1.1.2.2.1.3" xref="Sx4.E3.m1.1.1.2.2.1.3a.cmml">sin</mtext><mo id="Sx4.E3.m1.1.1.2.2.1.1a" xref="Sx4.E3.m1.1.1.2.2.1.1.cmml">⁢</mo><msub id="Sx4.E3.m1.1.1.2.2.1.4" xref="Sx4.E3.m1.1.1.2.2.1.4.cmml"><mi id="Sx4.E3.m1.1.1.2.2.1.4.2" xref="Sx4.E3.m1.1.1.2.2.1.4.2.cmml">θ</mi><mi id="Sx4.E3.m1.1.1.2.2.1.4.3" xref="Sx4.E3.m1.1.1.2.2.1.4.3.cmml">j</mi></msub></mrow></mtd><mtd id="Sx4.E3.m1.1.1i" xref="Sx4.E3.m1.1.1.cmml"><mrow id="Sx4.E3.m1.1.1.2.3.1" xref="Sx4.E3.m1.1.1.2.3.1.cmml"><mo id="Sx4.E3.m1.1.1.2.3.1a" xref="Sx4.E3.m1.1.1.2.3.1.cmml">−</mo><mrow id="Sx4.E3.m1.1.1.2.3.1.2" xref="Sx4.E3.m1.1.1.2.3.1.2.cmml"><msub id="Sx4.E3.m1.1.1.2.3.1.2.2" xref="Sx4.E3.m1.1.1.2.3.1.2.2.cmml"><mi id="Sx4.E3.m1.1.1.2.3.1.2.2.2" xref="Sx4.E3.m1.1.1.2.3.1.2.2.2.cmml">n</mi><msub id="Sx4.E3.m1.1.1.2.3.1.2.2.3" xref="Sx4.E3.m1.1.1.2.3.1.2.2.3.cmml"><mi id="Sx4.E3.m1.1.1.2.3.1.2.2.3.2" xref="Sx4.E3.m1.1.1.2.3.1.2.2.3.2.cmml">p</mi><mi id="Sx4.E3.m1.1.1.2.3.1.2.2.3.3" xref="Sx4.E3.m1.1.1.2.3.1.2.2.3.3.cmml">j</mi></msub></msub><mo id="Sx4.E3.m1.1.1.2.3.1.2.1" xref="Sx4.E3.m1.1.1.2.3.1.2.1.cmml">⁢</mo><mtext id="Sx4.E3.m1.1.1.2.3.1.2.3" xref="Sx4.E3.m1.1.1.2.3.1.2.3a.cmml">cos</mtext><mo id="Sx4.E3.m1.1.1.2.3.1.2.1a" xref="Sx4.E3.m1.1.1.2.3.1.2.1.cmml">⁢</mo><msub id="Sx4.E3.m1.1.1.2.3.1.2.4" xref="Sx4.E3.m1.1.1.2.3.1.2.4.cmml"><mi id="Sx4.E3.m1.1.1.2.3.1.2.4.2" xref="Sx4.E3.m1.1.1.2.3.1.2.4.2.cmml">θ</mi><mi id="Sx4.E3.m1.1.1.2.3.1.2.4.3" xref="Sx4.E3.m1.1.1.2.3.1.2.4.3.cmml">j</mi></msub></mrow></mrow></mtd><mtd id="Sx4.E3.m1.1.1j" xref="Sx4.E3.m1.1.1.cmml"><mrow id="Sx4.E3.m1.1.1.2.4.1" xref="Sx4.E3.m1.1.1.2.4.1.cmml"><msub id="Sx4.E3.m1.1.1.2.4.1.2" xref="Sx4.E3.m1.1.1.2.4.1.2.cmml"><mi 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xref="Sx4.E3.m1.1.1.3.1.1.2.cmml"><mi id="Sx4.E3.m1.1.1.3.1.1.2.2" xref="Sx4.E3.m1.1.1.3.1.1.2.2.cmml">n</mi><msub id="Sx4.E3.m1.1.1.3.1.1.2.3" xref="Sx4.E3.m1.1.1.3.1.1.2.3.cmml"><mi id="Sx4.E3.m1.1.1.3.1.1.2.3.2" xref="Sx4.E3.m1.1.1.3.1.1.2.3.2.cmml">s</mi><mi id="Sx4.E3.m1.1.1.3.1.1.2.3.3" xref="Sx4.E3.m1.1.1.3.1.1.2.3.3.cmml">j</mi></msub></msub><mo id="Sx4.E3.m1.1.1.3.1.1.1" xref="Sx4.E3.m1.1.1.3.1.1.1.cmml">⁢</mo><mtext id="Sx4.E3.m1.1.1.3.1.1.3" xref="Sx4.E3.m1.1.1.3.1.1.3a.cmml">cos</mtext><mo id="Sx4.E3.m1.1.1.3.1.1.1a" xref="Sx4.E3.m1.1.1.3.1.1.1.cmml">⁢</mo><msub id="Sx4.E3.m1.1.1.3.1.1.4" xref="Sx4.E3.m1.1.1.3.1.1.4.cmml"><mi id="Sx4.E3.m1.1.1.3.1.1.4.2" xref="Sx4.E3.m1.1.1.3.1.1.4.2.cmml">θ</mi><mi id="Sx4.E3.m1.1.1.3.1.1.4.3" xref="Sx4.E3.m1.1.1.3.1.1.4.3.cmml">j</mi></msub></mrow></mtd><mtd id="Sx4.E3.m1.1.1m" xref="Sx4.E3.m1.1.1.cmml"><mrow id="Sx4.E3.m1.1.1.3.2.1" xref="Sx4.E3.m1.1.1.3.2.1.cmml"><mo id="Sx4.E3.m1.1.1.3.2.1a" xref="Sx4.E3.m1.1.1.3.2.1.cmml">−</mo><mrow 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id="Sx4.E3.m1.1c">{D_{j}}=\left(\begin{array}[]{cccc}\textrm{sin}\theta_{j}&\textrm{sin}\theta_{% j}&\textrm{cos}\theta_{j}&\textrm{cos}\theta_{j}\\ -n_{s_{j}}\textrm{sin}\theta_{j}&n_{s_{j}}\textrm{sin}\theta_{j}&-n_{p_{j}}% \textrm{cos}\theta_{j}&n_{p_{j}}\textrm{cos}\theta_{j}\\ n_{s_{j}}\textrm{cos}\theta_{j}&-n_{s_{j}}\textrm{cos}\theta_{j}&-n_{p_{j}}% \textrm{sin}\theta_{j}&n_{p_{j}}\textrm{sin}\theta_{j}\\ \textrm{cos}\theta_{j}&\textrm{cos}\theta_{j}&-\textrm{sin}\theta_{j}&-\textrm% {sin}\theta_{j}\\ \end{array}\right)</annotation><annotation encoding="application/x-llamapun" id="Sx4.E3.m1.1d">italic_D start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT = ( start_ARRAY start_ROW start_CELL sin italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL sin italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL cos italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL cos italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL - italic_n start_POSTSUBSCRIPT italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT sin italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL italic_n start_POSTSUBSCRIPT italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT sin italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL - italic_n start_POSTSUBSCRIPT italic_p start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT cos italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL italic_n start_POSTSUBSCRIPT italic_p start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT cos italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_n start_POSTSUBSCRIPT italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT cos italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL - italic_n start_POSTSUBSCRIPT italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT cos italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL - italic_n start_POSTSUBSCRIPT italic_p start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT sin italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL italic_n start_POSTSUBSCRIPT italic_p start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT sin italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL cos italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL cos italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL - sin italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL - sin italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL end_ROW end_ARRAY )</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(3)</span></td> </tr></tbody> </table> <p class="ltx_p" id="Sx4.p2.49">and</p> <table class="ltx_equation ltx_eqn_table" id="Sx4.E4"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="{P_{j}}=\left(\begin{array}[]{cccc}e^{\textrm{i}k_{j,1}t_{j}}&0&0&0\\ 0&e^{\textrm{i}k_{j,2}t_{j}}&0&0\\ 0&0&e^{\textrm{i}k_{j,3}t_{j}}&0\\ 0&0&0&e^{\textrm{i}k_{j,4}t_{j}}\end{array}\right)," class="ltx_Math" display="block" id="Sx4.E4.m1.9"><semantics id="Sx4.E4.m1.9a"><mrow id="Sx4.E4.m1.9.9.1" xref="Sx4.E4.m1.9.9.1.1.cmml"><mrow id="Sx4.E4.m1.9.9.1.1" xref="Sx4.E4.m1.9.9.1.1.cmml"><msub id="Sx4.E4.m1.9.9.1.1.2" xref="Sx4.E4.m1.9.9.1.1.2.cmml"><mi id="Sx4.E4.m1.9.9.1.1.2.2" xref="Sx4.E4.m1.9.9.1.1.2.2.cmml">P</mi><mi id="Sx4.E4.m1.9.9.1.1.2.3" 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id="Sx4.E4.m1.9d">italic_P start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT = ( start_ARRAY start_ROW start_CELL italic_e start_POSTSUPERSCRIPT i italic_k start_POSTSUBSCRIPT italic_j , 1 end_POSTSUBSCRIPT italic_t start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUPERSCRIPT end_CELL start_CELL 0 end_CELL start_CELL 0 end_CELL start_CELL 0 end_CELL end_ROW start_ROW start_CELL 0 end_CELL start_CELL italic_e start_POSTSUPERSCRIPT i italic_k start_POSTSUBSCRIPT italic_j , 2 end_POSTSUBSCRIPT italic_t start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUPERSCRIPT end_CELL start_CELL 0 end_CELL start_CELL 0 end_CELL end_ROW start_ROW start_CELL 0 end_CELL start_CELL 0 end_CELL start_CELL italic_e start_POSTSUPERSCRIPT i italic_k start_POSTSUBSCRIPT italic_j , 3 end_POSTSUBSCRIPT italic_t start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUPERSCRIPT end_CELL start_CELL 0 end_CELL end_ROW start_ROW start_CELL 0 end_CELL start_CELL 0 end_CELL start_CELL 0 end_CELL start_CELL italic_e start_POSTSUPERSCRIPT i italic_k start_POSTSUBSCRIPT italic_j , 4 end_POSTSUBSCRIPT italic_t start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUPERSCRIPT end_CELL end_ROW end_ARRAY ) ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(4)</span></td> </tr></tbody> </table> <p class="ltx_p" id="Sx4.p2.44">for <math alttext="j" class="ltx_Math" display="inline" id="Sx4.p2.27.m1.1"><semantics id="Sx4.p2.27.m1.1a"><mi id="Sx4.p2.27.m1.1.1" xref="Sx4.p2.27.m1.1.1.cmml">j</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.27.m1.1b"><ci id="Sx4.p2.27.m1.1.1.cmml" xref="Sx4.p2.27.m1.1.1">𝑗</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.27.m1.1c">j</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.27.m1.1d">italic_j</annotation></semantics></math>-th layer and <math alttext="j\in[0,N+1]" class="ltx_Math" display="inline" id="Sx4.p2.28.m2.2"><semantics id="Sx4.p2.28.m2.2a"><mrow id="Sx4.p2.28.m2.2.2" xref="Sx4.p2.28.m2.2.2.cmml"><mi id="Sx4.p2.28.m2.2.2.3" xref="Sx4.p2.28.m2.2.2.3.cmml">j</mi><mo id="Sx4.p2.28.m2.2.2.2" xref="Sx4.p2.28.m2.2.2.2.cmml">∈</mo><mrow id="Sx4.p2.28.m2.2.2.1.1" xref="Sx4.p2.28.m2.2.2.1.2.cmml"><mo id="Sx4.p2.28.m2.2.2.1.1.2" stretchy="false" xref="Sx4.p2.28.m2.2.2.1.2.cmml">[</mo><mn id="Sx4.p2.28.m2.1.1" xref="Sx4.p2.28.m2.1.1.cmml">0</mn><mo id="Sx4.p2.28.m2.2.2.1.1.3" xref="Sx4.p2.28.m2.2.2.1.2.cmml">,</mo><mrow id="Sx4.p2.28.m2.2.2.1.1.1" xref="Sx4.p2.28.m2.2.2.1.1.1.cmml"><mi id="Sx4.p2.28.m2.2.2.1.1.1.2" xref="Sx4.p2.28.m2.2.2.1.1.1.2.cmml">N</mi><mo id="Sx4.p2.28.m2.2.2.1.1.1.1" xref="Sx4.p2.28.m2.2.2.1.1.1.1.cmml">+</mo><mn id="Sx4.p2.28.m2.2.2.1.1.1.3" xref="Sx4.p2.28.m2.2.2.1.1.1.3.cmml">1</mn></mrow><mo id="Sx4.p2.28.m2.2.2.1.1.4" stretchy="false" xref="Sx4.p2.28.m2.2.2.1.2.cmml">]</mo></mrow></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.28.m2.2b"><apply id="Sx4.p2.28.m2.2.2.cmml" xref="Sx4.p2.28.m2.2.2"><in id="Sx4.p2.28.m2.2.2.2.cmml" xref="Sx4.p2.28.m2.2.2.2"></in><ci id="Sx4.p2.28.m2.2.2.3.cmml" xref="Sx4.p2.28.m2.2.2.3">𝑗</ci><interval closure="closed" id="Sx4.p2.28.m2.2.2.1.2.cmml" xref="Sx4.p2.28.m2.2.2.1.1"><cn id="Sx4.p2.28.m2.1.1.cmml" type="integer" xref="Sx4.p2.28.m2.1.1">0</cn><apply id="Sx4.p2.28.m2.2.2.1.1.1.cmml" xref="Sx4.p2.28.m2.2.2.1.1.1"><plus id="Sx4.p2.28.m2.2.2.1.1.1.1.cmml" xref="Sx4.p2.28.m2.2.2.1.1.1.1"></plus><ci id="Sx4.p2.28.m2.2.2.1.1.1.2.cmml" xref="Sx4.p2.28.m2.2.2.1.1.1.2">𝑁</ci><cn id="Sx4.p2.28.m2.2.2.1.1.1.3.cmml" type="integer" xref="Sx4.p2.28.m2.2.2.1.1.1.3">1</cn></apply></interval></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.28.m2.2c">j\in[0,N+1]</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.28.m2.2d">italic_j ∈ [ 0 , italic_N + 1 ]</annotation></semantics></math>. Here, for the <math alttext="j" class="ltx_Math" display="inline" id="Sx4.p2.29.m3.1"><semantics id="Sx4.p2.29.m3.1a"><mi id="Sx4.p2.29.m3.1.1" xref="Sx4.p2.29.m3.1.1.cmml">j</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.29.m3.1b"><ci id="Sx4.p2.29.m3.1.1.cmml" xref="Sx4.p2.29.m3.1.1">𝑗</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.29.m3.1c">j</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.29.m3.1d">italic_j</annotation></semantics></math>-th layer, the <math alttext="t_{j}" class="ltx_Math" display="inline" id="Sx4.p2.30.m4.1"><semantics id="Sx4.p2.30.m4.1a"><msub id="Sx4.p2.30.m4.1.1" xref="Sx4.p2.30.m4.1.1.cmml"><mi id="Sx4.p2.30.m4.1.1.2" xref="Sx4.p2.30.m4.1.1.2.cmml">t</mi><mi id="Sx4.p2.30.m4.1.1.3" xref="Sx4.p2.30.m4.1.1.3.cmml">j</mi></msub><annotation-xml encoding="MathML-Content" id="Sx4.p2.30.m4.1b"><apply id="Sx4.p2.30.m4.1.1.cmml" xref="Sx4.p2.30.m4.1.1"><csymbol cd="ambiguous" id="Sx4.p2.30.m4.1.1.1.cmml" xref="Sx4.p2.30.m4.1.1">subscript</csymbol><ci id="Sx4.p2.30.m4.1.1.2.cmml" xref="Sx4.p2.30.m4.1.1.2">𝑡</ci><ci id="Sx4.p2.30.m4.1.1.3.cmml" xref="Sx4.p2.30.m4.1.1.3">𝑗</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.30.m4.1c">t_{j}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.30.m4.1d">italic_t start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT</annotation></semantics></math> is the thickness, <math alttext="k_{j,1}=-k_{j,2}=k_{0}n_{s_{j}}" class="ltx_Math" display="inline" id="Sx4.p2.31.m5.4"><semantics id="Sx4.p2.31.m5.4a"><mrow id="Sx4.p2.31.m5.4.5" xref="Sx4.p2.31.m5.4.5.cmml"><msub id="Sx4.p2.31.m5.4.5.2" xref="Sx4.p2.31.m5.4.5.2.cmml"><mi id="Sx4.p2.31.m5.4.5.2.2" xref="Sx4.p2.31.m5.4.5.2.2.cmml">k</mi><mrow id="Sx4.p2.31.m5.2.2.2.4" xref="Sx4.p2.31.m5.2.2.2.3.cmml"><mi id="Sx4.p2.31.m5.1.1.1.1" xref="Sx4.p2.31.m5.1.1.1.1.cmml">j</mi><mo id="Sx4.p2.31.m5.2.2.2.4.1" xref="Sx4.p2.31.m5.2.2.2.3.cmml">,</mo><mn id="Sx4.p2.31.m5.2.2.2.2" xref="Sx4.p2.31.m5.2.2.2.2.cmml">1</mn></mrow></msub><mo id="Sx4.p2.31.m5.4.5.3" xref="Sx4.p2.31.m5.4.5.3.cmml">=</mo><mrow id="Sx4.p2.31.m5.4.5.4" xref="Sx4.p2.31.m5.4.5.4.cmml"><mo id="Sx4.p2.31.m5.4.5.4a" xref="Sx4.p2.31.m5.4.5.4.cmml">−</mo><msub id="Sx4.p2.31.m5.4.5.4.2" xref="Sx4.p2.31.m5.4.5.4.2.cmml"><mi id="Sx4.p2.31.m5.4.5.4.2.2" xref="Sx4.p2.31.m5.4.5.4.2.2.cmml">k</mi><mrow id="Sx4.p2.31.m5.4.4.2.4" xref="Sx4.p2.31.m5.4.4.2.3.cmml"><mi id="Sx4.p2.31.m5.3.3.1.1" xref="Sx4.p2.31.m5.3.3.1.1.cmml">j</mi><mo id="Sx4.p2.31.m5.4.4.2.4.1" xref="Sx4.p2.31.m5.4.4.2.3.cmml">,</mo><mn id="Sx4.p2.31.m5.4.4.2.2" xref="Sx4.p2.31.m5.4.4.2.2.cmml">2</mn></mrow></msub></mrow><mo id="Sx4.p2.31.m5.4.5.5" xref="Sx4.p2.31.m5.4.5.5.cmml">=</mo><mrow id="Sx4.p2.31.m5.4.5.6" xref="Sx4.p2.31.m5.4.5.6.cmml"><msub id="Sx4.p2.31.m5.4.5.6.2" xref="Sx4.p2.31.m5.4.5.6.2.cmml"><mi id="Sx4.p2.31.m5.4.5.6.2.2" xref="Sx4.p2.31.m5.4.5.6.2.2.cmml">k</mi><mn id="Sx4.p2.31.m5.4.5.6.2.3" xref="Sx4.p2.31.m5.4.5.6.2.3.cmml">0</mn></msub><mo id="Sx4.p2.31.m5.4.5.6.1" xref="Sx4.p2.31.m5.4.5.6.1.cmml">⁢</mo><msub id="Sx4.p2.31.m5.4.5.6.3" xref="Sx4.p2.31.m5.4.5.6.3.cmml"><mi id="Sx4.p2.31.m5.4.5.6.3.2" xref="Sx4.p2.31.m5.4.5.6.3.2.cmml">n</mi><msub id="Sx4.p2.31.m5.4.5.6.3.3" xref="Sx4.p2.31.m5.4.5.6.3.3.cmml"><mi id="Sx4.p2.31.m5.4.5.6.3.3.2" xref="Sx4.p2.31.m5.4.5.6.3.3.2.cmml">s</mi><mi id="Sx4.p2.31.m5.4.5.6.3.3.3" xref="Sx4.p2.31.m5.4.5.6.3.3.3.cmml">j</mi></msub></msub></mrow></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.31.m5.4b"><apply id="Sx4.p2.31.m5.4.5.cmml" xref="Sx4.p2.31.m5.4.5"><and id="Sx4.p2.31.m5.4.5a.cmml" xref="Sx4.p2.31.m5.4.5"></and><apply id="Sx4.p2.31.m5.4.5b.cmml" xref="Sx4.p2.31.m5.4.5"><eq id="Sx4.p2.31.m5.4.5.3.cmml" xref="Sx4.p2.31.m5.4.5.3"></eq><apply id="Sx4.p2.31.m5.4.5.2.cmml" xref="Sx4.p2.31.m5.4.5.2"><csymbol cd="ambiguous" id="Sx4.p2.31.m5.4.5.2.1.cmml" xref="Sx4.p2.31.m5.4.5.2">subscript</csymbol><ci id="Sx4.p2.31.m5.4.5.2.2.cmml" xref="Sx4.p2.31.m5.4.5.2.2">𝑘</ci><list id="Sx4.p2.31.m5.2.2.2.3.cmml" xref="Sx4.p2.31.m5.2.2.2.4"><ci id="Sx4.p2.31.m5.1.1.1.1.cmml" xref="Sx4.p2.31.m5.1.1.1.1">𝑗</ci><cn id="Sx4.p2.31.m5.2.2.2.2.cmml" type="integer" xref="Sx4.p2.31.m5.2.2.2.2">1</cn></list></apply><apply id="Sx4.p2.31.m5.4.5.4.cmml" xref="Sx4.p2.31.m5.4.5.4"><minus id="Sx4.p2.31.m5.4.5.4.1.cmml" xref="Sx4.p2.31.m5.4.5.4"></minus><apply id="Sx4.p2.31.m5.4.5.4.2.cmml" xref="Sx4.p2.31.m5.4.5.4.2"><csymbol cd="ambiguous" id="Sx4.p2.31.m5.4.5.4.2.1.cmml" xref="Sx4.p2.31.m5.4.5.4.2">subscript</csymbol><ci id="Sx4.p2.31.m5.4.5.4.2.2.cmml" xref="Sx4.p2.31.m5.4.5.4.2.2">𝑘</ci><list id="Sx4.p2.31.m5.4.4.2.3.cmml" xref="Sx4.p2.31.m5.4.4.2.4"><ci id="Sx4.p2.31.m5.3.3.1.1.cmml" xref="Sx4.p2.31.m5.3.3.1.1">𝑗</ci><cn id="Sx4.p2.31.m5.4.4.2.2.cmml" type="integer" xref="Sx4.p2.31.m5.4.4.2.2">2</cn></list></apply></apply></apply><apply id="Sx4.p2.31.m5.4.5c.cmml" xref="Sx4.p2.31.m5.4.5"><eq 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cd="ambiguous" id="Sx4.p2.31.m5.4.5.6.3.3.1.cmml" xref="Sx4.p2.31.m5.4.5.6.3.3">subscript</csymbol><ci id="Sx4.p2.31.m5.4.5.6.3.3.2.cmml" xref="Sx4.p2.31.m5.4.5.6.3.3.2">𝑠</ci><ci id="Sx4.p2.31.m5.4.5.6.3.3.3.cmml" xref="Sx4.p2.31.m5.4.5.6.3.3.3">𝑗</ci></apply></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.31.m5.4c">k_{j,1}=-k_{j,2}=k_{0}n_{s_{j}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.31.m5.4d">italic_k start_POSTSUBSCRIPT italic_j , 1 end_POSTSUBSCRIPT = - italic_k start_POSTSUBSCRIPT italic_j , 2 end_POSTSUBSCRIPT = italic_k start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT</annotation></semantics></math>, <math alttext="k_{j,3}=-k_{j,4}=k_{0}n_{p_{j}}" class="ltx_Math" display="inline" id="Sx4.p2.32.m6.4"><semantics id="Sx4.p2.32.m6.4a"><mrow id="Sx4.p2.32.m6.4.5" xref="Sx4.p2.32.m6.4.5.cmml"><msub id="Sx4.p2.32.m6.4.5.2" xref="Sx4.p2.32.m6.4.5.2.cmml"><mi id="Sx4.p2.32.m6.4.5.2.2" xref="Sx4.p2.32.m6.4.5.2.2.cmml">k</mi><mrow id="Sx4.p2.32.m6.2.2.2.4" xref="Sx4.p2.32.m6.2.2.2.3.cmml"><mi id="Sx4.p2.32.m6.1.1.1.1" xref="Sx4.p2.32.m6.1.1.1.1.cmml">j</mi><mo id="Sx4.p2.32.m6.2.2.2.4.1" xref="Sx4.p2.32.m6.2.2.2.3.cmml">,</mo><mn id="Sx4.p2.32.m6.2.2.2.2" xref="Sx4.p2.32.m6.2.2.2.2.cmml">3</mn></mrow></msub><mo id="Sx4.p2.32.m6.4.5.3" xref="Sx4.p2.32.m6.4.5.3.cmml">=</mo><mrow id="Sx4.p2.32.m6.4.5.4" xref="Sx4.p2.32.m6.4.5.4.cmml"><mo id="Sx4.p2.32.m6.4.5.4a" xref="Sx4.p2.32.m6.4.5.4.cmml">−</mo><msub id="Sx4.p2.32.m6.4.5.4.2" xref="Sx4.p2.32.m6.4.5.4.2.cmml"><mi id="Sx4.p2.32.m6.4.5.4.2.2" xref="Sx4.p2.32.m6.4.5.4.2.2.cmml">k</mi><mrow id="Sx4.p2.32.m6.4.4.2.4" xref="Sx4.p2.32.m6.4.4.2.3.cmml"><mi id="Sx4.p2.32.m6.3.3.1.1" xref="Sx4.p2.32.m6.3.3.1.1.cmml">j</mi><mo id="Sx4.p2.32.m6.4.4.2.4.1" xref="Sx4.p2.32.m6.4.4.2.3.cmml">,</mo><mn id="Sx4.p2.32.m6.4.4.2.2" xref="Sx4.p2.32.m6.4.4.2.2.cmml">4</mn></mrow></msub></mrow><mo id="Sx4.p2.32.m6.4.5.5" xref="Sx4.p2.32.m6.4.5.5.cmml">=</mo><mrow id="Sx4.p2.32.m6.4.5.6" xref="Sx4.p2.32.m6.4.5.6.cmml"><msub id="Sx4.p2.32.m6.4.5.6.2" xref="Sx4.p2.32.m6.4.5.6.2.cmml"><mi id="Sx4.p2.32.m6.4.5.6.2.2" xref="Sx4.p2.32.m6.4.5.6.2.2.cmml">k</mi><mn id="Sx4.p2.32.m6.4.5.6.2.3" xref="Sx4.p2.32.m6.4.5.6.2.3.cmml">0</mn></msub><mo id="Sx4.p2.32.m6.4.5.6.1" xref="Sx4.p2.32.m6.4.5.6.1.cmml">⁢</mo><msub id="Sx4.p2.32.m6.4.5.6.3" xref="Sx4.p2.32.m6.4.5.6.3.cmml"><mi id="Sx4.p2.32.m6.4.5.6.3.2" xref="Sx4.p2.32.m6.4.5.6.3.2.cmml">n</mi><msub id="Sx4.p2.32.m6.4.5.6.3.3" xref="Sx4.p2.32.m6.4.5.6.3.3.cmml"><mi id="Sx4.p2.32.m6.4.5.6.3.3.2" xref="Sx4.p2.32.m6.4.5.6.3.3.2.cmml">p</mi><mi id="Sx4.p2.32.m6.4.5.6.3.3.3" xref="Sx4.p2.32.m6.4.5.6.3.3.3.cmml">j</mi></msub></msub></mrow></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.32.m6.4b"><apply id="Sx4.p2.32.m6.4.5.cmml" xref="Sx4.p2.32.m6.4.5"><and id="Sx4.p2.32.m6.4.5a.cmml" xref="Sx4.p2.32.m6.4.5"></and><apply id="Sx4.p2.32.m6.4.5b.cmml" xref="Sx4.p2.32.m6.4.5"><eq id="Sx4.p2.32.m6.4.5.3.cmml" xref="Sx4.p2.32.m6.4.5.3"></eq><apply id="Sx4.p2.32.m6.4.5.2.cmml" xref="Sx4.p2.32.m6.4.5.2"><csymbol cd="ambiguous" id="Sx4.p2.32.m6.4.5.2.1.cmml" xref="Sx4.p2.32.m6.4.5.2">subscript</csymbol><ci id="Sx4.p2.32.m6.4.5.2.2.cmml" xref="Sx4.p2.32.m6.4.5.2.2">𝑘</ci><list id="Sx4.p2.32.m6.2.2.2.3.cmml" xref="Sx4.p2.32.m6.2.2.2.4"><ci id="Sx4.p2.32.m6.1.1.1.1.cmml" xref="Sx4.p2.32.m6.1.1.1.1">𝑗</ci><cn id="Sx4.p2.32.m6.2.2.2.2.cmml" type="integer" xref="Sx4.p2.32.m6.2.2.2.2">3</cn></list></apply><apply id="Sx4.p2.32.m6.4.5.4.cmml" xref="Sx4.p2.32.m6.4.5.4"><minus id="Sx4.p2.32.m6.4.5.4.1.cmml" xref="Sx4.p2.32.m6.4.5.4"></minus><apply id="Sx4.p2.32.m6.4.5.4.2.cmml" xref="Sx4.p2.32.m6.4.5.4.2"><csymbol cd="ambiguous" id="Sx4.p2.32.m6.4.5.4.2.1.cmml" xref="Sx4.p2.32.m6.4.5.4.2">subscript</csymbol><ci id="Sx4.p2.32.m6.4.5.4.2.2.cmml" xref="Sx4.p2.32.m6.4.5.4.2.2">𝑘</ci><list id="Sx4.p2.32.m6.4.4.2.3.cmml" xref="Sx4.p2.32.m6.4.4.2.4"><ci id="Sx4.p2.32.m6.3.3.1.1.cmml" xref="Sx4.p2.32.m6.3.3.1.1">𝑗</ci><cn id="Sx4.p2.32.m6.4.4.2.2.cmml" type="integer" xref="Sx4.p2.32.m6.4.4.2.2">4</cn></list></apply></apply></apply><apply id="Sx4.p2.32.m6.4.5c.cmml" xref="Sx4.p2.32.m6.4.5"><eq id="Sx4.p2.32.m6.4.5.5.cmml" xref="Sx4.p2.32.m6.4.5.5"></eq><share href="https://arxiv.org/html/2406.13190v1#Sx4.p2.32.m6.4.5.4.cmml" id="Sx4.p2.32.m6.4.5d.cmml" xref="Sx4.p2.32.m6.4.5"></share><apply id="Sx4.p2.32.m6.4.5.6.cmml" xref="Sx4.p2.32.m6.4.5.6"><times id="Sx4.p2.32.m6.4.5.6.1.cmml" xref="Sx4.p2.32.m6.4.5.6.1"></times><apply id="Sx4.p2.32.m6.4.5.6.2.cmml" xref="Sx4.p2.32.m6.4.5.6.2"><csymbol cd="ambiguous" id="Sx4.p2.32.m6.4.5.6.2.1.cmml" xref="Sx4.p2.32.m6.4.5.6.2">subscript</csymbol><ci id="Sx4.p2.32.m6.4.5.6.2.2.cmml" xref="Sx4.p2.32.m6.4.5.6.2.2">𝑘</ci><cn id="Sx4.p2.32.m6.4.5.6.2.3.cmml" type="integer" xref="Sx4.p2.32.m6.4.5.6.2.3">0</cn></apply><apply id="Sx4.p2.32.m6.4.5.6.3.cmml" xref="Sx4.p2.32.m6.4.5.6.3"><csymbol cd="ambiguous" id="Sx4.p2.32.m6.4.5.6.3.1.cmml" xref="Sx4.p2.32.m6.4.5.6.3">subscript</csymbol><ci id="Sx4.p2.32.m6.4.5.6.3.2.cmml" xref="Sx4.p2.32.m6.4.5.6.3.2">𝑛</ci><apply id="Sx4.p2.32.m6.4.5.6.3.3.cmml" xref="Sx4.p2.32.m6.4.5.6.3.3"><csymbol cd="ambiguous" id="Sx4.p2.32.m6.4.5.6.3.3.1.cmml" xref="Sx4.p2.32.m6.4.5.6.3.3">subscript</csymbol><ci id="Sx4.p2.32.m6.4.5.6.3.3.2.cmml" xref="Sx4.p2.32.m6.4.5.6.3.3.2">𝑝</ci><ci id="Sx4.p2.32.m6.4.5.6.3.3.3.cmml" xref="Sx4.p2.32.m6.4.5.6.3.3.3">𝑗</ci></apply></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.32.m6.4c">k_{j,3}=-k_{j,4}=k_{0}n_{p_{j}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.32.m6.4d">italic_k start_POSTSUBSCRIPT italic_j , 3 end_POSTSUBSCRIPT = - italic_k start_POSTSUBSCRIPT italic_j , 4 end_POSTSUBSCRIPT = italic_k start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_p start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT</annotation></semantics></math>, <math alttext="n_{s_{j}}" class="ltx_Math" display="inline" id="Sx4.p2.33.m7.1"><semantics id="Sx4.p2.33.m7.1a"><msub id="Sx4.p2.33.m7.1.1" xref="Sx4.p2.33.m7.1.1.cmml"><mi id="Sx4.p2.33.m7.1.1.2" xref="Sx4.p2.33.m7.1.1.2.cmml">n</mi><msub id="Sx4.p2.33.m7.1.1.3" xref="Sx4.p2.33.m7.1.1.3.cmml"><mi id="Sx4.p2.33.m7.1.1.3.2" xref="Sx4.p2.33.m7.1.1.3.2.cmml">s</mi><mi id="Sx4.p2.33.m7.1.1.3.3" xref="Sx4.p2.33.m7.1.1.3.3.cmml">j</mi></msub></msub><annotation-xml encoding="MathML-Content" id="Sx4.p2.33.m7.1b"><apply id="Sx4.p2.33.m7.1.1.cmml" xref="Sx4.p2.33.m7.1.1"><csymbol cd="ambiguous" id="Sx4.p2.33.m7.1.1.1.cmml" xref="Sx4.p2.33.m7.1.1">subscript</csymbol><ci id="Sx4.p2.33.m7.1.1.2.cmml" xref="Sx4.p2.33.m7.1.1.2">𝑛</ci><apply id="Sx4.p2.33.m7.1.1.3.cmml" xref="Sx4.p2.33.m7.1.1.3"><csymbol cd="ambiguous" id="Sx4.p2.33.m7.1.1.3.1.cmml" xref="Sx4.p2.33.m7.1.1.3">subscript</csymbol><ci id="Sx4.p2.33.m7.1.1.3.2.cmml" xref="Sx4.p2.33.m7.1.1.3.2">𝑠</ci><ci id="Sx4.p2.33.m7.1.1.3.3.cmml" xref="Sx4.p2.33.m7.1.1.3.3">𝑗</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.33.m7.1c">n_{s_{j}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.33.m7.1d">italic_n start_POSTSUBSCRIPT italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT</annotation></semantics></math> is the refractive index along the <math alttext="s_{j}" class="ltx_Math" display="inline" id="Sx4.p2.34.m8.1"><semantics id="Sx4.p2.34.m8.1a"><msub id="Sx4.p2.34.m8.1.1" xref="Sx4.p2.34.m8.1.1.cmml"><mi id="Sx4.p2.34.m8.1.1.2" xref="Sx4.p2.34.m8.1.1.2.cmml">s</mi><mi id="Sx4.p2.34.m8.1.1.3" xref="Sx4.p2.34.m8.1.1.3.cmml">j</mi></msub><annotation-xml encoding="MathML-Content" id="Sx4.p2.34.m8.1b"><apply id="Sx4.p2.34.m8.1.1.cmml" xref="Sx4.p2.34.m8.1.1"><csymbol cd="ambiguous" id="Sx4.p2.34.m8.1.1.1.cmml" xref="Sx4.p2.34.m8.1.1">subscript</csymbol><ci id="Sx4.p2.34.m8.1.1.2.cmml" xref="Sx4.p2.34.m8.1.1.2">𝑠</ci><ci id="Sx4.p2.34.m8.1.1.3.cmml" xref="Sx4.p2.34.m8.1.1.3">𝑗</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.34.m8.1c">s_{j}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.34.m8.1d">italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT</annotation></semantics></math> axis, <math alttext="n_{p_{j}}" class="ltx_Math" display="inline" id="Sx4.p2.35.m9.1"><semantics id="Sx4.p2.35.m9.1a"><msub id="Sx4.p2.35.m9.1.1" xref="Sx4.p2.35.m9.1.1.cmml"><mi id="Sx4.p2.35.m9.1.1.2" xref="Sx4.p2.35.m9.1.1.2.cmml">n</mi><msub id="Sx4.p2.35.m9.1.1.3" xref="Sx4.p2.35.m9.1.1.3.cmml"><mi id="Sx4.p2.35.m9.1.1.3.2" xref="Sx4.p2.35.m9.1.1.3.2.cmml">p</mi><mi id="Sx4.p2.35.m9.1.1.3.3" xref="Sx4.p2.35.m9.1.1.3.3.cmml">j</mi></msub></msub><annotation-xml encoding="MathML-Content" id="Sx4.p2.35.m9.1b"><apply id="Sx4.p2.35.m9.1.1.cmml" xref="Sx4.p2.35.m9.1.1"><csymbol cd="ambiguous" id="Sx4.p2.35.m9.1.1.1.cmml" xref="Sx4.p2.35.m9.1.1">subscript</csymbol><ci id="Sx4.p2.35.m9.1.1.2.cmml" xref="Sx4.p2.35.m9.1.1.2">𝑛</ci><apply id="Sx4.p2.35.m9.1.1.3.cmml" xref="Sx4.p2.35.m9.1.1.3"><csymbol cd="ambiguous" id="Sx4.p2.35.m9.1.1.3.1.cmml" xref="Sx4.p2.35.m9.1.1.3">subscript</csymbol><ci id="Sx4.p2.35.m9.1.1.3.2.cmml" xref="Sx4.p2.35.m9.1.1.3.2">𝑝</ci><ci id="Sx4.p2.35.m9.1.1.3.3.cmml" xref="Sx4.p2.35.m9.1.1.3.3">𝑗</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.35.m9.1c">n_{p_{j}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.35.m9.1d">italic_n start_POSTSUBSCRIPT italic_p start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT</annotation></semantics></math> is the refractive index along the <math alttext="p_{j}" class="ltx_Math" display="inline" id="Sx4.p2.36.m10.1"><semantics id="Sx4.p2.36.m10.1a"><msub id="Sx4.p2.36.m10.1.1" xref="Sx4.p2.36.m10.1.1.cmml"><mi id="Sx4.p2.36.m10.1.1.2" xref="Sx4.p2.36.m10.1.1.2.cmml">p</mi><mi id="Sx4.p2.36.m10.1.1.3" xref="Sx4.p2.36.m10.1.1.3.cmml">j</mi></msub><annotation-xml encoding="MathML-Content" id="Sx4.p2.36.m10.1b"><apply id="Sx4.p2.36.m10.1.1.cmml" xref="Sx4.p2.36.m10.1.1"><csymbol cd="ambiguous" id="Sx4.p2.36.m10.1.1.1.cmml" xref="Sx4.p2.36.m10.1.1">subscript</csymbol><ci id="Sx4.p2.36.m10.1.1.2.cmml" xref="Sx4.p2.36.m10.1.1.2">𝑝</ci><ci id="Sx4.p2.36.m10.1.1.3.cmml" xref="Sx4.p2.36.m10.1.1.3">𝑗</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.36.m10.1c">p_{j}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.36.m10.1d">italic_p start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT</annotation></semantics></math> axis, <math alttext="\theta_{j}" class="ltx_Math" display="inline" id="Sx4.p2.37.m11.1"><semantics id="Sx4.p2.37.m11.1a"><msub id="Sx4.p2.37.m11.1.1" xref="Sx4.p2.37.m11.1.1.cmml"><mi id="Sx4.p2.37.m11.1.1.2" xref="Sx4.p2.37.m11.1.1.2.cmml">θ</mi><mi id="Sx4.p2.37.m11.1.1.3" xref="Sx4.p2.37.m11.1.1.3.cmml">j</mi></msub><annotation-xml encoding="MathML-Content" id="Sx4.p2.37.m11.1b"><apply id="Sx4.p2.37.m11.1.1.cmml" xref="Sx4.p2.37.m11.1.1"><csymbol cd="ambiguous" id="Sx4.p2.37.m11.1.1.1.cmml" xref="Sx4.p2.37.m11.1.1">subscript</csymbol><ci id="Sx4.p2.37.m11.1.1.2.cmml" xref="Sx4.p2.37.m11.1.1.2">𝜃</ci><ci id="Sx4.p2.37.m11.1.1.3.cmml" xref="Sx4.p2.37.m11.1.1.3">𝑗</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.37.m11.1c">\theta_{j}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.37.m11.1d">italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT</annotation></semantics></math> is the angle of the <math alttext="s_{j}" class="ltx_Math" display="inline" id="Sx4.p2.38.m12.1"><semantics id="Sx4.p2.38.m12.1a"><msub id="Sx4.p2.38.m12.1.1" xref="Sx4.p2.38.m12.1.1.cmml"><mi id="Sx4.p2.38.m12.1.1.2" xref="Sx4.p2.38.m12.1.1.2.cmml">s</mi><mi id="Sx4.p2.38.m12.1.1.3" xref="Sx4.p2.38.m12.1.1.3.cmml">j</mi></msub><annotation-xml encoding="MathML-Content" id="Sx4.p2.38.m12.1b"><apply id="Sx4.p2.38.m12.1.1.cmml" xref="Sx4.p2.38.m12.1.1"><csymbol cd="ambiguous" id="Sx4.p2.38.m12.1.1.1.cmml" xref="Sx4.p2.38.m12.1.1">subscript</csymbol><ci id="Sx4.p2.38.m12.1.1.2.cmml" xref="Sx4.p2.38.m12.1.1.2">𝑠</ci><ci id="Sx4.p2.38.m12.1.1.3.cmml" xref="Sx4.p2.38.m12.1.1.3">𝑗</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.38.m12.1c">s_{j}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.38.m12.1d">italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT</annotation></semantics></math> axis with respect to the <math alttext="x" class="ltx_Math" display="inline" id="Sx4.p2.39.m13.1"><semantics id="Sx4.p2.39.m13.1a"><mi id="Sx4.p2.39.m13.1.1" xref="Sx4.p2.39.m13.1.1.cmml">x</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.39.m13.1b"><ci id="Sx4.p2.39.m13.1.1.cmml" xref="Sx4.p2.39.m13.1.1">𝑥</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.39.m13.1c">x</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.39.m13.1d">italic_x</annotation></semantics></math>-axis in counterclockwise rotation, and <math alttext="k_{0}" class="ltx_Math" display="inline" id="Sx4.p2.40.m14.1"><semantics id="Sx4.p2.40.m14.1a"><msub id="Sx4.p2.40.m14.1.1" xref="Sx4.p2.40.m14.1.1.cmml"><mi id="Sx4.p2.40.m14.1.1.2" xref="Sx4.p2.40.m14.1.1.2.cmml">k</mi><mn id="Sx4.p2.40.m14.1.1.3" xref="Sx4.p2.40.m14.1.1.3.cmml">0</mn></msub><annotation-xml encoding="MathML-Content" id="Sx4.p2.40.m14.1b"><apply id="Sx4.p2.40.m14.1.1.cmml" xref="Sx4.p2.40.m14.1.1"><csymbol cd="ambiguous" id="Sx4.p2.40.m14.1.1.1.cmml" xref="Sx4.p2.40.m14.1.1">subscript</csymbol><ci id="Sx4.p2.40.m14.1.1.2.cmml" xref="Sx4.p2.40.m14.1.1.2">𝑘</ci><cn id="Sx4.p2.40.m14.1.1.3.cmml" type="integer" xref="Sx4.p2.40.m14.1.1.3">0</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.40.m14.1c">k_{0}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.40.m14.1d">italic_k start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT</annotation></semantics></math> is vacuum wavevector. For layers with isotropic materials, such as the input and output layers, the principal axes are chosen to be <math alttext="s_{1}=s_{N+1}=\hat{\textbf{x}}" class="ltx_Math" display="inline" id="Sx4.p2.41.m15.1"><semantics id="Sx4.p2.41.m15.1a"><mrow id="Sx4.p2.41.m15.1.1" xref="Sx4.p2.41.m15.1.1.cmml"><msub id="Sx4.p2.41.m15.1.1.2" xref="Sx4.p2.41.m15.1.1.2.cmml"><mi id="Sx4.p2.41.m15.1.1.2.2" xref="Sx4.p2.41.m15.1.1.2.2.cmml">s</mi><mn id="Sx4.p2.41.m15.1.1.2.3" xref="Sx4.p2.41.m15.1.1.2.3.cmml">1</mn></msub><mo id="Sx4.p2.41.m15.1.1.3" xref="Sx4.p2.41.m15.1.1.3.cmml">=</mo><msub id="Sx4.p2.41.m15.1.1.4" xref="Sx4.p2.41.m15.1.1.4.cmml"><mi id="Sx4.p2.41.m15.1.1.4.2" xref="Sx4.p2.41.m15.1.1.4.2.cmml">s</mi><mrow id="Sx4.p2.41.m15.1.1.4.3" xref="Sx4.p2.41.m15.1.1.4.3.cmml"><mi id="Sx4.p2.41.m15.1.1.4.3.2" xref="Sx4.p2.41.m15.1.1.4.3.2.cmml">N</mi><mo id="Sx4.p2.41.m15.1.1.4.3.1" xref="Sx4.p2.41.m15.1.1.4.3.1.cmml">+</mo><mn id="Sx4.p2.41.m15.1.1.4.3.3" xref="Sx4.p2.41.m15.1.1.4.3.3.cmml">1</mn></mrow></msub><mo id="Sx4.p2.41.m15.1.1.5" xref="Sx4.p2.41.m15.1.1.5.cmml">=</mo><mover accent="true" id="Sx4.p2.41.m15.1.1.6" xref="Sx4.p2.41.m15.1.1.6.cmml"><mtext class="ltx_mathvariant_bold" id="Sx4.p2.41.m15.1.1.6.2" xref="Sx4.p2.41.m15.1.1.6.2a.cmml">x</mtext><mo id="Sx4.p2.41.m15.1.1.6.1" xref="Sx4.p2.41.m15.1.1.6.1.cmml">^</mo></mover></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.41.m15.1b"><apply id="Sx4.p2.41.m15.1.1.cmml" xref="Sx4.p2.41.m15.1.1"><and id="Sx4.p2.41.m15.1.1a.cmml" xref="Sx4.p2.41.m15.1.1"></and><apply id="Sx4.p2.41.m15.1.1b.cmml" xref="Sx4.p2.41.m15.1.1"><eq id="Sx4.p2.41.m15.1.1.3.cmml" xref="Sx4.p2.41.m15.1.1.3"></eq><apply id="Sx4.p2.41.m15.1.1.2.cmml" xref="Sx4.p2.41.m15.1.1.2"><csymbol cd="ambiguous" id="Sx4.p2.41.m15.1.1.2.1.cmml" xref="Sx4.p2.41.m15.1.1.2">subscript</csymbol><ci id="Sx4.p2.41.m15.1.1.2.2.cmml" xref="Sx4.p2.41.m15.1.1.2.2">𝑠</ci><cn id="Sx4.p2.41.m15.1.1.2.3.cmml" type="integer" xref="Sx4.p2.41.m15.1.1.2.3">1</cn></apply><apply id="Sx4.p2.41.m15.1.1.4.cmml" xref="Sx4.p2.41.m15.1.1.4"><csymbol cd="ambiguous" id="Sx4.p2.41.m15.1.1.4.1.cmml" xref="Sx4.p2.41.m15.1.1.4">subscript</csymbol><ci id="Sx4.p2.41.m15.1.1.4.2.cmml" xref="Sx4.p2.41.m15.1.1.4.2">𝑠</ci><apply id="Sx4.p2.41.m15.1.1.4.3.cmml" xref="Sx4.p2.41.m15.1.1.4.3"><plus id="Sx4.p2.41.m15.1.1.4.3.1.cmml" xref="Sx4.p2.41.m15.1.1.4.3.1"></plus><ci id="Sx4.p2.41.m15.1.1.4.3.2.cmml" xref="Sx4.p2.41.m15.1.1.4.3.2">𝑁</ci><cn id="Sx4.p2.41.m15.1.1.4.3.3.cmml" type="integer" xref="Sx4.p2.41.m15.1.1.4.3.3">1</cn></apply></apply></apply><apply id="Sx4.p2.41.m15.1.1c.cmml" xref="Sx4.p2.41.m15.1.1"><eq id="Sx4.p2.41.m15.1.1.5.cmml" xref="Sx4.p2.41.m15.1.1.5"></eq><share href="https://arxiv.org/html/2406.13190v1#Sx4.p2.41.m15.1.1.4.cmml" id="Sx4.p2.41.m15.1.1d.cmml" xref="Sx4.p2.41.m15.1.1"></share><apply id="Sx4.p2.41.m15.1.1.6.cmml" xref="Sx4.p2.41.m15.1.1.6"><ci id="Sx4.p2.41.m15.1.1.6.1.cmml" xref="Sx4.p2.41.m15.1.1.6.1">^</ci><ci id="Sx4.p2.41.m15.1.1.6.2a.cmml" xref="Sx4.p2.41.m15.1.1.6.2"><mtext class="ltx_mathvariant_bold" id="Sx4.p2.41.m15.1.1.6.2.cmml" xref="Sx4.p2.41.m15.1.1.6.2">x</mtext></ci></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.41.m15.1c">s_{1}=s_{N+1}=\hat{\textbf{x}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.41.m15.1d">italic_s start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = italic_s start_POSTSUBSCRIPT italic_N + 1 end_POSTSUBSCRIPT = over^ start_ARG x end_ARG</annotation></semantics></math> and <math alttext="p_{1}=p_{N+1}=\hat{\textbf{y}}" class="ltx_Math" display="inline" id="Sx4.p2.42.m16.1"><semantics id="Sx4.p2.42.m16.1a"><mrow id="Sx4.p2.42.m16.1.1" xref="Sx4.p2.42.m16.1.1.cmml"><msub id="Sx4.p2.42.m16.1.1.2" xref="Sx4.p2.42.m16.1.1.2.cmml"><mi id="Sx4.p2.42.m16.1.1.2.2" xref="Sx4.p2.42.m16.1.1.2.2.cmml">p</mi><mn id="Sx4.p2.42.m16.1.1.2.3" xref="Sx4.p2.42.m16.1.1.2.3.cmml">1</mn></msub><mo id="Sx4.p2.42.m16.1.1.3" xref="Sx4.p2.42.m16.1.1.3.cmml">=</mo><msub id="Sx4.p2.42.m16.1.1.4" xref="Sx4.p2.42.m16.1.1.4.cmml"><mi id="Sx4.p2.42.m16.1.1.4.2" xref="Sx4.p2.42.m16.1.1.4.2.cmml">p</mi><mrow id="Sx4.p2.42.m16.1.1.4.3" xref="Sx4.p2.42.m16.1.1.4.3.cmml"><mi id="Sx4.p2.42.m16.1.1.4.3.2" xref="Sx4.p2.42.m16.1.1.4.3.2.cmml">N</mi><mo id="Sx4.p2.42.m16.1.1.4.3.1" xref="Sx4.p2.42.m16.1.1.4.3.1.cmml">+</mo><mn id="Sx4.p2.42.m16.1.1.4.3.3" xref="Sx4.p2.42.m16.1.1.4.3.3.cmml">1</mn></mrow></msub><mo id="Sx4.p2.42.m16.1.1.5" xref="Sx4.p2.42.m16.1.1.5.cmml">=</mo><mover accent="true" id="Sx4.p2.42.m16.1.1.6" xref="Sx4.p2.42.m16.1.1.6.cmml"><mtext class="ltx_mathvariant_bold" id="Sx4.p2.42.m16.1.1.6.2" xref="Sx4.p2.42.m16.1.1.6.2a.cmml">y</mtext><mo id="Sx4.p2.42.m16.1.1.6.1" xref="Sx4.p2.42.m16.1.1.6.1.cmml">^</mo></mover></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.42.m16.1b"><apply id="Sx4.p2.42.m16.1.1.cmml" xref="Sx4.p2.42.m16.1.1"><and id="Sx4.p2.42.m16.1.1a.cmml" xref="Sx4.p2.42.m16.1.1"></and><apply id="Sx4.p2.42.m16.1.1b.cmml" xref="Sx4.p2.42.m16.1.1"><eq id="Sx4.p2.42.m16.1.1.3.cmml" xref="Sx4.p2.42.m16.1.1.3"></eq><apply id="Sx4.p2.42.m16.1.1.2.cmml" xref="Sx4.p2.42.m16.1.1.2"><csymbol cd="ambiguous" id="Sx4.p2.42.m16.1.1.2.1.cmml" xref="Sx4.p2.42.m16.1.1.2">subscript</csymbol><ci id="Sx4.p2.42.m16.1.1.2.2.cmml" xref="Sx4.p2.42.m16.1.1.2.2">𝑝</ci><cn id="Sx4.p2.42.m16.1.1.2.3.cmml" type="integer" xref="Sx4.p2.42.m16.1.1.2.3">1</cn></apply><apply id="Sx4.p2.42.m16.1.1.4.cmml" xref="Sx4.p2.42.m16.1.1.4"><csymbol cd="ambiguous" id="Sx4.p2.42.m16.1.1.4.1.cmml" xref="Sx4.p2.42.m16.1.1.4">subscript</csymbol><ci id="Sx4.p2.42.m16.1.1.4.2.cmml" xref="Sx4.p2.42.m16.1.1.4.2">𝑝</ci><apply id="Sx4.p2.42.m16.1.1.4.3.cmml" xref="Sx4.p2.42.m16.1.1.4.3"><plus id="Sx4.p2.42.m16.1.1.4.3.1.cmml" xref="Sx4.p2.42.m16.1.1.4.3.1"></plus><ci id="Sx4.p2.42.m16.1.1.4.3.2.cmml" xref="Sx4.p2.42.m16.1.1.4.3.2">𝑁</ci><cn id="Sx4.p2.42.m16.1.1.4.3.3.cmml" type="integer" xref="Sx4.p2.42.m16.1.1.4.3.3">1</cn></apply></apply></apply><apply id="Sx4.p2.42.m16.1.1c.cmml" xref="Sx4.p2.42.m16.1.1"><eq id="Sx4.p2.42.m16.1.1.5.cmml" xref="Sx4.p2.42.m16.1.1.5"></eq><share href="https://arxiv.org/html/2406.13190v1#Sx4.p2.42.m16.1.1.4.cmml" id="Sx4.p2.42.m16.1.1d.cmml" xref="Sx4.p2.42.m16.1.1"></share><apply id="Sx4.p2.42.m16.1.1.6.cmml" xref="Sx4.p2.42.m16.1.1.6"><ci id="Sx4.p2.42.m16.1.1.6.1.cmml" xref="Sx4.p2.42.m16.1.1.6.1">^</ci><ci id="Sx4.p2.42.m16.1.1.6.2a.cmml" xref="Sx4.p2.42.m16.1.1.6.2"><mtext class="ltx_mathvariant_bold" id="Sx4.p2.42.m16.1.1.6.2.cmml" xref="Sx4.p2.42.m16.1.1.6.2">y</mtext></ci></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.42.m16.1c">p_{1}=p_{N+1}=\hat{\textbf{y}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.42.m16.1d">italic_p start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = italic_p start_POSTSUBSCRIPT italic_N + 1 end_POSTSUBSCRIPT = over^ start_ARG y end_ARG</annotation></semantics></math>. For layers with anisotropic materials, the dielectric function tensor <math alttext="\boldsymbol{\varepsilon}_{j}" class="ltx_Math" display="inline" id="Sx4.p2.43.m17.1"><semantics id="Sx4.p2.43.m17.1a"><msub id="Sx4.p2.43.m17.1.1" xref="Sx4.p2.43.m17.1.1.cmml"><mi id="Sx4.p2.43.m17.1.1.2" xref="Sx4.p2.43.m17.1.1.2.cmml">𝜺</mi><mi id="Sx4.p2.43.m17.1.1.3" xref="Sx4.p2.43.m17.1.1.3.cmml">j</mi></msub><annotation-xml encoding="MathML-Content" id="Sx4.p2.43.m17.1b"><apply id="Sx4.p2.43.m17.1.1.cmml" xref="Sx4.p2.43.m17.1.1"><csymbol cd="ambiguous" id="Sx4.p2.43.m17.1.1.1.cmml" xref="Sx4.p2.43.m17.1.1">subscript</csymbol><ci id="Sx4.p2.43.m17.1.1.2.cmml" xref="Sx4.p2.43.m17.1.1.2">𝜺</ci><ci id="Sx4.p2.43.m17.1.1.3.cmml" xref="Sx4.p2.43.m17.1.1.3">𝑗</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.43.m17.1c">\boldsymbol{\varepsilon}_{j}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.43.m17.1d">bold_italic_ε start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT</annotation></semantics></math> in <math alttext="xy" class="ltx_Math" display="inline" id="Sx4.p2.44.m18.1"><semantics id="Sx4.p2.44.m18.1a"><mrow id="Sx4.p2.44.m18.1.1" xref="Sx4.p2.44.m18.1.1.cmml"><mi id="Sx4.p2.44.m18.1.1.2" xref="Sx4.p2.44.m18.1.1.2.cmml">x</mi><mo id="Sx4.p2.44.m18.1.1.1" xref="Sx4.p2.44.m18.1.1.1.cmml">⁢</mo><mi id="Sx4.p2.44.m18.1.1.3" xref="Sx4.p2.44.m18.1.1.3.cmml">y</mi></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.44.m18.1b"><apply id="Sx4.p2.44.m18.1.1.cmml" xref="Sx4.p2.44.m18.1.1"><times id="Sx4.p2.44.m18.1.1.1.cmml" xref="Sx4.p2.44.m18.1.1.1"></times><ci id="Sx4.p2.44.m18.1.1.2.cmml" xref="Sx4.p2.44.m18.1.1.2">𝑥</ci><ci id="Sx4.p2.44.m18.1.1.3.cmml" xref="Sx4.p2.44.m18.1.1.3">𝑦</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.44.m18.1c">xy</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.44.m18.1d">italic_x italic_y</annotation></semantics></math> coordinate systems can be written as</p> <table class="ltx_equationgroup ltx_eqn_align ltx_eqn_table" id="Sx8.EGx1"> <tbody id="Sx4.E7"><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_td ltx_align_right ltx_eqn_cell"><math alttext="\displaystyle\boldsymbol{\varepsilon}_{j}=R_{j}\left(\begin{array}[]{cc}% \varepsilon_{s_{j}}&0\\ 0&\varepsilon_{p_{j}}\end{array}\right){R_{j}}^{-1}," class="ltx_Math" display="inline" id="Sx4.E7.m1.2"><semantics id="Sx4.E7.m1.2a"><mrow id="Sx4.E7.m1.2.2.1" xref="Sx4.E7.m1.2.2.1.1.cmml"><mrow id="Sx4.E7.m1.2.2.1.1" xref="Sx4.E7.m1.2.2.1.1.cmml"><msub id="Sx4.E7.m1.2.2.1.1.2" xref="Sx4.E7.m1.2.2.1.1.2.cmml"><mi id="Sx4.E7.m1.2.2.1.1.2.2" xref="Sx4.E7.m1.2.2.1.1.2.2.cmml">𝜺</mi><mi id="Sx4.E7.m1.2.2.1.1.2.3" xref="Sx4.E7.m1.2.2.1.1.2.3.cmml">j</mi></msub><mo id="Sx4.E7.m1.2.2.1.1.1" xref="Sx4.E7.m1.2.2.1.1.1.cmml">=</mo><mrow id="Sx4.E7.m1.2.2.1.1.3" xref="Sx4.E7.m1.2.2.1.1.3.cmml"><msub id="Sx4.E7.m1.2.2.1.1.3.2" xref="Sx4.E7.m1.2.2.1.1.3.2.cmml"><mi id="Sx4.E7.m1.2.2.1.1.3.2.2" xref="Sx4.E7.m1.2.2.1.1.3.2.2.cmml">R</mi><mi id="Sx4.E7.m1.2.2.1.1.3.2.3" xref="Sx4.E7.m1.2.2.1.1.3.2.3.cmml">j</mi></msub><mo id="Sx4.E7.m1.2.2.1.1.3.1" xref="Sx4.E7.m1.2.2.1.1.3.1.cmml">⁢</mo><mrow id="Sx4.E7.m1.2.2.1.1.3.3.2" xref="Sx4.E7.m1.1.1.cmml"><mo id="Sx4.E7.m1.2.2.1.1.3.3.2.1" xref="Sx4.E7.m1.1.1.cmml">(</mo><mtable columnspacing="5pt" id="Sx4.E7.m1.1.1" rowspacing="0pt" xref="Sx4.E7.m1.1.1.cmml"><mtr id="Sx4.E7.m1.1.1a" xref="Sx4.E7.m1.1.1.cmml"><mtd id="Sx4.E7.m1.1.1b" xref="Sx4.E7.m1.1.1.cmml"><msub id="Sx4.E5.1.1" xref="Sx4.E5.1.1.cmml"><mi id="Sx4.E5.1.1.2" xref="Sx4.E5.1.1.2.cmml">ε</mi><msub id="Sx4.E5.1.1.3" xref="Sx4.E5.1.1.3.cmml"><mi id="Sx4.E5.1.1.3.2" xref="Sx4.E5.1.1.3.2.cmml">s</mi><mi id="Sx4.E5.1.1.3.3" xref="Sx4.E5.1.1.3.3.cmml">j</mi></msub></msub></mtd><mtd id="Sx4.E7.m1.1.1c" xref="Sx4.E7.m1.1.1.cmml"><mn id="Sx4.E5.2.1" xref="Sx4.E5.2.1.cmml">0</mn></mtd></mtr><mtr id="Sx4.E7.m1.1.1d" xref="Sx4.E7.m1.1.1.cmml"><mtd id="Sx4.E7.m1.1.1e" xref="Sx4.E7.m1.1.1.cmml"><mn id="Sx4.E6.1.1" xref="Sx4.E6.1.1.cmml">0</mn></mtd><mtd id="Sx4.E7.m1.1.1f" xref="Sx4.E7.m1.1.1.cmml"><msub id="Sx4.E6.2.1" xref="Sx4.E6.2.1.cmml"><mi id="Sx4.E6.2.1.2" xref="Sx4.E6.2.1.2.cmml">ε</mi><msub id="Sx4.E6.2.1.3" xref="Sx4.E6.2.1.3.cmml"><mi id="Sx4.E6.2.1.3.2" xref="Sx4.E6.2.1.3.2.cmml">p</mi><mi id="Sx4.E6.2.1.3.3" xref="Sx4.E6.2.1.3.3.cmml">j</mi></msub></msub></mtd></mtr></mtable><mo id="Sx4.E7.m1.2.2.1.1.3.3.2.2" xref="Sx4.E7.m1.1.1.cmml">)</mo></mrow><mo id="Sx4.E7.m1.2.2.1.1.3.1a" xref="Sx4.E7.m1.2.2.1.1.3.1.cmml">⁢</mo><mmultiscripts id="Sx4.E7.m1.2.2.1.1.3.4" xref="Sx4.E7.m1.2.2.1.1.3.4.cmml"><mi id="Sx4.E7.m1.2.2.1.1.3.4.2.2" xref="Sx4.E7.m1.2.2.1.1.3.4.2.2.cmml">R</mi><mi id="Sx4.E7.m1.2.2.1.1.3.4.2.3" xref="Sx4.E7.m1.2.2.1.1.3.4.2.3.cmml">j</mi><mrow id="Sx4.E7.m1.2.2.1.1.3.4a" xref="Sx4.E7.m1.2.2.1.1.3.4.cmml"></mrow><mrow id="Sx4.E7.m1.2.2.1.1.3.4b" xref="Sx4.E7.m1.2.2.1.1.3.4.cmml"></mrow><mrow id="Sx4.E7.m1.2.2.1.1.3.4.3" xref="Sx4.E7.m1.2.2.1.1.3.4.3.cmml"><mo id="Sx4.E7.m1.2.2.1.1.3.4.3a" xref="Sx4.E7.m1.2.2.1.1.3.4.3.cmml">−</mo><mn id="Sx4.E7.m1.2.2.1.1.3.4.3.2" xref="Sx4.E7.m1.2.2.1.1.3.4.3.2.cmml">1</mn></mrow></mmultiscripts></mrow></mrow><mo id="Sx4.E7.m1.2.2.1.2" xref="Sx4.E7.m1.2.2.1.1.cmml">,</mo></mrow><annotation-xml encoding="MathML-Content" id="Sx4.E7.m1.2b"><apply id="Sx4.E7.m1.2.2.1.1.cmml" xref="Sx4.E7.m1.2.2.1"><eq id="Sx4.E7.m1.2.2.1.1.1.cmml" xref="Sx4.E7.m1.2.2.1.1.1"></eq><apply id="Sx4.E7.m1.2.2.1.1.2.cmml" xref="Sx4.E7.m1.2.2.1.1.2"><csymbol cd="ambiguous" id="Sx4.E7.m1.2.2.1.1.2.1.cmml" xref="Sx4.E7.m1.2.2.1.1.2">subscript</csymbol><ci id="Sx4.E7.m1.2.2.1.1.2.2.cmml" xref="Sx4.E7.m1.2.2.1.1.2.2">𝜺</ci><ci id="Sx4.E7.m1.2.2.1.1.2.3.cmml" xref="Sx4.E7.m1.2.2.1.1.2.3">𝑗</ci></apply><apply id="Sx4.E7.m1.2.2.1.1.3.cmml" xref="Sx4.E7.m1.2.2.1.1.3"><times id="Sx4.E7.m1.2.2.1.1.3.1.cmml" xref="Sx4.E7.m1.2.2.1.1.3.1"></times><apply id="Sx4.E7.m1.2.2.1.1.3.2.cmml" xref="Sx4.E7.m1.2.2.1.1.3.2"><csymbol cd="ambiguous" id="Sx4.E7.m1.2.2.1.1.3.2.1.cmml" xref="Sx4.E7.m1.2.2.1.1.3.2">subscript</csymbol><ci id="Sx4.E7.m1.2.2.1.1.3.2.2.cmml" xref="Sx4.E7.m1.2.2.1.1.3.2.2">𝑅</ci><ci id="Sx4.E7.m1.2.2.1.1.3.2.3.cmml" xref="Sx4.E7.m1.2.2.1.1.3.2.3">𝑗</ci></apply><matrix id="Sx4.E7.m1.1.1.cmml" xref="Sx4.E7.m1.2.2.1.1.3.3.2"><matrixrow id="Sx4.E7.m1.1.1a.cmml" xref="Sx4.E7.m1.2.2.1.1.3.3.2"><apply id="Sx4.E5.1.1.cmml" xref="Sx4.E5.1.1"><csymbol cd="ambiguous" id="Sx4.E5.1.1.1.cmml" xref="Sx4.E5.1.1">subscript</csymbol><ci id="Sx4.E5.1.1.2.cmml" xref="Sx4.E5.1.1.2">𝜀</ci><apply id="Sx4.E5.1.1.3.cmml" xref="Sx4.E5.1.1.3"><csymbol cd="ambiguous" id="Sx4.E5.1.1.3.1.cmml" xref="Sx4.E5.1.1.3">subscript</csymbol><ci id="Sx4.E5.1.1.3.2.cmml" xref="Sx4.E5.1.1.3.2">𝑠</ci><ci id="Sx4.E5.1.1.3.3.cmml" xref="Sx4.E5.1.1.3.3">𝑗</ci></apply></apply><cn id="Sx4.E5.2.1.cmml" type="integer" xref="Sx4.E5.2.1">0</cn></matrixrow><matrixrow id="Sx4.E7.m1.1.1b.cmml" xref="Sx4.E7.m1.2.2.1.1.3.3.2"><cn id="Sx4.E6.1.1.cmml" type="integer" xref="Sx4.E6.1.1">0</cn><apply id="Sx4.E6.2.1.cmml" xref="Sx4.E6.2.1"><csymbol cd="ambiguous" id="Sx4.E6.2.1.1.cmml" xref="Sx4.E6.2.1">subscript</csymbol><ci id="Sx4.E6.2.1.2.cmml" xref="Sx4.E6.2.1.2">𝜀</ci><apply id="Sx4.E6.2.1.3.cmml" xref="Sx4.E6.2.1.3"><csymbol cd="ambiguous" id="Sx4.E6.2.1.3.1.cmml" xref="Sx4.E6.2.1.3">subscript</csymbol><ci id="Sx4.E6.2.1.3.2.cmml" xref="Sx4.E6.2.1.3.2">𝑝</ci><ci id="Sx4.E6.2.1.3.3.cmml" xref="Sx4.E6.2.1.3.3">𝑗</ci></apply></apply></matrixrow></matrix><apply id="Sx4.E7.m1.2.2.1.1.3.4.cmml" xref="Sx4.E7.m1.2.2.1.1.3.4"><csymbol cd="ambiguous" id="Sx4.E7.m1.2.2.1.1.3.4.1.cmml" xref="Sx4.E7.m1.2.2.1.1.3.4">superscript</csymbol><apply id="Sx4.E7.m1.2.2.1.1.3.4.2.cmml" xref="Sx4.E7.m1.2.2.1.1.3.4"><csymbol cd="ambiguous" id="Sx4.E7.m1.2.2.1.1.3.4.2.1.cmml" xref="Sx4.E7.m1.2.2.1.1.3.4">subscript</csymbol><ci id="Sx4.E7.m1.2.2.1.1.3.4.2.2.cmml" xref="Sx4.E7.m1.2.2.1.1.3.4.2.2">𝑅</ci><ci id="Sx4.E7.m1.2.2.1.1.3.4.2.3.cmml" xref="Sx4.E7.m1.2.2.1.1.3.4.2.3">𝑗</ci></apply><apply id="Sx4.E7.m1.2.2.1.1.3.4.3.cmml" xref="Sx4.E7.m1.2.2.1.1.3.4.3"><minus id="Sx4.E7.m1.2.2.1.1.3.4.3.1.cmml" xref="Sx4.E7.m1.2.2.1.1.3.4.3"></minus><cn id="Sx4.E7.m1.2.2.1.1.3.4.3.2.cmml" type="integer" xref="Sx4.E7.m1.2.2.1.1.3.4.3.2">1</cn></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.E7.m1.2c">\displaystyle\boldsymbol{\varepsilon}_{j}=R_{j}\left(\begin{array}[]{cc}% \varepsilon_{s_{j}}&0\\ 0&\varepsilon_{p_{j}}\end{array}\right){R_{j}}^{-1},</annotation><annotation encoding="application/x-llamapun" id="Sx4.E7.m1.2d">bold_italic_ε start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT = italic_R start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT ( start_ARRAY start_ROW start_CELL italic_ε start_POSTSUBSCRIPT italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT end_CELL start_CELL 0 end_CELL end_ROW start_ROW start_CELL 0 end_CELL start_CELL italic_ε start_POSTSUBSCRIPT italic_p start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT end_CELL end_ROW end_ARRAY ) italic_R start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(7)</span></td> </tr></tbody> <tbody id="Sx4.E10"><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_td ltx_align_right ltx_eqn_cell"><math alttext="\displaystyle{R_{j}}=\left(\begin{array}[]{cc}\textrm{cos}\theta_{j}&-\textrm{% sin}\theta_{j}\\ \textrm{sin}\theta_{j}&\textrm{cos}\theta_{j}\end{array}\right)," class="ltx_Math" display="inline" id="Sx4.E10.m1.2"><semantics id="Sx4.E10.m1.2a"><mrow id="Sx4.E10.m1.2.2.1" xref="Sx4.E10.m1.2.2.1.1.cmml"><mrow id="Sx4.E10.m1.2.2.1.1" xref="Sx4.E10.m1.2.2.1.1.cmml"><msub id="Sx4.E10.m1.2.2.1.1.2" xref="Sx4.E10.m1.2.2.1.1.2.cmml"><mi id="Sx4.E10.m1.2.2.1.1.2.2" xref="Sx4.E10.m1.2.2.1.1.2.2.cmml">R</mi><mi id="Sx4.E10.m1.2.2.1.1.2.3" xref="Sx4.E10.m1.2.2.1.1.2.3.cmml">j</mi></msub><mo id="Sx4.E10.m1.2.2.1.1.1" xref="Sx4.E10.m1.2.2.1.1.1.cmml">=</mo><mrow id="Sx4.E10.m1.2.2.1.1.3.2" xref="Sx4.E10.m1.1.1.cmml"><mo id="Sx4.E10.m1.2.2.1.1.3.2.1" xref="Sx4.E10.m1.1.1.cmml">(</mo><mtable columnspacing="5pt" id="Sx4.E10.m1.1.1" rowspacing="0pt" xref="Sx4.E10.m1.1.1.cmml"><mtr id="Sx4.E10.m1.1.1a" xref="Sx4.E10.m1.1.1.cmml"><mtd id="Sx4.E10.m1.1.1b" xref="Sx4.E10.m1.1.1.cmml"><mrow id="Sx4.E8.1.1" xref="Sx4.E8.1.1.cmml"><mtext id="Sx4.E8.1.1.2" xref="Sx4.E8.1.1.2a.cmml">cos</mtext><mo id="Sx4.E8.1.1.1" xref="Sx4.E8.1.1.1.cmml">⁢</mo><msub id="Sx4.E8.1.1.3" xref="Sx4.E8.1.1.3.cmml"><mi id="Sx4.E8.1.1.3.2" xref="Sx4.E8.1.1.3.2.cmml">θ</mi><mi id="Sx4.E8.1.1.3.3" xref="Sx4.E8.1.1.3.3.cmml">j</mi></msub></mrow></mtd><mtd id="Sx4.E10.m1.1.1c" xref="Sx4.E10.m1.1.1.cmml"><mrow id="Sx4.E8.2.1" xref="Sx4.E8.2.1.cmml"><mo id="Sx4.E8.2.1a" xref="Sx4.E8.2.1.cmml">−</mo><mrow id="Sx4.E8.2.1.2" xref="Sx4.E8.2.1.2.cmml"><mtext id="Sx4.E8.2.1.2.2" xref="Sx4.E8.2.1.2.2a.cmml">sin</mtext><mo id="Sx4.E8.2.1.2.1" xref="Sx4.E8.2.1.2.1.cmml">⁢</mo><msub id="Sx4.E8.2.1.2.3" xref="Sx4.E8.2.1.2.3.cmml"><mi id="Sx4.E8.2.1.2.3.2" xref="Sx4.E8.2.1.2.3.2.cmml">θ</mi><mi id="Sx4.E8.2.1.2.3.3" xref="Sx4.E8.2.1.2.3.3.cmml">j</mi></msub></mrow></mrow></mtd></mtr><mtr id="Sx4.E10.m1.1.1d" xref="Sx4.E10.m1.1.1.cmml"><mtd id="Sx4.E10.m1.1.1e" xref="Sx4.E10.m1.1.1.cmml"><mrow id="Sx4.E9.1.1" xref="Sx4.E9.1.1.cmml"><mtext id="Sx4.E9.1.1.2" xref="Sx4.E9.1.1.2a.cmml">sin</mtext><mo id="Sx4.E9.1.1.1" xref="Sx4.E9.1.1.1.cmml">⁢</mo><msub id="Sx4.E9.1.1.3" xref="Sx4.E9.1.1.3.cmml"><mi id="Sx4.E9.1.1.3.2" xref="Sx4.E9.1.1.3.2.cmml">θ</mi><mi id="Sx4.E9.1.1.3.3" xref="Sx4.E9.1.1.3.3.cmml">j</mi></msub></mrow></mtd><mtd id="Sx4.E10.m1.1.1f" xref="Sx4.E10.m1.1.1.cmml"><mrow id="Sx4.E9.2.1" xref="Sx4.E9.2.1.cmml"><mtext id="Sx4.E9.2.1.2" xref="Sx4.E9.2.1.2a.cmml">cos</mtext><mo id="Sx4.E9.2.1.1" xref="Sx4.E9.2.1.1.cmml">⁢</mo><msub id="Sx4.E9.2.1.3" xref="Sx4.E9.2.1.3.cmml"><mi id="Sx4.E9.2.1.3.2" xref="Sx4.E9.2.1.3.2.cmml">θ</mi><mi id="Sx4.E9.2.1.3.3" xref="Sx4.E9.2.1.3.3.cmml">j</mi></msub></mrow></mtd></mtr></mtable><mo id="Sx4.E10.m1.2.2.1.1.3.2.2" xref="Sx4.E10.m1.1.1.cmml">)</mo></mrow></mrow><mo id="Sx4.E10.m1.2.2.1.2" xref="Sx4.E10.m1.2.2.1.1.cmml">,</mo></mrow><annotation-xml encoding="MathML-Content" id="Sx4.E10.m1.2b"><apply id="Sx4.E10.m1.2.2.1.1.cmml" xref="Sx4.E10.m1.2.2.1"><eq id="Sx4.E10.m1.2.2.1.1.1.cmml" xref="Sx4.E10.m1.2.2.1.1.1"></eq><apply 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id="Sx4.E10.m1.2d">italic_R start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT = ( start_ARRAY start_ROW start_CELL cos italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL - sin italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL sin italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL start_CELL cos italic_θ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_CELL end_ROW end_ARRAY ) ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(10)</span></td> </tr></tbody> </table> <p class="ltx_p" id="Sx4.p2.47">with <math alttext="n_{s_{j}}=\sqrt{\varepsilon_{s_{j}}}" class="ltx_Math" display="inline" id="Sx4.p2.45.m1.1"><semantics id="Sx4.p2.45.m1.1a"><mrow id="Sx4.p2.45.m1.1.1" xref="Sx4.p2.45.m1.1.1.cmml"><msub id="Sx4.p2.45.m1.1.1.2" xref="Sx4.p2.45.m1.1.1.2.cmml"><mi id="Sx4.p2.45.m1.1.1.2.2" xref="Sx4.p2.45.m1.1.1.2.2.cmml">n</mi><msub id="Sx4.p2.45.m1.1.1.2.3" xref="Sx4.p2.45.m1.1.1.2.3.cmml"><mi id="Sx4.p2.45.m1.1.1.2.3.2" xref="Sx4.p2.45.m1.1.1.2.3.2.cmml">s</mi><mi id="Sx4.p2.45.m1.1.1.2.3.3" xref="Sx4.p2.45.m1.1.1.2.3.3.cmml">j</mi></msub></msub><mo id="Sx4.p2.45.m1.1.1.1" xref="Sx4.p2.45.m1.1.1.1.cmml">=</mo><msqrt id="Sx4.p2.45.m1.1.1.3" xref="Sx4.p2.45.m1.1.1.3.cmml"><msub id="Sx4.p2.45.m1.1.1.3.2" xref="Sx4.p2.45.m1.1.1.3.2.cmml"><mi id="Sx4.p2.45.m1.1.1.3.2.2" xref="Sx4.p2.45.m1.1.1.3.2.2.cmml">ε</mi><msub id="Sx4.p2.45.m1.1.1.3.2.3" xref="Sx4.p2.45.m1.1.1.3.2.3.cmml"><mi id="Sx4.p2.45.m1.1.1.3.2.3.2" xref="Sx4.p2.45.m1.1.1.3.2.3.2.cmml">s</mi><mi id="Sx4.p2.45.m1.1.1.3.2.3.3" xref="Sx4.p2.45.m1.1.1.3.2.3.3.cmml">j</mi></msub></msub></msqrt></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.45.m1.1b"><apply id="Sx4.p2.45.m1.1.1.cmml" xref="Sx4.p2.45.m1.1.1"><eq id="Sx4.p2.45.m1.1.1.1.cmml" xref="Sx4.p2.45.m1.1.1.1"></eq><apply id="Sx4.p2.45.m1.1.1.2.cmml" xref="Sx4.p2.45.m1.1.1.2"><csymbol cd="ambiguous" id="Sx4.p2.45.m1.1.1.2.1.cmml" xref="Sx4.p2.45.m1.1.1.2">subscript</csymbol><ci id="Sx4.p2.45.m1.1.1.2.2.cmml" xref="Sx4.p2.45.m1.1.1.2.2">𝑛</ci><apply id="Sx4.p2.45.m1.1.1.2.3.cmml" xref="Sx4.p2.45.m1.1.1.2.3"><csymbol cd="ambiguous" id="Sx4.p2.45.m1.1.1.2.3.1.cmml" xref="Sx4.p2.45.m1.1.1.2.3">subscript</csymbol><ci id="Sx4.p2.45.m1.1.1.2.3.2.cmml" xref="Sx4.p2.45.m1.1.1.2.3.2">𝑠</ci><ci id="Sx4.p2.45.m1.1.1.2.3.3.cmml" xref="Sx4.p2.45.m1.1.1.2.3.3">𝑗</ci></apply></apply><apply id="Sx4.p2.45.m1.1.1.3.cmml" xref="Sx4.p2.45.m1.1.1.3"><root id="Sx4.p2.45.m1.1.1.3a.cmml" xref="Sx4.p2.45.m1.1.1.3"></root><apply id="Sx4.p2.45.m1.1.1.3.2.cmml" xref="Sx4.p2.45.m1.1.1.3.2"><csymbol cd="ambiguous" id="Sx4.p2.45.m1.1.1.3.2.1.cmml" xref="Sx4.p2.45.m1.1.1.3.2">subscript</csymbol><ci id="Sx4.p2.45.m1.1.1.3.2.2.cmml" xref="Sx4.p2.45.m1.1.1.3.2.2">𝜀</ci><apply id="Sx4.p2.45.m1.1.1.3.2.3.cmml" xref="Sx4.p2.45.m1.1.1.3.2.3"><csymbol cd="ambiguous" id="Sx4.p2.45.m1.1.1.3.2.3.1.cmml" xref="Sx4.p2.45.m1.1.1.3.2.3">subscript</csymbol><ci id="Sx4.p2.45.m1.1.1.3.2.3.2.cmml" xref="Sx4.p2.45.m1.1.1.3.2.3.2">𝑠</ci><ci id="Sx4.p2.45.m1.1.1.3.2.3.3.cmml" xref="Sx4.p2.45.m1.1.1.3.2.3.3">𝑗</ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.45.m1.1c">n_{s_{j}}=\sqrt{\varepsilon_{s_{j}}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.45.m1.1d">italic_n start_POSTSUBSCRIPT italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT = square-root start_ARG italic_ε start_POSTSUBSCRIPT italic_s start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT end_ARG</annotation></semantics></math> and <math alttext="n_{p_{j}}=\sqrt{\varepsilon_{p_{j}}}" class="ltx_Math" display="inline" id="Sx4.p2.46.m2.1"><semantics id="Sx4.p2.46.m2.1a"><mrow id="Sx4.p2.46.m2.1.1" xref="Sx4.p2.46.m2.1.1.cmml"><msub id="Sx4.p2.46.m2.1.1.2" xref="Sx4.p2.46.m2.1.1.2.cmml"><mi id="Sx4.p2.46.m2.1.1.2.2" xref="Sx4.p2.46.m2.1.1.2.2.cmml">n</mi><msub id="Sx4.p2.46.m2.1.1.2.3" xref="Sx4.p2.46.m2.1.1.2.3.cmml"><mi id="Sx4.p2.46.m2.1.1.2.3.2" xref="Sx4.p2.46.m2.1.1.2.3.2.cmml">p</mi><mi id="Sx4.p2.46.m2.1.1.2.3.3" xref="Sx4.p2.46.m2.1.1.2.3.3.cmml">j</mi></msub></msub><mo id="Sx4.p2.46.m2.1.1.1" xref="Sx4.p2.46.m2.1.1.1.cmml">=</mo><msqrt id="Sx4.p2.46.m2.1.1.3" xref="Sx4.p2.46.m2.1.1.3.cmml"><msub id="Sx4.p2.46.m2.1.1.3.2" xref="Sx4.p2.46.m2.1.1.3.2.cmml"><mi id="Sx4.p2.46.m2.1.1.3.2.2" xref="Sx4.p2.46.m2.1.1.3.2.2.cmml">ε</mi><msub id="Sx4.p2.46.m2.1.1.3.2.3" xref="Sx4.p2.46.m2.1.1.3.2.3.cmml"><mi id="Sx4.p2.46.m2.1.1.3.2.3.2" xref="Sx4.p2.46.m2.1.1.3.2.3.2.cmml">p</mi><mi id="Sx4.p2.46.m2.1.1.3.2.3.3" xref="Sx4.p2.46.m2.1.1.3.2.3.3.cmml">j</mi></msub></msub></msqrt></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p2.46.m2.1b"><apply id="Sx4.p2.46.m2.1.1.cmml" xref="Sx4.p2.46.m2.1.1"><eq id="Sx4.p2.46.m2.1.1.1.cmml" xref="Sx4.p2.46.m2.1.1.1"></eq><apply id="Sx4.p2.46.m2.1.1.2.cmml" xref="Sx4.p2.46.m2.1.1.2"><csymbol cd="ambiguous" id="Sx4.p2.46.m2.1.1.2.1.cmml" xref="Sx4.p2.46.m2.1.1.2">subscript</csymbol><ci id="Sx4.p2.46.m2.1.1.2.2.cmml" xref="Sx4.p2.46.m2.1.1.2.2">𝑛</ci><apply id="Sx4.p2.46.m2.1.1.2.3.cmml" xref="Sx4.p2.46.m2.1.1.2.3"><csymbol cd="ambiguous" id="Sx4.p2.46.m2.1.1.2.3.1.cmml" xref="Sx4.p2.46.m2.1.1.2.3">subscript</csymbol><ci id="Sx4.p2.46.m2.1.1.2.3.2.cmml" xref="Sx4.p2.46.m2.1.1.2.3.2">𝑝</ci><ci id="Sx4.p2.46.m2.1.1.2.3.3.cmml" xref="Sx4.p2.46.m2.1.1.2.3.3">𝑗</ci></apply></apply><apply id="Sx4.p2.46.m2.1.1.3.cmml" xref="Sx4.p2.46.m2.1.1.3"><root id="Sx4.p2.46.m2.1.1.3a.cmml" xref="Sx4.p2.46.m2.1.1.3"></root><apply id="Sx4.p2.46.m2.1.1.3.2.cmml" xref="Sx4.p2.46.m2.1.1.3.2"><csymbol cd="ambiguous" id="Sx4.p2.46.m2.1.1.3.2.1.cmml" xref="Sx4.p2.46.m2.1.1.3.2">subscript</csymbol><ci id="Sx4.p2.46.m2.1.1.3.2.2.cmml" xref="Sx4.p2.46.m2.1.1.3.2.2">𝜀</ci><apply id="Sx4.p2.46.m2.1.1.3.2.3.cmml" xref="Sx4.p2.46.m2.1.1.3.2.3"><csymbol cd="ambiguous" id="Sx4.p2.46.m2.1.1.3.2.3.1.cmml" xref="Sx4.p2.46.m2.1.1.3.2.3">subscript</csymbol><ci id="Sx4.p2.46.m2.1.1.3.2.3.2.cmml" xref="Sx4.p2.46.m2.1.1.3.2.3.2">𝑝</ci><ci id="Sx4.p2.46.m2.1.1.3.2.3.3.cmml" xref="Sx4.p2.46.m2.1.1.3.2.3.3">𝑗</ci></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.46.m2.1c">n_{p_{j}}=\sqrt{\varepsilon_{p_{j}}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.46.m2.1d">italic_n start_POSTSUBSCRIPT italic_p start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT = square-root start_ARG italic_ε start_POSTSUBSCRIPT italic_p start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_POSTSUBSCRIPT end_ARG</annotation></semantics></math>. As a result, we can obtain transmission and reflection coefficients in terms of the matrix elements of <math alttext="Q" class="ltx_Math" display="inline" id="Sx4.p2.47.m3.1"><semantics id="Sx4.p2.47.m3.1a"><mi id="Sx4.p2.47.m3.1.1" xref="Sx4.p2.47.m3.1.1.cmml">Q</mi><annotation-xml encoding="MathML-Content" id="Sx4.p2.47.m3.1b"><ci id="Sx4.p2.47.m3.1.1.cmml" xref="Sx4.p2.47.m3.1.1">𝑄</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p2.47.m3.1c">Q</annotation><annotation encoding="application/x-llamapun" id="Sx4.p2.47.m3.1d">italic_Q</annotation></semantics></math> as</p> </div> <div class="ltx_para" id="Sx4.p3"> <table class="ltx_equation ltx_eqn_table" id="Sx4.E11"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="r_{ss}=\left.\frac{E_{r,s}}{E_{i,s}}\right|_{E_{i,p}=0}=\frac{Q_{24}Q_{41}-Q_{% 21}Q_{44}}{Q_{22}Q_{44}-Q_{24}Q_{42}}," 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start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT end_ARG start_ARG italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT end_ARG ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(11)</span></td> </tr></tbody> </table> </div> <div class="ltx_para" id="Sx4.p4"> <table class="ltx_equation ltx_eqn_table" id="Sx4.E12"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="r_{sp}=\left.\frac{E_{r,p}}{E_{i,s}}\right|_{E_{i,p}=0}=\frac{Q_{21}Q_{42}-Q_{% 22}Q_{41}}{Q_{22}Q_{44}-Q_{24}Q_{42}}," class="ltx_Math" display="block" id="Sx4.E12.m1.7"><semantics 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start_POSTSUBSCRIPT 41 end_POSTSUBSCRIPT end_ARG start_ARG italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT end_ARG ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(12)</span></td> </tr></tbody> </table> </div> <div class="ltx_para" id="Sx4.p5"> <table class="ltx_equation ltx_eqn_table" id="Sx4.E13"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="t_{ss}=\left.\frac{E_{t,s}}{E_{i,s}}\right|_{E_{i,p}=0}=Q_{11}+\frac{Q_{12}(Q_% {24}Q_{41}-Q_{21}Q_{44})+Q_{14}(Q_{21}Q_{42}-Q_{22}Q_{41})}{Q_{22}Q_{44}-Q_{24% }Q_{42}}" class="ltx_Math" 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start_POSTSUBSCRIPT italic_s italic_s end_POSTSUBSCRIPT = divide start_ARG italic_E start_POSTSUBSCRIPT italic_t , italic_s end_POSTSUBSCRIPT end_ARG start_ARG italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT end_ARG | start_POSTSUBSCRIPT italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT = 0 end_POSTSUBSCRIPT = italic_Q start_POSTSUBSCRIPT 11 end_POSTSUBSCRIPT + divide start_ARG italic_Q start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT ( italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 41 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 21 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT ) + italic_Q start_POSTSUBSCRIPT 14 end_POSTSUBSCRIPT ( italic_Q start_POSTSUBSCRIPT 21 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 41 end_POSTSUBSCRIPT ) end_ARG start_ARG italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT end_ARG</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(13)</span></td> </tr></tbody> </table> </div> <div class="ltx_para" id="Sx4.p6"> <table class="ltx_equation ltx_eqn_table" id="Sx4.E14"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="t_{sp}=\left.\frac{E_{t,p}}{E_{i,s}}\right|_{E_{i,p}=0}=Q_{31}+\frac{Q_{32}(Q_% {24}Q_{41}-Q_{21}Q_{44})+Q_{34}(Q_{21}Q_{42}-Q_{22}Q_{41})}{Q_{22}Q_{44}-Q_{24% }Q_{42}}\ ." class="ltx_Math" display="block" id="Sx4.E14.m1.9"><semantics id="Sx4.E14.m1.9a"><mrow id="Sx4.E14.m1.9.9.1" 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encoding="application/x-tex" id="Sx4.E14.m1.9c">t_{sp}=\left.\frac{E_{t,p}}{E_{i,s}}\right|_{E_{i,p}=0}=Q_{31}+\frac{Q_{32}(Q_% {24}Q_{41}-Q_{21}Q_{44})+Q_{34}(Q_{21}Q_{42}-Q_{22}Q_{41})}{Q_{22}Q_{44}-Q_{24% }Q_{42}}\ .</annotation><annotation encoding="application/x-llamapun" id="Sx4.E14.m1.9d">italic_t start_POSTSUBSCRIPT italic_s italic_p end_POSTSUBSCRIPT = divide start_ARG italic_E start_POSTSUBSCRIPT italic_t , italic_p end_POSTSUBSCRIPT end_ARG start_ARG italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT end_ARG | start_POSTSUBSCRIPT italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT = 0 end_POSTSUBSCRIPT = italic_Q start_POSTSUBSCRIPT 31 end_POSTSUBSCRIPT + divide start_ARG italic_Q start_POSTSUBSCRIPT 32 end_POSTSUBSCRIPT ( italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 41 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 21 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT ) + italic_Q start_POSTSUBSCRIPT 34 end_POSTSUBSCRIPT ( italic_Q start_POSTSUBSCRIPT 21 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 41 end_POSTSUBSCRIPT ) end_ARG start_ARG italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT end_ARG .</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(14)</span></td> </tr></tbody> </table> </div> <div class="ltx_para" id="Sx4.p7"> <table class="ltx_equation ltx_eqn_table" id="Sx4.E15"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell 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start_POSTSUBSCRIPT 43 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT end_ARG start_ARG italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT end_ARG ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(15)</span></td> </tr></tbody> </table> </div> <div class="ltx_para" id="Sx4.p8"> <table class="ltx_equation ltx_eqn_table" id="Sx4.E16"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="r_{pp}=\left.\frac{E_{r,p}}{E_{i,p}}\right|_{E_{i,s}=0}=\frac{Q_{23}Q_{42}-Q_{% 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start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 43 end_POSTSUBSCRIPT end_ARG start_ARG italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT end_ARG ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(16)</span></td> </tr></tbody> </table> </div> <div class="ltx_para" id="Sx4.p9"> <table class="ltx_equation ltx_eqn_table" id="Sx4.E17"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="t_{pp}=\left.\frac{E_{t,s}}{E_{i,p}}\right|_{E_{i,s}=0}=Q_{33}+\frac{Q_{32}(Q_% 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xref="Sx4.E17.m1.8.8.4.3.3.2">𝑄</ci><cn id="Sx4.E17.m1.8.8.4.3.3.3.cmml" type="integer" xref="Sx4.E17.m1.8.8.4.3.3.3">42</cn></apply></apply></apply></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.E17.m1.9c">t_{pp}=\left.\frac{E_{t,s}}{E_{i,p}}\right|_{E_{i,s}=0}=Q_{33}+\frac{Q_{32}(Q_% {24}Q_{43}-Q_{23}Q_{44})+Q_{34}(Q_{23}Q_{42}-Q_{22}Q_{43})}{Q_{22}Q_{44}-Q_{24% }Q_{42}},</annotation><annotation encoding="application/x-llamapun" id="Sx4.E17.m1.9d">italic_t start_POSTSUBSCRIPT italic_p italic_p end_POSTSUBSCRIPT = divide start_ARG italic_E start_POSTSUBSCRIPT italic_t , italic_s end_POSTSUBSCRIPT end_ARG start_ARG italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT end_ARG | start_POSTSUBSCRIPT italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT = 0 end_POSTSUBSCRIPT = italic_Q start_POSTSUBSCRIPT 33 end_POSTSUBSCRIPT + divide start_ARG italic_Q start_POSTSUBSCRIPT 32 end_POSTSUBSCRIPT ( italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 43 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT ) + italic_Q start_POSTSUBSCRIPT 34 end_POSTSUBSCRIPT ( italic_Q start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 43 end_POSTSUBSCRIPT ) end_ARG start_ARG italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT end_ARG ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(17)</span></td> </tr></tbody> </table> </div> <div class="ltx_para" id="Sx4.p10"> <table 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xref="Sx4.E18.m1.8.8.2.2"><times id="Sx4.E18.m1.8.8.2.2.2.cmml" xref="Sx4.E18.m1.8.8.2.2.2"></times><apply id="Sx4.E18.m1.8.8.2.2.3.cmml" xref="Sx4.E18.m1.8.8.2.2.3"><csymbol cd="ambiguous" id="Sx4.E18.m1.8.8.2.2.3.1.cmml" xref="Sx4.E18.m1.8.8.2.2.3">subscript</csymbol><ci id="Sx4.E18.m1.8.8.2.2.3.2.cmml" xref="Sx4.E18.m1.8.8.2.2.3.2">𝑄</ci><cn id="Sx4.E18.m1.8.8.2.2.3.3.cmml" type="integer" xref="Sx4.E18.m1.8.8.2.2.3.3">14</cn></apply><apply id="Sx4.E18.m1.8.8.2.2.1.1.1.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1"><minus id="Sx4.E18.m1.8.8.2.2.1.1.1.1.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.1"></minus><apply id="Sx4.E18.m1.8.8.2.2.1.1.1.2.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.2"><times id="Sx4.E18.m1.8.8.2.2.1.1.1.2.1.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.2.1"></times><apply id="Sx4.E18.m1.8.8.2.2.1.1.1.2.2.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.2.2"><csymbol cd="ambiguous" id="Sx4.E18.m1.8.8.2.2.1.1.1.2.2.1.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.2.2">subscript</csymbol><ci id="Sx4.E18.m1.8.8.2.2.1.1.1.2.2.2.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.2.2.2">𝑄</ci><cn id="Sx4.E18.m1.8.8.2.2.1.1.1.2.2.3.cmml" type="integer" xref="Sx4.E18.m1.8.8.2.2.1.1.1.2.2.3">23</cn></apply><apply id="Sx4.E18.m1.8.8.2.2.1.1.1.2.3.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.2.3"><csymbol cd="ambiguous" id="Sx4.E18.m1.8.8.2.2.1.1.1.2.3.1.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.2.3">subscript</csymbol><ci id="Sx4.E18.m1.8.8.2.2.1.1.1.2.3.2.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.2.3.2">𝑄</ci><cn id="Sx4.E18.m1.8.8.2.2.1.1.1.2.3.3.cmml" type="integer" xref="Sx4.E18.m1.8.8.2.2.1.1.1.2.3.3">42</cn></apply></apply><apply id="Sx4.E18.m1.8.8.2.2.1.1.1.3.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.3"><times id="Sx4.E18.m1.8.8.2.2.1.1.1.3.1.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.3.1"></times><apply id="Sx4.E18.m1.8.8.2.2.1.1.1.3.2.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.3.2"><csymbol cd="ambiguous" id="Sx4.E18.m1.8.8.2.2.1.1.1.3.2.1.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.3.2">subscript</csymbol><ci id="Sx4.E18.m1.8.8.2.2.1.1.1.3.2.2.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.3.2.2">𝑄</ci><cn id="Sx4.E18.m1.8.8.2.2.1.1.1.3.2.3.cmml" type="integer" xref="Sx4.E18.m1.8.8.2.2.1.1.1.3.2.3">22</cn></apply><apply id="Sx4.E18.m1.8.8.2.2.1.1.1.3.3.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.3.3"><csymbol cd="ambiguous" id="Sx4.E18.m1.8.8.2.2.1.1.1.3.3.1.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.3.3">subscript</csymbol><ci id="Sx4.E18.m1.8.8.2.2.1.1.1.3.3.2.cmml" xref="Sx4.E18.m1.8.8.2.2.1.1.1.3.3.2">𝑄</ci><cn id="Sx4.E18.m1.8.8.2.2.1.1.1.3.3.3.cmml" type="integer" xref="Sx4.E18.m1.8.8.2.2.1.1.1.3.3.3">43</cn></apply></apply></apply></apply></apply><apply id="Sx4.E18.m1.8.8.4.cmml" xref="Sx4.E18.m1.8.8.4"><minus id="Sx4.E18.m1.8.8.4.1.cmml" xref="Sx4.E18.m1.8.8.4.1"></minus><apply id="Sx4.E18.m1.8.8.4.2.cmml" xref="Sx4.E18.m1.8.8.4.2"><times id="Sx4.E18.m1.8.8.4.2.1.cmml" xref="Sx4.E18.m1.8.8.4.2.1"></times><apply id="Sx4.E18.m1.8.8.4.2.2.cmml" xref="Sx4.E18.m1.8.8.4.2.2"><csymbol cd="ambiguous" id="Sx4.E18.m1.8.8.4.2.2.1.cmml" xref="Sx4.E18.m1.8.8.4.2.2">subscript</csymbol><ci id="Sx4.E18.m1.8.8.4.2.2.2.cmml" xref="Sx4.E18.m1.8.8.4.2.2.2">𝑄</ci><cn id="Sx4.E18.m1.8.8.4.2.2.3.cmml" type="integer" xref="Sx4.E18.m1.8.8.4.2.2.3">22</cn></apply><apply id="Sx4.E18.m1.8.8.4.2.3.cmml" xref="Sx4.E18.m1.8.8.4.2.3"><csymbol cd="ambiguous" id="Sx4.E18.m1.8.8.4.2.3.1.cmml" xref="Sx4.E18.m1.8.8.4.2.3">subscript</csymbol><ci id="Sx4.E18.m1.8.8.4.2.3.2.cmml" xref="Sx4.E18.m1.8.8.4.2.3.2">𝑄</ci><cn id="Sx4.E18.m1.8.8.4.2.3.3.cmml" type="integer" xref="Sx4.E18.m1.8.8.4.2.3.3">44</cn></apply></apply><apply id="Sx4.E18.m1.8.8.4.3.cmml" xref="Sx4.E18.m1.8.8.4.3"><times id="Sx4.E18.m1.8.8.4.3.1.cmml" xref="Sx4.E18.m1.8.8.4.3.1"></times><apply id="Sx4.E18.m1.8.8.4.3.2.cmml" xref="Sx4.E18.m1.8.8.4.3.2"><csymbol cd="ambiguous" id="Sx4.E18.m1.8.8.4.3.2.1.cmml" xref="Sx4.E18.m1.8.8.4.3.2">subscript</csymbol><ci id="Sx4.E18.m1.8.8.4.3.2.2.cmml" xref="Sx4.E18.m1.8.8.4.3.2.2">𝑄</ci><cn id="Sx4.E18.m1.8.8.4.3.2.3.cmml" type="integer" xref="Sx4.E18.m1.8.8.4.3.2.3">24</cn></apply><apply id="Sx4.E18.m1.8.8.4.3.3.cmml" xref="Sx4.E18.m1.8.8.4.3.3"><csymbol cd="ambiguous" id="Sx4.E18.m1.8.8.4.3.3.1.cmml" xref="Sx4.E18.m1.8.8.4.3.3">subscript</csymbol><ci id="Sx4.E18.m1.8.8.4.3.3.2.cmml" xref="Sx4.E18.m1.8.8.4.3.3.2">𝑄</ci><cn id="Sx4.E18.m1.8.8.4.3.3.3.cmml" type="integer" xref="Sx4.E18.m1.8.8.4.3.3.3">42</cn></apply></apply></apply></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.E18.m1.9c">t_{ps}=\left.\frac{E_{t,p}}{E_{i,p}}\right|_{E_{i,s}=0}=Q_{13}+\frac{Q_{12}(Q_% {24}Q_{43}-Q_{23}Q_{44})+Q_{14}(Q_{23}Q_{42}-Q_{22}Q_{43})}{Q_{22}Q_{44}-Q_{24% }Q_{42}}.</annotation><annotation encoding="application/x-llamapun" id="Sx4.E18.m1.9d">italic_t start_POSTSUBSCRIPT italic_p italic_s end_POSTSUBSCRIPT = divide start_ARG italic_E start_POSTSUBSCRIPT italic_t , italic_p end_POSTSUBSCRIPT end_ARG start_ARG italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT end_ARG | start_POSTSUBSCRIPT italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT = 0 end_POSTSUBSCRIPT = italic_Q start_POSTSUBSCRIPT 13 end_POSTSUBSCRIPT + divide start_ARG italic_Q start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT ( italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 43 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT ) + italic_Q start_POSTSUBSCRIPT 14 end_POSTSUBSCRIPT ( italic_Q start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 43 end_POSTSUBSCRIPT ) end_ARG start_ARG italic_Q start_POSTSUBSCRIPT 22 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 44 end_POSTSUBSCRIPT - italic_Q start_POSTSUBSCRIPT 24 end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT 42 end_POSTSUBSCRIPT end_ARG .</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(18)</span></td> </tr></tbody> </table> </div> <div class="ltx_para" id="Sx4.p11"> <p class="ltx_p" id="Sx4.p11.8">The input light of any other polarization states can be represented as a linear combination of <math alttext="E_{i,s}" class="ltx_Math" display="inline" id="Sx4.p11.1.m1.2"><semantics id="Sx4.p11.1.m1.2a"><msub id="Sx4.p11.1.m1.2.3" xref="Sx4.p11.1.m1.2.3.cmml"><mi id="Sx4.p11.1.m1.2.3.2" xref="Sx4.p11.1.m1.2.3.2.cmml">E</mi><mrow id="Sx4.p11.1.m1.2.2.2.4" xref="Sx4.p11.1.m1.2.2.2.3.cmml"><mi id="Sx4.p11.1.m1.1.1.1.1" xref="Sx4.p11.1.m1.1.1.1.1.cmml">i</mi><mo id="Sx4.p11.1.m1.2.2.2.4.1" xref="Sx4.p11.1.m1.2.2.2.3.cmml">,</mo><mi id="Sx4.p11.1.m1.2.2.2.2" xref="Sx4.p11.1.m1.2.2.2.2.cmml">s</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="Sx4.p11.1.m1.2b"><apply id="Sx4.p11.1.m1.2.3.cmml" xref="Sx4.p11.1.m1.2.3"><csymbol cd="ambiguous" id="Sx4.p11.1.m1.2.3.1.cmml" xref="Sx4.p11.1.m1.2.3">subscript</csymbol><ci id="Sx4.p11.1.m1.2.3.2.cmml" xref="Sx4.p11.1.m1.2.3.2">𝐸</ci><list id="Sx4.p11.1.m1.2.2.2.3.cmml" xref="Sx4.p11.1.m1.2.2.2.4"><ci id="Sx4.p11.1.m1.1.1.1.1.cmml" xref="Sx4.p11.1.m1.1.1.1.1">𝑖</ci><ci id="Sx4.p11.1.m1.2.2.2.2.cmml" xref="Sx4.p11.1.m1.2.2.2.2">𝑠</ci></list></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p11.1.m1.2c">E_{i,s}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p11.1.m1.2d">italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT</annotation></semantics></math> and <math alttext="E_{i,p}" class="ltx_Math" display="inline" id="Sx4.p11.2.m2.2"><semantics id="Sx4.p11.2.m2.2a"><msub id="Sx4.p11.2.m2.2.3" xref="Sx4.p11.2.m2.2.3.cmml"><mi id="Sx4.p11.2.m2.2.3.2" xref="Sx4.p11.2.m2.2.3.2.cmml">E</mi><mrow id="Sx4.p11.2.m2.2.2.2.4" xref="Sx4.p11.2.m2.2.2.2.3.cmml"><mi id="Sx4.p11.2.m2.1.1.1.1" xref="Sx4.p11.2.m2.1.1.1.1.cmml">i</mi><mo id="Sx4.p11.2.m2.2.2.2.4.1" xref="Sx4.p11.2.m2.2.2.2.3.cmml">,</mo><mi id="Sx4.p11.2.m2.2.2.2.2" xref="Sx4.p11.2.m2.2.2.2.2.cmml">p</mi></mrow></msub><annotation-xml encoding="MathML-Content" id="Sx4.p11.2.m2.2b"><apply id="Sx4.p11.2.m2.2.3.cmml" xref="Sx4.p11.2.m2.2.3"><csymbol cd="ambiguous" id="Sx4.p11.2.m2.2.3.1.cmml" xref="Sx4.p11.2.m2.2.3">subscript</csymbol><ci id="Sx4.p11.2.m2.2.3.2.cmml" xref="Sx4.p11.2.m2.2.3.2">𝐸</ci><list id="Sx4.p11.2.m2.2.2.2.3.cmml" xref="Sx4.p11.2.m2.2.2.2.4"><ci id="Sx4.p11.2.m2.1.1.1.1.cmml" xref="Sx4.p11.2.m2.1.1.1.1">𝑖</ci><ci id="Sx4.p11.2.m2.2.2.2.2.cmml" xref="Sx4.p11.2.m2.2.2.2.2">𝑝</ci></list></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p11.2.m2.2c">E_{i,p}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p11.2.m2.2d">italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT</annotation></semantics></math>. For example, LCP light can be represented as <math alttext="0.5E_{i,s}+0.5iE_{i,p}" class="ltx_Math" display="inline" id="Sx4.p11.3.m3.4"><semantics id="Sx4.p11.3.m3.4a"><mrow id="Sx4.p11.3.m3.4.5" xref="Sx4.p11.3.m3.4.5.cmml"><mrow id="Sx4.p11.3.m3.4.5.2" xref="Sx4.p11.3.m3.4.5.2.cmml"><mn id="Sx4.p11.3.m3.4.5.2.2" xref="Sx4.p11.3.m3.4.5.2.2.cmml">0.5</mn><mo id="Sx4.p11.3.m3.4.5.2.1" xref="Sx4.p11.3.m3.4.5.2.1.cmml">⁢</mo><msub id="Sx4.p11.3.m3.4.5.2.3" xref="Sx4.p11.3.m3.4.5.2.3.cmml"><mi id="Sx4.p11.3.m3.4.5.2.3.2" xref="Sx4.p11.3.m3.4.5.2.3.2.cmml">E</mi><mrow id="Sx4.p11.3.m3.2.2.2.4" xref="Sx4.p11.3.m3.2.2.2.3.cmml"><mi id="Sx4.p11.3.m3.1.1.1.1" xref="Sx4.p11.3.m3.1.1.1.1.cmml">i</mi><mo id="Sx4.p11.3.m3.2.2.2.4.1" xref="Sx4.p11.3.m3.2.2.2.3.cmml">,</mo><mi id="Sx4.p11.3.m3.2.2.2.2" xref="Sx4.p11.3.m3.2.2.2.2.cmml">s</mi></mrow></msub></mrow><mo id="Sx4.p11.3.m3.4.5.1" xref="Sx4.p11.3.m3.4.5.1.cmml">+</mo><mrow id="Sx4.p11.3.m3.4.5.3" xref="Sx4.p11.3.m3.4.5.3.cmml"><mn id="Sx4.p11.3.m3.4.5.3.2" xref="Sx4.p11.3.m3.4.5.3.2.cmml">0.5</mn><mo id="Sx4.p11.3.m3.4.5.3.1" xref="Sx4.p11.3.m3.4.5.3.1.cmml">⁢</mo><mi id="Sx4.p11.3.m3.4.5.3.3" xref="Sx4.p11.3.m3.4.5.3.3.cmml">i</mi><mo id="Sx4.p11.3.m3.4.5.3.1a" xref="Sx4.p11.3.m3.4.5.3.1.cmml">⁢</mo><msub id="Sx4.p11.3.m3.4.5.3.4" xref="Sx4.p11.3.m3.4.5.3.4.cmml"><mi id="Sx4.p11.3.m3.4.5.3.4.2" xref="Sx4.p11.3.m3.4.5.3.4.2.cmml">E</mi><mrow id="Sx4.p11.3.m3.4.4.2.4" xref="Sx4.p11.3.m3.4.4.2.3.cmml"><mi id="Sx4.p11.3.m3.3.3.1.1" xref="Sx4.p11.3.m3.3.3.1.1.cmml">i</mi><mo id="Sx4.p11.3.m3.4.4.2.4.1" xref="Sx4.p11.3.m3.4.4.2.3.cmml">,</mo><mi id="Sx4.p11.3.m3.4.4.2.2" xref="Sx4.p11.3.m3.4.4.2.2.cmml">p</mi></mrow></msub></mrow></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p11.3.m3.4b"><apply id="Sx4.p11.3.m3.4.5.cmml" xref="Sx4.p11.3.m3.4.5"><plus id="Sx4.p11.3.m3.4.5.1.cmml" xref="Sx4.p11.3.m3.4.5.1"></plus><apply id="Sx4.p11.3.m3.4.5.2.cmml" xref="Sx4.p11.3.m3.4.5.2"><times id="Sx4.p11.3.m3.4.5.2.1.cmml" xref="Sx4.p11.3.m3.4.5.2.1"></times><cn id="Sx4.p11.3.m3.4.5.2.2.cmml" type="float" xref="Sx4.p11.3.m3.4.5.2.2">0.5</cn><apply id="Sx4.p11.3.m3.4.5.2.3.cmml" xref="Sx4.p11.3.m3.4.5.2.3"><csymbol cd="ambiguous" id="Sx4.p11.3.m3.4.5.2.3.1.cmml" xref="Sx4.p11.3.m3.4.5.2.3">subscript</csymbol><ci id="Sx4.p11.3.m3.4.5.2.3.2.cmml" xref="Sx4.p11.3.m3.4.5.2.3.2">𝐸</ci><list id="Sx4.p11.3.m3.2.2.2.3.cmml" xref="Sx4.p11.3.m3.2.2.2.4"><ci id="Sx4.p11.3.m3.1.1.1.1.cmml" xref="Sx4.p11.3.m3.1.1.1.1">𝑖</ci><ci id="Sx4.p11.3.m3.2.2.2.2.cmml" xref="Sx4.p11.3.m3.2.2.2.2">𝑠</ci></list></apply></apply><apply id="Sx4.p11.3.m3.4.5.3.cmml" xref="Sx4.p11.3.m3.4.5.3"><times id="Sx4.p11.3.m3.4.5.3.1.cmml" xref="Sx4.p11.3.m3.4.5.3.1"></times><cn id="Sx4.p11.3.m3.4.5.3.2.cmml" type="float" xref="Sx4.p11.3.m3.4.5.3.2">0.5</cn><ci id="Sx4.p11.3.m3.4.5.3.3.cmml" xref="Sx4.p11.3.m3.4.5.3.3">𝑖</ci><apply id="Sx4.p11.3.m3.4.5.3.4.cmml" xref="Sx4.p11.3.m3.4.5.3.4"><csymbol cd="ambiguous" id="Sx4.p11.3.m3.4.5.3.4.1.cmml" xref="Sx4.p11.3.m3.4.5.3.4">subscript</csymbol><ci id="Sx4.p11.3.m3.4.5.3.4.2.cmml" xref="Sx4.p11.3.m3.4.5.3.4.2">𝐸</ci><list id="Sx4.p11.3.m3.4.4.2.3.cmml" xref="Sx4.p11.3.m3.4.4.2.4"><ci id="Sx4.p11.3.m3.3.3.1.1.cmml" xref="Sx4.p11.3.m3.3.3.1.1">𝑖</ci><ci id="Sx4.p11.3.m3.4.4.2.2.cmml" xref="Sx4.p11.3.m3.4.4.2.2">𝑝</ci></list></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p11.3.m3.4c">0.5E_{i,s}+0.5iE_{i,p}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p11.3.m3.4d">0.5 italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT + 0.5 italic_i italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT</annotation></semantics></math>, RCP light can be represented as <math alttext="0.5E_{i,s}-0.5iE_{i,p}" class="ltx_Math" display="inline" id="Sx4.p11.4.m4.4"><semantics id="Sx4.p11.4.m4.4a"><mrow id="Sx4.p11.4.m4.4.5" xref="Sx4.p11.4.m4.4.5.cmml"><mrow id="Sx4.p11.4.m4.4.5.2" xref="Sx4.p11.4.m4.4.5.2.cmml"><mn id="Sx4.p11.4.m4.4.5.2.2" xref="Sx4.p11.4.m4.4.5.2.2.cmml">0.5</mn><mo id="Sx4.p11.4.m4.4.5.2.1" xref="Sx4.p11.4.m4.4.5.2.1.cmml">⁢</mo><msub id="Sx4.p11.4.m4.4.5.2.3" xref="Sx4.p11.4.m4.4.5.2.3.cmml"><mi id="Sx4.p11.4.m4.4.5.2.3.2" xref="Sx4.p11.4.m4.4.5.2.3.2.cmml">E</mi><mrow id="Sx4.p11.4.m4.2.2.2.4" xref="Sx4.p11.4.m4.2.2.2.3.cmml"><mi id="Sx4.p11.4.m4.1.1.1.1" xref="Sx4.p11.4.m4.1.1.1.1.cmml">i</mi><mo id="Sx4.p11.4.m4.2.2.2.4.1" xref="Sx4.p11.4.m4.2.2.2.3.cmml">,</mo><mi id="Sx4.p11.4.m4.2.2.2.2" xref="Sx4.p11.4.m4.2.2.2.2.cmml">s</mi></mrow></msub></mrow><mo id="Sx4.p11.4.m4.4.5.1" xref="Sx4.p11.4.m4.4.5.1.cmml">−</mo><mrow id="Sx4.p11.4.m4.4.5.3" xref="Sx4.p11.4.m4.4.5.3.cmml"><mn id="Sx4.p11.4.m4.4.5.3.2" xref="Sx4.p11.4.m4.4.5.3.2.cmml">0.5</mn><mo id="Sx4.p11.4.m4.4.5.3.1" xref="Sx4.p11.4.m4.4.5.3.1.cmml">⁢</mo><mi id="Sx4.p11.4.m4.4.5.3.3" xref="Sx4.p11.4.m4.4.5.3.3.cmml">i</mi><mo id="Sx4.p11.4.m4.4.5.3.1a" xref="Sx4.p11.4.m4.4.5.3.1.cmml">⁢</mo><msub id="Sx4.p11.4.m4.4.5.3.4" xref="Sx4.p11.4.m4.4.5.3.4.cmml"><mi id="Sx4.p11.4.m4.4.5.3.4.2" xref="Sx4.p11.4.m4.4.5.3.4.2.cmml">E</mi><mrow id="Sx4.p11.4.m4.4.4.2.4" xref="Sx4.p11.4.m4.4.4.2.3.cmml"><mi id="Sx4.p11.4.m4.3.3.1.1" xref="Sx4.p11.4.m4.3.3.1.1.cmml">i</mi><mo id="Sx4.p11.4.m4.4.4.2.4.1" xref="Sx4.p11.4.m4.4.4.2.3.cmml">,</mo><mi id="Sx4.p11.4.m4.4.4.2.2" xref="Sx4.p11.4.m4.4.4.2.2.cmml">p</mi></mrow></msub></mrow></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p11.4.m4.4b"><apply id="Sx4.p11.4.m4.4.5.cmml" xref="Sx4.p11.4.m4.4.5"><minus id="Sx4.p11.4.m4.4.5.1.cmml" xref="Sx4.p11.4.m4.4.5.1"></minus><apply id="Sx4.p11.4.m4.4.5.2.cmml" xref="Sx4.p11.4.m4.4.5.2"><times id="Sx4.p11.4.m4.4.5.2.1.cmml" xref="Sx4.p11.4.m4.4.5.2.1"></times><cn id="Sx4.p11.4.m4.4.5.2.2.cmml" type="float" xref="Sx4.p11.4.m4.4.5.2.2">0.5</cn><apply id="Sx4.p11.4.m4.4.5.2.3.cmml" xref="Sx4.p11.4.m4.4.5.2.3"><csymbol cd="ambiguous" id="Sx4.p11.4.m4.4.5.2.3.1.cmml" xref="Sx4.p11.4.m4.4.5.2.3">subscript</csymbol><ci id="Sx4.p11.4.m4.4.5.2.3.2.cmml" xref="Sx4.p11.4.m4.4.5.2.3.2">𝐸</ci><list id="Sx4.p11.4.m4.2.2.2.3.cmml" xref="Sx4.p11.4.m4.2.2.2.4"><ci id="Sx4.p11.4.m4.1.1.1.1.cmml" xref="Sx4.p11.4.m4.1.1.1.1">𝑖</ci><ci id="Sx4.p11.4.m4.2.2.2.2.cmml" xref="Sx4.p11.4.m4.2.2.2.2">𝑠</ci></list></apply></apply><apply id="Sx4.p11.4.m4.4.5.3.cmml" xref="Sx4.p11.4.m4.4.5.3"><times id="Sx4.p11.4.m4.4.5.3.1.cmml" xref="Sx4.p11.4.m4.4.5.3.1"></times><cn id="Sx4.p11.4.m4.4.5.3.2.cmml" type="float" xref="Sx4.p11.4.m4.4.5.3.2">0.5</cn><ci id="Sx4.p11.4.m4.4.5.3.3.cmml" xref="Sx4.p11.4.m4.4.5.3.3">𝑖</ci><apply id="Sx4.p11.4.m4.4.5.3.4.cmml" xref="Sx4.p11.4.m4.4.5.3.4"><csymbol cd="ambiguous" id="Sx4.p11.4.m4.4.5.3.4.1.cmml" xref="Sx4.p11.4.m4.4.5.3.4">subscript</csymbol><ci id="Sx4.p11.4.m4.4.5.3.4.2.cmml" xref="Sx4.p11.4.m4.4.5.3.4.2">𝐸</ci><list id="Sx4.p11.4.m4.4.4.2.3.cmml" xref="Sx4.p11.4.m4.4.4.2.4"><ci id="Sx4.p11.4.m4.3.3.1.1.cmml" xref="Sx4.p11.4.m4.3.3.1.1">𝑖</ci><ci id="Sx4.p11.4.m4.4.4.2.2.cmml" xref="Sx4.p11.4.m4.4.4.2.2">𝑝</ci></list></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p11.4.m4.4c">0.5E_{i,s}-0.5iE_{i,p}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p11.4.m4.4d">0.5 italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT - 0.5 italic_i italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT</annotation></semantics></math>. Any linearly polarized with the angle between polarization direction and <math alttext="s" class="ltx_Math" display="inline" id="Sx4.p11.5.m5.1"><semantics id="Sx4.p11.5.m5.1a"><mi id="Sx4.p11.5.m5.1.1" xref="Sx4.p11.5.m5.1.1.cmml">s</mi><annotation-xml encoding="MathML-Content" id="Sx4.p11.5.m5.1b"><ci id="Sx4.p11.5.m5.1.1.cmml" xref="Sx4.p11.5.m5.1.1">𝑠</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p11.5.m5.1c">s</annotation><annotation encoding="application/x-llamapun" id="Sx4.p11.5.m5.1d">italic_s</annotation></semantics></math>-wave polarization direction, <math alttext="\alpha" class="ltx_Math" display="inline" id="Sx4.p11.6.m6.1"><semantics id="Sx4.p11.6.m6.1a"><mi id="Sx4.p11.6.m6.1.1" xref="Sx4.p11.6.m6.1.1.cmml">α</mi><annotation-xml encoding="MathML-Content" id="Sx4.p11.6.m6.1b"><ci id="Sx4.p11.6.m6.1.1.cmml" xref="Sx4.p11.6.m6.1.1">𝛼</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p11.6.m6.1c">\alpha</annotation><annotation encoding="application/x-llamapun" id="Sx4.p11.6.m6.1d">italic_α</annotation></semantics></math>, can be represented as cos<math alttext="(\alpha)E_{i,s}" class="ltx_Math" display="inline" id="Sx4.p11.7.m7.3"><semantics id="Sx4.p11.7.m7.3a"><mrow id="Sx4.p11.7.m7.3.4" xref="Sx4.p11.7.m7.3.4.cmml"><mrow id="Sx4.p11.7.m7.3.4.2.2" xref="Sx4.p11.7.m7.3.4.cmml"><mo id="Sx4.p11.7.m7.3.4.2.2.1" stretchy="false" xref="Sx4.p11.7.m7.3.4.cmml">(</mo><mi id="Sx4.p11.7.m7.3.3" xref="Sx4.p11.7.m7.3.3.cmml">α</mi><mo id="Sx4.p11.7.m7.3.4.2.2.2" stretchy="false" xref="Sx4.p11.7.m7.3.4.cmml">)</mo></mrow><mo id="Sx4.p11.7.m7.3.4.1" xref="Sx4.p11.7.m7.3.4.1.cmml">⁢</mo><msub id="Sx4.p11.7.m7.3.4.3" xref="Sx4.p11.7.m7.3.4.3.cmml"><mi id="Sx4.p11.7.m7.3.4.3.2" xref="Sx4.p11.7.m7.3.4.3.2.cmml">E</mi><mrow id="Sx4.p11.7.m7.2.2.2.4" xref="Sx4.p11.7.m7.2.2.2.3.cmml"><mi id="Sx4.p11.7.m7.1.1.1.1" xref="Sx4.p11.7.m7.1.1.1.1.cmml">i</mi><mo id="Sx4.p11.7.m7.2.2.2.4.1" xref="Sx4.p11.7.m7.2.2.2.3.cmml">,</mo><mi id="Sx4.p11.7.m7.2.2.2.2" xref="Sx4.p11.7.m7.2.2.2.2.cmml">s</mi></mrow></msub></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p11.7.m7.3b"><apply id="Sx4.p11.7.m7.3.4.cmml" xref="Sx4.p11.7.m7.3.4"><times id="Sx4.p11.7.m7.3.4.1.cmml" xref="Sx4.p11.7.m7.3.4.1"></times><ci id="Sx4.p11.7.m7.3.3.cmml" xref="Sx4.p11.7.m7.3.3">𝛼</ci><apply id="Sx4.p11.7.m7.3.4.3.cmml" xref="Sx4.p11.7.m7.3.4.3"><csymbol cd="ambiguous" id="Sx4.p11.7.m7.3.4.3.1.cmml" xref="Sx4.p11.7.m7.3.4.3">subscript</csymbol><ci id="Sx4.p11.7.m7.3.4.3.2.cmml" xref="Sx4.p11.7.m7.3.4.3.2">𝐸</ci><list id="Sx4.p11.7.m7.2.2.2.3.cmml" xref="Sx4.p11.7.m7.2.2.2.4"><ci id="Sx4.p11.7.m7.1.1.1.1.cmml" xref="Sx4.p11.7.m7.1.1.1.1">𝑖</ci><ci id="Sx4.p11.7.m7.2.2.2.2.cmml" xref="Sx4.p11.7.m7.2.2.2.2">𝑠</ci></list></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p11.7.m7.3c">(\alpha)E_{i,s}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p11.7.m7.3d">( italic_α ) italic_E start_POSTSUBSCRIPT italic_i , italic_s end_POSTSUBSCRIPT</annotation></semantics></math> + sin<math alttext="(\alpha)E_{i,p}" class="ltx_Math" display="inline" id="Sx4.p11.8.m8.3"><semantics id="Sx4.p11.8.m8.3a"><mrow id="Sx4.p11.8.m8.3.4" xref="Sx4.p11.8.m8.3.4.cmml"><mrow id="Sx4.p11.8.m8.3.4.2.2" xref="Sx4.p11.8.m8.3.4.cmml"><mo id="Sx4.p11.8.m8.3.4.2.2.1" stretchy="false" xref="Sx4.p11.8.m8.3.4.cmml">(</mo><mi id="Sx4.p11.8.m8.3.3" xref="Sx4.p11.8.m8.3.3.cmml">α</mi><mo id="Sx4.p11.8.m8.3.4.2.2.2" stretchy="false" xref="Sx4.p11.8.m8.3.4.cmml">)</mo></mrow><mo id="Sx4.p11.8.m8.3.4.1" xref="Sx4.p11.8.m8.3.4.1.cmml">⁢</mo><msub id="Sx4.p11.8.m8.3.4.3" xref="Sx4.p11.8.m8.3.4.3.cmml"><mi id="Sx4.p11.8.m8.3.4.3.2" xref="Sx4.p11.8.m8.3.4.3.2.cmml">E</mi><mrow id="Sx4.p11.8.m8.2.2.2.4" xref="Sx4.p11.8.m8.2.2.2.3.cmml"><mi id="Sx4.p11.8.m8.1.1.1.1" xref="Sx4.p11.8.m8.1.1.1.1.cmml">i</mi><mo id="Sx4.p11.8.m8.2.2.2.4.1" xref="Sx4.p11.8.m8.2.2.2.3.cmml">,</mo><mi id="Sx4.p11.8.m8.2.2.2.2" xref="Sx4.p11.8.m8.2.2.2.2.cmml">p</mi></mrow></msub></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p11.8.m8.3b"><apply id="Sx4.p11.8.m8.3.4.cmml" xref="Sx4.p11.8.m8.3.4"><times id="Sx4.p11.8.m8.3.4.1.cmml" xref="Sx4.p11.8.m8.3.4.1"></times><ci id="Sx4.p11.8.m8.3.3.cmml" xref="Sx4.p11.8.m8.3.3">𝛼</ci><apply id="Sx4.p11.8.m8.3.4.3.cmml" xref="Sx4.p11.8.m8.3.4.3"><csymbol cd="ambiguous" id="Sx4.p11.8.m8.3.4.3.1.cmml" xref="Sx4.p11.8.m8.3.4.3">subscript</csymbol><ci id="Sx4.p11.8.m8.3.4.3.2.cmml" xref="Sx4.p11.8.m8.3.4.3.2">𝐸</ci><list id="Sx4.p11.8.m8.2.2.2.3.cmml" xref="Sx4.p11.8.m8.2.2.2.4"><ci id="Sx4.p11.8.m8.1.1.1.1.cmml" xref="Sx4.p11.8.m8.1.1.1.1">𝑖</ci><ci id="Sx4.p11.8.m8.2.2.2.2.cmml" xref="Sx4.p11.8.m8.2.2.2.2">𝑝</ci></list></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p11.8.m8.3c">(\alpha)E_{i,p}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p11.8.m8.3d">( italic_α ) italic_E start_POSTSUBSCRIPT italic_i , italic_p end_POSTSUBSCRIPT</annotation></semantics></math>. Hence, the output fields and their amplitude and phase can be calculated using the input field vector in Eq. <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx4.E1" title="In Methods ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">1</span></a>. Since the operations described above are all matrix-matrix multiplications, <span class="ltx_text ltx_font_typewriter" id="Sx4.p11.8.1">PyTorch</span> (version 1.9.0) was used to implement the TMM calculation framework with a built-in backpropagation algorithm for gradient descent-based optimization. A Nvidia GeForce RTX 3090 GPU card with a cuda version 11.1 was used to accelerate calculations.</p> </div> <div class="ltx_para ltx_noindent" id="Sx4.p12"> <p class="ltx_p" id="Sx4.p12.47"><span class="ltx_text ltx_font_bold" id="Sx4.p12.47.1">Four-configuration CD simulation and measurement</span> – Theoretical analyses <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib14" title="">14</a>, <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib15" title="">15</a>]</cite> have shown that the observed CD signals from solid-state samples (CD<math alttext="{}_{\textrm{obs}}" class="ltx_Math" display="inline" id="Sx4.p12.1.m1.1"><semantics id="Sx4.p12.1.m1.1a"><msub id="Sx4.p12.1.m1.1.1" xref="Sx4.p12.1.m1.1.1.cmml"><mi id="Sx4.p12.1.m1.1.1a" xref="Sx4.p12.1.m1.1.1.cmml"></mi><mtext id="Sx4.p12.1.m1.1.1.1" xref="Sx4.p12.1.m1.1.1.1a.cmml">obs</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx4.p12.1.m1.1b"><apply id="Sx4.p12.1.m1.1.1.cmml" xref="Sx4.p12.1.m1.1.1"><ci id="Sx4.p12.1.m1.1.1.1a.cmml" xref="Sx4.p12.1.m1.1.1.1"><mtext id="Sx4.p12.1.m1.1.1.1.cmml" mathsize="70%" xref="Sx4.p12.1.m1.1.1.1">obs</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.1.m1.1c">{}_{\textrm{obs}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.1.m1.1d">start_FLOATSUBSCRIPT obs end_FLOATSUBSCRIPT</annotation></semantics></math>) can be described as CD<math alttext="{}_{\textrm{obs}}" class="ltx_Math" display="inline" id="Sx4.p12.2.m2.1"><semantics id="Sx4.p12.2.m2.1a"><msub id="Sx4.p12.2.m2.1.1" xref="Sx4.p12.2.m2.1.1.cmml"><mi id="Sx4.p12.2.m2.1.1a" xref="Sx4.p12.2.m2.1.1.cmml"></mi><mtext id="Sx4.p12.2.m2.1.1.1" xref="Sx4.p12.2.m2.1.1.1a.cmml">obs</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx4.p12.2.m2.1b"><apply id="Sx4.p12.2.m2.1.1.cmml" xref="Sx4.p12.2.m2.1.1"><ci id="Sx4.p12.2.m2.1.1.1a.cmml" xref="Sx4.p12.2.m2.1.1.1"><mtext id="Sx4.p12.2.m2.1.1.1.cmml" mathsize="70%" xref="Sx4.p12.2.m2.1.1.1">obs</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.2.m2.1c">{}_{\textrm{obs}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.2.m2.1d">start_FLOATSUBSCRIPT obs end_FLOATSUBSCRIPT</annotation></semantics></math> = CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx4.p12.3.m3.1"><semantics id="Sx4.p12.3.m3.1a"><msub id="Sx4.p12.3.m3.1.1" xref="Sx4.p12.3.m3.1.1.cmml"><mi id="Sx4.p12.3.m3.1.1a" xref="Sx4.p12.3.m3.1.1.cmml"></mi><mtext id="Sx4.p12.3.m3.1.1.1" xref="Sx4.p12.3.m3.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx4.p12.3.m3.1b"><apply id="Sx4.p12.3.m3.1.1.cmml" xref="Sx4.p12.3.m3.1.1"><ci id="Sx4.p12.3.m3.1.1.1a.cmml" xref="Sx4.p12.3.m3.1.1.1"><mtext id="Sx4.p12.3.m3.1.1.1.cmml" mathsize="70%" xref="Sx4.p12.3.m3.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.3.m3.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.3.m3.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> + 0.5(LD<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx4.p12.4.m4.1"><semantics id="Sx4.p12.4.m4.1a"><msup id="Sx4.p12.4.m4.1.1" xref="Sx4.p12.4.m4.1.1.cmml"><mi id="Sx4.p12.4.m4.1.1a" xref="Sx4.p12.4.m4.1.1.cmml"></mi><msup id="Sx4.p12.4.m4.1.1.1" xref="Sx4.p12.4.m4.1.1.1.cmml"><mi id="Sx4.p12.4.m4.1.1.1a" xref="Sx4.p12.4.m4.1.1.1.cmml"></mi><mo id="Sx4.p12.4.m4.1.1.1.1" xref="Sx4.p12.4.m4.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx4.p12.4.m4.1b"><apply id="Sx4.p12.4.m4.1.1.cmml" xref="Sx4.p12.4.m4.1.1"><apply id="Sx4.p12.4.m4.1.1.1.cmml" xref="Sx4.p12.4.m4.1.1.1"><ci id="Sx4.p12.4.m4.1.1.1.1.cmml" xref="Sx4.p12.4.m4.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.4.m4.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.4.m4.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>LB <math alttext="-" class="ltx_Math" display="inline" id="Sx4.p12.5.m5.1"><semantics id="Sx4.p12.5.m5.1a"><mo id="Sx4.p12.5.m5.1.1" xref="Sx4.p12.5.m5.1.1.cmml">−</mo><annotation-xml encoding="MathML-Content" id="Sx4.p12.5.m5.1b"><minus id="Sx4.p12.5.m5.1.1.cmml" xref="Sx4.p12.5.m5.1.1"></minus></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.5.m5.1c">-</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.5.m5.1d">-</annotation></semantics></math> LDLB<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx4.p12.6.m6.1"><semantics id="Sx4.p12.6.m6.1a"><msup id="Sx4.p12.6.m6.1.1" xref="Sx4.p12.6.m6.1.1.cmml"><mi id="Sx4.p12.6.m6.1.1a" xref="Sx4.p12.6.m6.1.1.cmml"></mi><msup id="Sx4.p12.6.m6.1.1.1" xref="Sx4.p12.6.m6.1.1.1.cmml"><mi id="Sx4.p12.6.m6.1.1.1a" xref="Sx4.p12.6.m6.1.1.1.cmml"></mi><mo id="Sx4.p12.6.m6.1.1.1.1" xref="Sx4.p12.6.m6.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx4.p12.6.m6.1b"><apply id="Sx4.p12.6.m6.1.1.cmml" xref="Sx4.p12.6.m6.1.1"><apply id="Sx4.p12.6.m6.1.1.1.cmml" xref="Sx4.p12.6.m6.1.1.1"><ci id="Sx4.p12.6.m6.1.1.1.1.cmml" xref="Sx4.p12.6.m6.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.6.m6.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.6.m6.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>) + <math alttext="\alpha_{\mathrm{c}}" class="ltx_Math" display="inline" id="Sx4.p12.7.m7.1"><semantics id="Sx4.p12.7.m7.1a"><msub id="Sx4.p12.7.m7.1.1" xref="Sx4.p12.7.m7.1.1.cmml"><mi id="Sx4.p12.7.m7.1.1.2" xref="Sx4.p12.7.m7.1.1.2.cmml">α</mi><mi id="Sx4.p12.7.m7.1.1.3" mathvariant="normal" xref="Sx4.p12.7.m7.1.1.3.cmml">c</mi></msub><annotation-xml encoding="MathML-Content" id="Sx4.p12.7.m7.1b"><apply id="Sx4.p12.7.m7.1.1.cmml" xref="Sx4.p12.7.m7.1.1"><csymbol cd="ambiguous" id="Sx4.p12.7.m7.1.1.1.cmml" xref="Sx4.p12.7.m7.1.1">subscript</csymbol><ci id="Sx4.p12.7.m7.1.1.2.cmml" xref="Sx4.p12.7.m7.1.1.2">𝛼</ci><ci id="Sx4.p12.7.m7.1.1.3.cmml" xref="Sx4.p12.7.m7.1.1.3">c</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.7.m7.1c">\alpha_{\mathrm{c}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.7.m7.1d">italic_α start_POSTSUBSCRIPT roman_c end_POSTSUBSCRIPT</annotation></semantics></math>(LD<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx4.p12.8.m8.1"><semantics id="Sx4.p12.8.m8.1a"><msup id="Sx4.p12.8.m8.1.1" xref="Sx4.p12.8.m8.1.1.cmml"><mi id="Sx4.p12.8.m8.1.1a" xref="Sx4.p12.8.m8.1.1.cmml"></mi><msup id="Sx4.p12.8.m8.1.1.1" xref="Sx4.p12.8.m8.1.1.1.cmml"><mi id="Sx4.p12.8.m8.1.1.1a" xref="Sx4.p12.8.m8.1.1.1.cmml"></mi><mo id="Sx4.p12.8.m8.1.1.1.1" xref="Sx4.p12.8.m8.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx4.p12.8.m8.1b"><apply id="Sx4.p12.8.m8.1.1.cmml" xref="Sx4.p12.8.m8.1.1"><apply id="Sx4.p12.8.m8.1.1.1.cmml" xref="Sx4.p12.8.m8.1.1.1"><ci id="Sx4.p12.8.m8.1.1.1.1.cmml" xref="Sx4.p12.8.m8.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.8.m8.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.8.m8.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>sin(<math alttext="2\theta" class="ltx_Math" display="inline" id="Sx4.p12.9.m9.1"><semantics id="Sx4.p12.9.m9.1a"><mrow id="Sx4.p12.9.m9.1.1" xref="Sx4.p12.9.m9.1.1.cmml"><mn id="Sx4.p12.9.m9.1.1.2" xref="Sx4.p12.9.m9.1.1.2.cmml">2</mn><mo id="Sx4.p12.9.m9.1.1.1" xref="Sx4.p12.9.m9.1.1.1.cmml">⁢</mo><mi id="Sx4.p12.9.m9.1.1.3" xref="Sx4.p12.9.m9.1.1.3.cmml">θ</mi></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p12.9.m9.1b"><apply id="Sx4.p12.9.m9.1.1.cmml" xref="Sx4.p12.9.m9.1.1"><times id="Sx4.p12.9.m9.1.1.1.cmml" xref="Sx4.p12.9.m9.1.1.1"></times><cn id="Sx4.p12.9.m9.1.1.2.cmml" type="integer" xref="Sx4.p12.9.m9.1.1.2">2</cn><ci id="Sx4.p12.9.m9.1.1.3.cmml" xref="Sx4.p12.9.m9.1.1.3">𝜃</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.9.m9.1c">2\theta</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.9.m9.1d">2 italic_θ</annotation></semantics></math>) - LDcos(<math alttext="2\theta" class="ltx_Math" display="inline" id="Sx4.p12.10.m10.1"><semantics id="Sx4.p12.10.m10.1a"><mrow id="Sx4.p12.10.m10.1.1" xref="Sx4.p12.10.m10.1.1.cmml"><mn id="Sx4.p12.10.m10.1.1.2" xref="Sx4.p12.10.m10.1.1.2.cmml">2</mn><mo id="Sx4.p12.10.m10.1.1.1" xref="Sx4.p12.10.m10.1.1.1.cmml">⁢</mo><mi id="Sx4.p12.10.m10.1.1.3" xref="Sx4.p12.10.m10.1.1.3.cmml">θ</mi></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p12.10.m10.1b"><apply id="Sx4.p12.10.m10.1.1.cmml" xref="Sx4.p12.10.m10.1.1"><times id="Sx4.p12.10.m10.1.1.1.cmml" xref="Sx4.p12.10.m10.1.1.1"></times><cn id="Sx4.p12.10.m10.1.1.2.cmml" type="integer" xref="Sx4.p12.10.m10.1.1.2">2</cn><ci id="Sx4.p12.10.m10.1.1.3.cmml" xref="Sx4.p12.10.m10.1.1.3">𝜃</ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.10.m10.1c">2\theta</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.10.m10.1d">2 italic_θ</annotation></semantics></math>)). The first term CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx4.p12.11.m11.1"><semantics id="Sx4.p12.11.m11.1a"><msub id="Sx4.p12.11.m11.1.1" xref="Sx4.p12.11.m11.1.1.cmml"><mi id="Sx4.p12.11.m11.1.1a" xref="Sx4.p12.11.m11.1.1.cmml"></mi><mtext id="Sx4.p12.11.m11.1.1.1" xref="Sx4.p12.11.m11.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx4.p12.11.m11.1b"><apply id="Sx4.p12.11.m11.1.1.cmml" xref="Sx4.p12.11.m11.1.1"><ci id="Sx4.p12.11.m11.1.1.1a.cmml" xref="Sx4.p12.11.m11.1.1.1"><mtext id="Sx4.p12.11.m11.1.1.1.cmml" mathsize="70%" xref="Sx4.p12.11.m11.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.11.m11.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.11.m11.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> is the intrinsic component of CD, which is from excitonic transitions in CNTs and is isotropic and independent of sample orientation. The second LDLB term is from the interference of the sample’s LD and LB responses. This term is not from excitons, independent of instrumental faults, and not an artifact. It represents a real, perfectly reproducible differential attenuation of LCP and RCP light. This LDLB term is invariant upon sample rotation around the axis perpendicular to the sample plane but inverts the sign under sample flipping. The third term artifact comes from the coupling of residual birefringence in the instrument and LD and LB of samples. This artifact term inverts the sign under <math alttext="90^{\circ}" class="ltx_Math" display="inline" id="Sx4.p12.12.m12.1"><semantics id="Sx4.p12.12.m12.1a"><msup id="Sx4.p12.12.m12.1.1" xref="Sx4.p12.12.m12.1.1.cmml"><mn id="Sx4.p12.12.m12.1.1.2" xref="Sx4.p12.12.m12.1.1.2.cmml">90</mn><mo id="Sx4.p12.12.m12.1.1.3" xref="Sx4.p12.12.m12.1.1.3.cmml">∘</mo></msup><annotation-xml encoding="MathML-Content" id="Sx4.p12.12.m12.1b"><apply id="Sx4.p12.12.m12.1.1.cmml" xref="Sx4.p12.12.m12.1.1"><csymbol cd="ambiguous" id="Sx4.p12.12.m12.1.1.1.cmml" xref="Sx4.p12.12.m12.1.1">superscript</csymbol><cn id="Sx4.p12.12.m12.1.1.2.cmml" type="integer" xref="Sx4.p12.12.m12.1.1.2">90</cn><compose id="Sx4.p12.12.m12.1.1.3.cmml" xref="Sx4.p12.12.m12.1.1.3"></compose></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.12.m12.1c">90^{\circ}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.12.m12.1d">90 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT</annotation></semantics></math> sample rotation around the axis perpendicular to the sample plane. Based on these properties, a four-configuration protocol was employed to extract the CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx4.p12.13.m13.1"><semantics id="Sx4.p12.13.m13.1a"><msub id="Sx4.p12.13.m13.1.1" xref="Sx4.p12.13.m13.1.1.cmml"><mi id="Sx4.p12.13.m13.1.1a" xref="Sx4.p12.13.m13.1.1.cmml"></mi><mtext id="Sx4.p12.13.m13.1.1.1" xref="Sx4.p12.13.m13.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx4.p12.13.m13.1b"><apply id="Sx4.p12.13.m13.1.1.cmml" xref="Sx4.p12.13.m13.1.1"><ci id="Sx4.p12.13.m13.1.1.1a.cmml" xref="Sx4.p12.13.m13.1.1.1"><mtext id="Sx4.p12.13.m13.1.1.1.cmml" mathsize="70%" xref="Sx4.p12.13.m13.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.13.m13.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.13.m13.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> and LDLB terms. Specifically, when the sample was positioned as illustrated in Supplementary Fig. 3, four CD spectra were calculated or measured and denoted as CD<sub class="ltx_sub" id="Sx4.p12.47.2"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.2.1">m1</span></sub>, CD<sub class="ltx_sub" id="Sx4.p12.47.3"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.3.1">m2</span></sub>, CD<sub class="ltx_sub" id="Sx4.p12.47.4"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.4.1">m3</span></sub>, and CD<sub class="ltx_sub" id="Sx4.p12.47.5"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.5.1">m4</span></sub>. The average spectra under in-plane rotation, which are 0.5(CD<sub class="ltx_sub" id="Sx4.p12.47.6"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.6.1">m1</span></sub> + CD<sub class="ltx_sub" id="Sx4.p12.47.7"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.7.1">m2</span></sub>) or 0.5(CD<sub class="ltx_sub" id="Sx4.p12.47.8"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.8.1">m3</span></sub> + CD<sub class="ltx_sub" id="Sx4.p12.47.9"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.9.1">m4</span></sub>), can remove the third term. Hence, the term 0.5(CD<sub class="ltx_sub" id="Sx4.p12.47.10"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.10.1">m1</span></sub> + CD<sub class="ltx_sub" id="Sx4.p12.47.11"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.11.1">m2</span></sub>) (i.e., the observed CD, CD<sub class="ltx_sub" id="Sx4.p12.47.12">obs</sub>, from the front side) corresponds to CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx4.p12.25.m25.1"><semantics id="Sx4.p12.25.m25.1a"><msub id="Sx4.p12.25.m25.1.1" xref="Sx4.p12.25.m25.1.1.cmml"><mi id="Sx4.p12.25.m25.1.1a" xref="Sx4.p12.25.m25.1.1.cmml"></mi><mtext id="Sx4.p12.25.m25.1.1.1" xref="Sx4.p12.25.m25.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx4.p12.25.m25.1b"><apply id="Sx4.p12.25.m25.1.1.cmml" xref="Sx4.p12.25.m25.1.1"><ci id="Sx4.p12.25.m25.1.1.1a.cmml" xref="Sx4.p12.25.m25.1.1.1"><mtext id="Sx4.p12.25.m25.1.1.1.cmml" mathsize="70%" xref="Sx4.p12.25.m25.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.25.m25.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.25.m25.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> + 0.5(LD<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx4.p12.26.m26.1"><semantics id="Sx4.p12.26.m26.1a"><msup id="Sx4.p12.26.m26.1.1" xref="Sx4.p12.26.m26.1.1.cmml"><mi id="Sx4.p12.26.m26.1.1a" xref="Sx4.p12.26.m26.1.1.cmml"></mi><msup id="Sx4.p12.26.m26.1.1.1" xref="Sx4.p12.26.m26.1.1.1.cmml"><mi id="Sx4.p12.26.m26.1.1.1a" xref="Sx4.p12.26.m26.1.1.1.cmml"></mi><mo id="Sx4.p12.26.m26.1.1.1.1" xref="Sx4.p12.26.m26.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx4.p12.26.m26.1b"><apply id="Sx4.p12.26.m26.1.1.cmml" xref="Sx4.p12.26.m26.1.1"><apply id="Sx4.p12.26.m26.1.1.1.cmml" xref="Sx4.p12.26.m26.1.1.1"><ci id="Sx4.p12.26.m26.1.1.1.1.cmml" xref="Sx4.p12.26.m26.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.26.m26.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.26.m26.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>LB <math alttext="-" class="ltx_Math" display="inline" id="Sx4.p12.27.m27.1"><semantics id="Sx4.p12.27.m27.1a"><mo id="Sx4.p12.27.m27.1.1" xref="Sx4.p12.27.m27.1.1.cmml">−</mo><annotation-xml encoding="MathML-Content" id="Sx4.p12.27.m27.1b"><minus id="Sx4.p12.27.m27.1.1.cmml" xref="Sx4.p12.27.m27.1.1"></minus></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.27.m27.1c">-</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.27.m27.1d">-</annotation></semantics></math> LDLB<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx4.p12.28.m28.1"><semantics id="Sx4.p12.28.m28.1a"><msup id="Sx4.p12.28.m28.1.1" xref="Sx4.p12.28.m28.1.1.cmml"><mi id="Sx4.p12.28.m28.1.1a" xref="Sx4.p12.28.m28.1.1.cmml"></mi><msup id="Sx4.p12.28.m28.1.1.1" xref="Sx4.p12.28.m28.1.1.1.cmml"><mi id="Sx4.p12.28.m28.1.1.1a" xref="Sx4.p12.28.m28.1.1.1.cmml"></mi><mo id="Sx4.p12.28.m28.1.1.1.1" xref="Sx4.p12.28.m28.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx4.p12.28.m28.1b"><apply id="Sx4.p12.28.m28.1.1.cmml" xref="Sx4.p12.28.m28.1.1"><apply id="Sx4.p12.28.m28.1.1.1.cmml" xref="Sx4.p12.28.m28.1.1.1"><ci id="Sx4.p12.28.m28.1.1.1.1.cmml" xref="Sx4.p12.28.m28.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.28.m28.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.28.m28.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>) and the term 0.5(CD<sub class="ltx_sub" id="Sx4.p12.47.13"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.13.1">m3</span></sub> + CD<sub class="ltx_sub" id="Sx4.p12.47.14"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.14.1">m4</span></sub>) (i.e., the observed CD, CD<sub class="ltx_sub" id="Sx4.p12.47.15">obs</sub>, from the back side) corresponds to CD<math alttext="{}_{\textrm{iso}}-" class="ltx_math_unparsed" display="inline" id="Sx4.p12.32.m32.1"><semantics id="Sx4.p12.32.m32.1a"><mmultiscripts id="Sx4.p12.32.m32.1.1"><mo id="Sx4.p12.32.m32.1.1.2">−</mo><mprescripts id="Sx4.p12.32.m32.1.1a"></mprescripts><mtext id="Sx4.p12.32.m32.1.1.3">iso</mtext><mrow id="Sx4.p12.32.m32.1.1b"></mrow></mmultiscripts><annotation encoding="application/x-tex" id="Sx4.p12.32.m32.1b">{}_{\textrm{iso}}-</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.32.m32.1c">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT -</annotation></semantics></math> 0.5(LD<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx4.p12.33.m33.1"><semantics id="Sx4.p12.33.m33.1a"><msup id="Sx4.p12.33.m33.1.1" xref="Sx4.p12.33.m33.1.1.cmml"><mi id="Sx4.p12.33.m33.1.1a" xref="Sx4.p12.33.m33.1.1.cmml"></mi><msup id="Sx4.p12.33.m33.1.1.1" xref="Sx4.p12.33.m33.1.1.1.cmml"><mi id="Sx4.p12.33.m33.1.1.1a" xref="Sx4.p12.33.m33.1.1.1.cmml"></mi><mo id="Sx4.p12.33.m33.1.1.1.1" xref="Sx4.p12.33.m33.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx4.p12.33.m33.1b"><apply id="Sx4.p12.33.m33.1.1.cmml" xref="Sx4.p12.33.m33.1.1"><apply id="Sx4.p12.33.m33.1.1.1.cmml" xref="Sx4.p12.33.m33.1.1.1"><ci id="Sx4.p12.33.m33.1.1.1.1.cmml" xref="Sx4.p12.33.m33.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.33.m33.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.33.m33.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>LB <math alttext="-" class="ltx_Math" display="inline" id="Sx4.p12.34.m34.1"><semantics id="Sx4.p12.34.m34.1a"><mo id="Sx4.p12.34.m34.1.1" xref="Sx4.p12.34.m34.1.1.cmml">−</mo><annotation-xml encoding="MathML-Content" id="Sx4.p12.34.m34.1b"><minus id="Sx4.p12.34.m34.1.1.cmml" xref="Sx4.p12.34.m34.1.1"></minus></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.34.m34.1c">-</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.34.m34.1d">-</annotation></semantics></math> LDLB<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx4.p12.35.m35.1"><semantics id="Sx4.p12.35.m35.1a"><msup id="Sx4.p12.35.m35.1.1" xref="Sx4.p12.35.m35.1.1.cmml"><mi id="Sx4.p12.35.m35.1.1a" xref="Sx4.p12.35.m35.1.1.cmml"></mi><msup id="Sx4.p12.35.m35.1.1.1" xref="Sx4.p12.35.m35.1.1.1.cmml"><mi id="Sx4.p12.35.m35.1.1.1a" xref="Sx4.p12.35.m35.1.1.1.cmml"></mi><mo id="Sx4.p12.35.m35.1.1.1.1" xref="Sx4.p12.35.m35.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx4.p12.35.m35.1b"><apply id="Sx4.p12.35.m35.1.1.cmml" xref="Sx4.p12.35.m35.1.1"><apply id="Sx4.p12.35.m35.1.1.1.cmml" xref="Sx4.p12.35.m35.1.1.1"><ci id="Sx4.p12.35.m35.1.1.1.1.cmml" xref="Sx4.p12.35.m35.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.35.m35.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.35.m35.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>). Hence, CD<math alttext="{}_{\textrm{iso}}" class="ltx_Math" display="inline" id="Sx4.p12.36.m36.1"><semantics id="Sx4.p12.36.m36.1a"><msub id="Sx4.p12.36.m36.1.1" xref="Sx4.p12.36.m36.1.1.cmml"><mi id="Sx4.p12.36.m36.1.1a" xref="Sx4.p12.36.m36.1.1.cmml"></mi><mtext id="Sx4.p12.36.m36.1.1.1" xref="Sx4.p12.36.m36.1.1.1a.cmml">iso</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx4.p12.36.m36.1b"><apply id="Sx4.p12.36.m36.1.1.cmml" xref="Sx4.p12.36.m36.1.1"><ci id="Sx4.p12.36.m36.1.1.1a.cmml" xref="Sx4.p12.36.m36.1.1.1"><mtext id="Sx4.p12.36.m36.1.1.1.cmml" mathsize="70%" xref="Sx4.p12.36.m36.1.1.1">iso</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.36.m36.1c">{}_{\textrm{iso}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.36.m36.1d">start_FLOATSUBSCRIPT iso end_FLOATSUBSCRIPT</annotation></semantics></math> = 0.25(CD<sub class="ltx_sub" id="Sx4.p12.47.16"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.16.1">m1</span></sub> + CD<sub class="ltx_sub" id="Sx4.p12.47.17"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.17.1">m2</span></sub> + CD<sub class="ltx_sub" id="Sx4.p12.47.18"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.18.1">m3</span></sub> + CD<sub class="ltx_sub" id="Sx4.p12.47.19"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.19.1">m4</span></sub>) and 0.5(LD<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx4.p12.41.m41.1"><semantics id="Sx4.p12.41.m41.1a"><msup id="Sx4.p12.41.m41.1.1" xref="Sx4.p12.41.m41.1.1.cmml"><mi id="Sx4.p12.41.m41.1.1a" xref="Sx4.p12.41.m41.1.1.cmml"></mi><msup id="Sx4.p12.41.m41.1.1.1" xref="Sx4.p12.41.m41.1.1.1.cmml"><mi id="Sx4.p12.41.m41.1.1.1a" xref="Sx4.p12.41.m41.1.1.1.cmml"></mi><mo id="Sx4.p12.41.m41.1.1.1.1" xref="Sx4.p12.41.m41.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx4.p12.41.m41.1b"><apply id="Sx4.p12.41.m41.1.1.cmml" xref="Sx4.p12.41.m41.1.1"><apply id="Sx4.p12.41.m41.1.1.1.cmml" xref="Sx4.p12.41.m41.1.1.1"><ci id="Sx4.p12.41.m41.1.1.1.1.cmml" xref="Sx4.p12.41.m41.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.41.m41.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.41.m41.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>LB <math alttext="-" class="ltx_Math" display="inline" id="Sx4.p12.42.m42.1"><semantics id="Sx4.p12.42.m42.1a"><mo id="Sx4.p12.42.m42.1.1" xref="Sx4.p12.42.m42.1.1.cmml">−</mo><annotation-xml encoding="MathML-Content" id="Sx4.p12.42.m42.1b"><minus id="Sx4.p12.42.m42.1.1.cmml" xref="Sx4.p12.42.m42.1.1"></minus></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.42.m42.1c">-</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.42.m42.1d">-</annotation></semantics></math> LDLB<math alttext="{}^{{}^{\prime}}" class="ltx_Math" display="inline" id="Sx4.p12.43.m43.1"><semantics id="Sx4.p12.43.m43.1a"><msup id="Sx4.p12.43.m43.1.1" xref="Sx4.p12.43.m43.1.1.cmml"><mi id="Sx4.p12.43.m43.1.1a" xref="Sx4.p12.43.m43.1.1.cmml"></mi><msup id="Sx4.p12.43.m43.1.1.1" xref="Sx4.p12.43.m43.1.1.1.cmml"><mi id="Sx4.p12.43.m43.1.1.1a" xref="Sx4.p12.43.m43.1.1.1.cmml"></mi><mo id="Sx4.p12.43.m43.1.1.1.1" xref="Sx4.p12.43.m43.1.1.1.1.cmml">′</mo></msup></msup><annotation-xml encoding="MathML-Content" id="Sx4.p12.43.m43.1b"><apply id="Sx4.p12.43.m43.1.1.cmml" xref="Sx4.p12.43.m43.1.1"><apply id="Sx4.p12.43.m43.1.1.1.cmml" xref="Sx4.p12.43.m43.1.1.1"><ci id="Sx4.p12.43.m43.1.1.1.1.cmml" xref="Sx4.p12.43.m43.1.1.1.1">′</ci></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p12.43.m43.1c">{}^{{}^{\prime}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.43.m43.1d">start_FLOATSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_FLOATSUPERSCRIPT</annotation></semantics></math>) = 0.25(CD<sub class="ltx_sub" id="Sx4.p12.47.20"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.20.1">m1</span></sub> + CD<math alttext="{}_{\mathrm{m2}}-" class="ltx_math_unparsed" display="inline" id="Sx4.p12.45.m45.1"><semantics id="Sx4.p12.45.m45.1a"><mmultiscripts id="Sx4.p12.45.m45.1.1"><mo id="Sx4.p12.45.m45.1.1.2">−</mo><mprescripts id="Sx4.p12.45.m45.1.1a"></mprescripts><mi id="Sx4.p12.45.m45.1.1.3">m2</mi><mrow id="Sx4.p12.45.m45.1.1b"></mrow></mmultiscripts><annotation encoding="application/x-tex" id="Sx4.p12.45.m45.1b">{}_{\mathrm{m2}}-</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.45.m45.1c">start_FLOATSUBSCRIPT m2 end_FLOATSUBSCRIPT -</annotation></semantics></math> CD<math alttext="{}_{\mathrm{m3}}-" class="ltx_math_unparsed" display="inline" id="Sx4.p12.46.m46.1"><semantics id="Sx4.p12.46.m46.1a"><mmultiscripts id="Sx4.p12.46.m46.1.1"><mo id="Sx4.p12.46.m46.1.1.2">−</mo><mprescripts id="Sx4.p12.46.m46.1.1a"></mprescripts><mi id="Sx4.p12.46.m46.1.1.3">m3</mi><mrow id="Sx4.p12.46.m46.1.1b"></mrow></mmultiscripts><annotation encoding="application/x-tex" id="Sx4.p12.46.m46.1b">{}_{\mathrm{m3}}-</annotation><annotation encoding="application/x-llamapun" id="Sx4.p12.46.m46.1c">start_FLOATSUBSCRIPT m3 end_FLOATSUBSCRIPT -</annotation></semantics></math> CD<sub class="ltx_sub" id="Sx4.p12.47.21"><span class="ltx_text ltx_font_italic" id="Sx4.p12.47.21.1">m4</span></sub>).</p> </div> <div class="ltx_para ltx_noindent" id="Sx4.p13"> <p class="ltx_p" id="Sx4.p13.1"><span class="ltx_text ltx_font_bold" id="Sx4.p13.1.1">Linear- and circular-polarization dependent optical spectroscopy</span> – CD spectra and average absorption spectra of LCP and RCP light were measured using a Jasco J-810 CD spectrometer, covering a wavelength range of <math alttext="200-900" class="ltx_Math" display="inline" id="Sx4.p13.1.m1.1"><semantics id="Sx4.p13.1.m1.1a"><mrow id="Sx4.p13.1.m1.1.1" xref="Sx4.p13.1.m1.1.1.cmml"><mn id="Sx4.p13.1.m1.1.1.2" xref="Sx4.p13.1.m1.1.1.2.cmml">200</mn><mo id="Sx4.p13.1.m1.1.1.1" xref="Sx4.p13.1.m1.1.1.1.cmml">−</mo><mn id="Sx4.p13.1.m1.1.1.3" xref="Sx4.p13.1.m1.1.1.3.cmml">900</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p13.1.m1.1b"><apply id="Sx4.p13.1.m1.1.1.cmml" xref="Sx4.p13.1.m1.1.1"><minus id="Sx4.p13.1.m1.1.1.1.cmml" xref="Sx4.p13.1.m1.1.1.1"></minus><cn id="Sx4.p13.1.m1.1.1.2.cmml" type="integer" xref="Sx4.p13.1.m1.1.1.2">200</cn><cn id="Sx4.p13.1.m1.1.1.3.cmml" type="integer" xref="Sx4.p13.1.m1.1.1.3">900</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p13.1.m1.1c">200-900</annotation><annotation encoding="application/x-llamapun" id="Sx4.p13.1.m1.1d">200 - 900</annotation></semantics></math> nm. Linearly polarized absorption spectra were measured using an ultraviolet–visible-near-infrared (UV–vis-NIR) spectrometer (Perkin Elmer Lambda 950 UV–vis-NIR) equipped with an automatically controlled rotating broadband polarizer in the same wavelength range. The incident beam with a diameter of 2 mm was defined by a customized 3D-printed sample holder, and was the same in all measurements. In the design and fitting of heterostructures, the thicknesses of aligned CNT films were benchmarked by comparing the peak average absorption of LCP and RCP light in the UV range with that of a reference sample whose thickness was measured using an atomic force microscope (Parksystems NX20) <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib17" title="">17</a>]</cite>. The peak average UV absorption was assumed to be proportional to the sample thickness.</p> </div> <div class="ltx_para ltx_noindent" id="Sx4.p14"> <p class="ltx_p" id="Sx4.p14.1"><span class="ltx_text ltx_font_bold" id="Sx4.p14.1.1">Measurement of dielectric functions of aligned CNTs</span> – The dielectric functions parallel and perpendicular to the CNT alignment direction from the UV to NIR ranges were modeled as a summation of Voigt functions <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib48" title="">48</a>]</cite></p> </div> <div class="ltx_para" id="Sx4.p15"> <table class="ltx_equation ltx_eqn_table" id="Sx4.E19"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="\epsilon_{s,p}(\omega)=\epsilon_{\infty,s,p}+\sum_{n=1}^{N}\left.C_{\textrm{V}% 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end_POSTSUBSCRIPT end_POSTSUBSCRIPT</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(19)</span></td> </tr></tbody> </table> <p class="ltx_p" id="Sx4.p15.14">with</p> <table class="ltx_equationgroup ltx_eqn_align ltx_eqn_table" id="Sx8.EGx2"> <tbody id="Sx4.E20"><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_td ltx_align_right ltx_eqn_cell"><math alttext="\displaystyle\left.C_{\textrm{V}}(\omega)\right|_{A,\omega_{0},\gamma_{\textrm% {L}},\gamma_{\textrm{G}}}" class="ltx_Math" display="inline" id="Sx4.E20.m1.6"><semantics id="Sx4.E20.m1.6a"><msub id="Sx4.E20.m1.6.6.1" xref="Sx4.E20.m1.6.6.2.cmml"><mrow id="Sx4.E20.m1.6.6.1.1" xref="Sx4.E20.m1.6.6.2.cmml"><mrow id="Sx4.E20.m1.6.6.1.1.1" xref="Sx4.E20.m1.6.6.1.1.1.cmml"><msub 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))}{\textrm{Re}(F(\textrm{i}y))}</annotation><annotation encoding="application/x-llamapun" id="Sx4.E20.m2.2d">= - italic_A divide start_ARG Im ( italic_F ( italic_x - italic_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT - i italic_y ) + italic_F ( italic_x + italic_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT + i italic_y ) ) end_ARG start_ARG Re ( italic_F ( i italic_y ) ) end_ARG</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(20)</span></td> </tr></tbody> <tbody id="Sx4.E21"><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_td ltx_eqn_cell"></td> <td class="ltx_td ltx_align_left ltx_eqn_cell"><math alttext="\displaystyle+\textrm{i}A\frac{\textrm{Re}(F(x-x_{0}+\textrm{i}y)-F(x+x_{0}+% \textrm{i}y))}{\textrm{Re}(F(\textrm{i}y))}" 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id="Sx4.E21.m1.2.2.2.1.1.1.1.1.1.1.cmml" xref="Sx4.E21.m1.2.2.2.1.1.1.1.1.1.1"></times><ci id="Sx4.E21.m1.2.2.2.1.1.1.1.1.1.2a.cmml" xref="Sx4.E21.m1.2.2.2.1.1.1.1.1.1.2"><mtext id="Sx4.E21.m1.2.2.2.1.1.1.1.1.1.2.cmml" xref="Sx4.E21.m1.2.2.2.1.1.1.1.1.1.2">i</mtext></ci><ci id="Sx4.E21.m1.2.2.2.1.1.1.1.1.1.3.cmml" xref="Sx4.E21.m1.2.2.2.1.1.1.1.1.1.3">𝑦</ci></apply></apply></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.E21.m1.2c">\displaystyle+\textrm{i}A\frac{\textrm{Re}(F(x-x_{0}+\textrm{i}y)-F(x+x_{0}+% \textrm{i}y))}{\textrm{Re}(F(\textrm{i}y))}</annotation><annotation encoding="application/x-llamapun" id="Sx4.E21.m1.2d">+ i italic_A divide start_ARG Re ( italic_F ( italic_x - italic_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT + i italic_y ) - italic_F ( italic_x + italic_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT + i italic_y ) ) end_ARG start_ARG Re ( italic_F ( i italic_y ) ) end_ARG</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(21)</span></td> </tr></tbody> </table> <p class="ltx_p" id="Sx4.p15.15">and</p> <table class="ltx_equation ltx_eqn_table" id="Sx4.E22"> <tbody><tr class="ltx_equation ltx_eqn_row ltx_align_baseline"> <td class="ltx_eqn_cell ltx_eqn_left_padleft"></td> <td class="ltx_eqn_cell ltx_align_left"><math alttext="x=\frac{2\sqrt{\textrm{ln}2}}{\gamma_{\textrm{G}}}\omega,x_{0}=\frac{2\sqrt{% \textrm{ln}2}}{\gamma_{\textrm{G}}}\omega_{0},y=\frac{\gamma_{\textrm{L}}\sqrt% {\textrm{ln}2}}{\gamma_{\textrm{G}}}," class="ltx_Math" display="block" id="Sx4.E22.m1.1"><semantics id="Sx4.E22.m1.1a"><mrow id="Sx4.E22.m1.1.1.1"><mrow id="Sx4.E22.m1.1.1.1.1.2" xref="Sx4.E22.m1.1.1.1.1.3.cmml"><mrow id="Sx4.E22.m1.1.1.1.1.1.1" xref="Sx4.E22.m1.1.1.1.1.1.1.cmml"><mi id="Sx4.E22.m1.1.1.1.1.1.1.2" 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xref="Sx4.E22.m1.1.1.1.1.2.2.1.1.3.3">subscript</csymbol><ci id="Sx4.E22.m1.1.1.1.1.2.2.1.1.3.3.2.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.1.1.3.3.2">𝜔</ci><cn id="Sx4.E22.m1.1.1.1.1.2.2.1.1.3.3.3.cmml" type="integer" xref="Sx4.E22.m1.1.1.1.1.2.2.1.1.3.3.3">0</cn></apply></apply></apply><apply id="Sx4.E22.m1.1.1.1.1.2.2.2.2.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2"><eq id="Sx4.E22.m1.1.1.1.1.2.2.2.2.1.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.1"></eq><ci id="Sx4.E22.m1.1.1.1.1.2.2.2.2.2.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.2">𝑦</ci><apply id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3"><divide id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.1.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3"></divide><apply id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2"><times id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.1.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.1"></times><apply id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.2.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.2"><csymbol cd="ambiguous" id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.2.1.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.2">subscript</csymbol><ci id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.2.2.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.2.2">𝛾</ci><ci id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.2.3a.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.2.3"><mtext id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.2.3.cmml" mathsize="70%" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.2.3">L</mtext></ci></apply><apply id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3"><root id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3a.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3"></root><apply id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.2.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.2"><times id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.2.1.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.2.1"></times><ci id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.2.2a.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.2.2"><mtext id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.2.2.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.2.2">ln</mtext></ci><cn id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.2.3.cmml" type="integer" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.2.3.2.3">2</cn></apply></apply></apply><apply id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.3.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.3"><csymbol cd="ambiguous" id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.3.1.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.3">subscript</csymbol><ci id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.3.2.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.3.2">𝛾</ci><ci id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.3.3a.cmml" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.3.3"><mtext id="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.3.3.cmml" mathsize="70%" xref="Sx4.E22.m1.1.1.1.1.2.2.2.2.3.3.3">G</mtext></ci></apply></apply></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.E22.m1.1c">x=\frac{2\sqrt{\textrm{ln}2}}{\gamma_{\textrm{G}}}\omega,x_{0}=\frac{2\sqrt{% \textrm{ln}2}}{\gamma_{\textrm{G}}}\omega_{0},y=\frac{\gamma_{\textrm{L}}\sqrt% {\textrm{ln}2}}{\gamma_{\textrm{G}}},</annotation><annotation encoding="application/x-llamapun" id="Sx4.E22.m1.1d">italic_x = divide start_ARG 2 square-root start_ARG ln 2 end_ARG end_ARG start_ARG italic_γ start_POSTSUBSCRIPT G end_POSTSUBSCRIPT end_ARG italic_ω , italic_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = divide start_ARG 2 square-root start_ARG ln 2 end_ARG end_ARG start_ARG italic_γ start_POSTSUBSCRIPT G end_POSTSUBSCRIPT end_ARG italic_ω start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT , italic_y = divide start_ARG italic_γ start_POSTSUBSCRIPT L end_POSTSUBSCRIPT square-root start_ARG ln 2 end_ARG end_ARG start_ARG italic_γ start_POSTSUBSCRIPT G end_POSTSUBSCRIPT end_ARG ,</annotation></semantics></math></td> <td class="ltx_eqn_cell ltx_eqn_left_padright"></td> <td class="ltx_eqn_cell ltx_eqn_eqno ltx_align_middle ltx_align_right" rowspan="1"><span class="ltx_tag ltx_tag_equation ltx_align_right">(22)</span></td> </tr></tbody> </table> <p class="ltx_p" id="Sx4.p15.13">where <math alttext="\omega" class="ltx_Math" display="inline" id="Sx4.p15.1.m1.1"><semantics id="Sx4.p15.1.m1.1a"><mi id="Sx4.p15.1.m1.1.1" xref="Sx4.p15.1.m1.1.1.cmml">ω</mi><annotation-xml encoding="MathML-Content" id="Sx4.p15.1.m1.1b"><ci id="Sx4.p15.1.m1.1.1.cmml" xref="Sx4.p15.1.m1.1.1">𝜔</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p15.1.m1.1c">\omega</annotation><annotation encoding="application/x-llamapun" id="Sx4.p15.1.m1.1d">italic_ω</annotation></semantics></math> is angular frequency, <math alttext="A" class="ltx_Math" display="inline" id="Sx4.p15.2.m2.1"><semantics id="Sx4.p15.2.m2.1a"><mi id="Sx4.p15.2.m2.1.1" xref="Sx4.p15.2.m2.1.1.cmml">A</mi><annotation-xml encoding="MathML-Content" id="Sx4.p15.2.m2.1b"><ci id="Sx4.p15.2.m2.1.1.cmml" xref="Sx4.p15.2.m2.1.1">𝐴</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p15.2.m2.1c">A</annotation><annotation encoding="application/x-llamapun" id="Sx4.p15.2.m2.1d">italic_A</annotation></semantics></math> is amplitude factor, <math alttext="\omega_{0}" class="ltx_Math" display="inline" id="Sx4.p15.3.m3.1"><semantics id="Sx4.p15.3.m3.1a"><msub id="Sx4.p15.3.m3.1.1" xref="Sx4.p15.3.m3.1.1.cmml"><mi id="Sx4.p15.3.m3.1.1.2" xref="Sx4.p15.3.m3.1.1.2.cmml">ω</mi><mn id="Sx4.p15.3.m3.1.1.3" xref="Sx4.p15.3.m3.1.1.3.cmml">0</mn></msub><annotation-xml encoding="MathML-Content" id="Sx4.p15.3.m3.1b"><apply id="Sx4.p15.3.m3.1.1.cmml" xref="Sx4.p15.3.m3.1.1"><csymbol cd="ambiguous" id="Sx4.p15.3.m3.1.1.1.cmml" xref="Sx4.p15.3.m3.1.1">subscript</csymbol><ci id="Sx4.p15.3.m3.1.1.2.cmml" xref="Sx4.p15.3.m3.1.1.2">𝜔</ci><cn id="Sx4.p15.3.m3.1.1.3.cmml" type="integer" xref="Sx4.p15.3.m3.1.1.3">0</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p15.3.m3.1c">\omega_{0}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p15.3.m3.1d">italic_ω start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT</annotation></semantics></math> is resonance frequency, <math alttext="\gamma_{\textrm{L}}" class="ltx_Math" display="inline" id="Sx4.p15.4.m4.1"><semantics id="Sx4.p15.4.m4.1a"><msub id="Sx4.p15.4.m4.1.1" xref="Sx4.p15.4.m4.1.1.cmml"><mi id="Sx4.p15.4.m4.1.1.2" xref="Sx4.p15.4.m4.1.1.2.cmml">γ</mi><mtext id="Sx4.p15.4.m4.1.1.3" xref="Sx4.p15.4.m4.1.1.3a.cmml">L</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx4.p15.4.m4.1b"><apply id="Sx4.p15.4.m4.1.1.cmml" xref="Sx4.p15.4.m4.1.1"><csymbol cd="ambiguous" id="Sx4.p15.4.m4.1.1.1.cmml" xref="Sx4.p15.4.m4.1.1">subscript</csymbol><ci id="Sx4.p15.4.m4.1.1.2.cmml" xref="Sx4.p15.4.m4.1.1.2">𝛾</ci><ci id="Sx4.p15.4.m4.1.1.3a.cmml" xref="Sx4.p15.4.m4.1.1.3"><mtext id="Sx4.p15.4.m4.1.1.3.cmml" mathsize="70%" xref="Sx4.p15.4.m4.1.1.3">L</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p15.4.m4.1c">\gamma_{\textrm{L}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p15.4.m4.1d">italic_γ start_POSTSUBSCRIPT L end_POSTSUBSCRIPT</annotation></semantics></math> is Lorentz linewidth, <math alttext="\gamma_{\textrm{G}}" class="ltx_Math" display="inline" id="Sx4.p15.5.m5.1"><semantics id="Sx4.p15.5.m5.1a"><msub id="Sx4.p15.5.m5.1.1" xref="Sx4.p15.5.m5.1.1.cmml"><mi id="Sx4.p15.5.m5.1.1.2" xref="Sx4.p15.5.m5.1.1.2.cmml">γ</mi><mtext id="Sx4.p15.5.m5.1.1.3" xref="Sx4.p15.5.m5.1.1.3a.cmml">G</mtext></msub><annotation-xml encoding="MathML-Content" id="Sx4.p15.5.m5.1b"><apply id="Sx4.p15.5.m5.1.1.cmml" xref="Sx4.p15.5.m5.1.1"><csymbol cd="ambiguous" id="Sx4.p15.5.m5.1.1.1.cmml" xref="Sx4.p15.5.m5.1.1">subscript</csymbol><ci id="Sx4.p15.5.m5.1.1.2.cmml" xref="Sx4.p15.5.m5.1.1.2">𝛾</ci><ci id="Sx4.p15.5.m5.1.1.3a.cmml" xref="Sx4.p15.5.m5.1.1.3"><mtext id="Sx4.p15.5.m5.1.1.3.cmml" mathsize="70%" xref="Sx4.p15.5.m5.1.1.3">G</mtext></ci></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p15.5.m5.1c">\gamma_{\textrm{G}}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p15.5.m5.1d">italic_γ start_POSTSUBSCRIPT G end_POSTSUBSCRIPT</annotation></semantics></math> is Gaussian linewidth, and <math alttext="F" class="ltx_Math" display="inline" id="Sx4.p15.6.m6.1"><semantics id="Sx4.p15.6.m6.1a"><mi id="Sx4.p15.6.m6.1.1" xref="Sx4.p15.6.m6.1.1.cmml">F</mi><annotation-xml encoding="MathML-Content" id="Sx4.p15.6.m6.1b"><ci id="Sx4.p15.6.m6.1.1.cmml" xref="Sx4.p15.6.m6.1.1">𝐹</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p15.6.m6.1c">F</annotation><annotation encoding="application/x-llamapun" id="Sx4.p15.6.m6.1d">italic_F</annotation></semantics></math> is Faddeeva function. <math alttext="N" class="ltx_Math" display="inline" id="Sx4.p15.7.m7.1"><semantics id="Sx4.p15.7.m7.1a"><mi id="Sx4.p15.7.m7.1.1" xref="Sx4.p15.7.m7.1.1.cmml">N</mi><annotation-xml encoding="MathML-Content" id="Sx4.p15.7.m7.1b"><ci id="Sx4.p15.7.m7.1.1.cmml" 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Hence, for each polarization (<math alttext="s" class="ltx_Math" display="inline" id="Sx4.p15.8.m8.1"><semantics id="Sx4.p15.8.m8.1a"><mi id="Sx4.p15.8.m8.1.1" xref="Sx4.p15.8.m8.1.1.cmml">s</mi><annotation-xml encoding="MathML-Content" id="Sx4.p15.8.m8.1b"><ci id="Sx4.p15.8.m8.1.1.cmml" xref="Sx4.p15.8.m8.1.1">𝑠</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p15.8.m8.1c">s</annotation><annotation encoding="application/x-llamapun" id="Sx4.p15.8.m8.1d">italic_s</annotation></semantics></math> or <math alttext="p" class="ltx_Math" display="inline" id="Sx4.p15.9.m9.1"><semantics id="Sx4.p15.9.m9.1a"><mi id="Sx4.p15.9.m9.1.1" xref="Sx4.p15.9.m9.1.1.cmml">p</mi><annotation-xml encoding="MathML-Content" id="Sx4.p15.9.m9.1b"><ci id="Sx4.p15.9.m9.1.1.cmml" xref="Sx4.p15.9.m9.1.1">𝑝</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p15.9.m9.1c">p</annotation><annotation encoding="application/x-llamapun" id="Sx4.p15.9.m9.1d">italic_p</annotation></semantics></math>), there were 21 fitting parameters, including {<math alttext="A_{n},\omega_{0,n},\gamma_{\textrm{L},n},\gamma_{\textrm{G},n}" class="ltx_Math" display="inline" id="Sx4.p15.10.m10.10"><semantics id="Sx4.p15.10.m10.10a"><mrow id="Sx4.p15.10.m10.10.10.4" xref="Sx4.p15.10.m10.10.10.5.cmml"><msub id="Sx4.p15.10.m10.7.7.1.1" xref="Sx4.p15.10.m10.7.7.1.1.cmml"><mi id="Sx4.p15.10.m10.7.7.1.1.2" xref="Sx4.p15.10.m10.7.7.1.1.2.cmml">A</mi><mi id="Sx4.p15.10.m10.7.7.1.1.3" xref="Sx4.p15.10.m10.7.7.1.1.3.cmml">n</mi></msub><mo id="Sx4.p15.10.m10.10.10.4.5" xref="Sx4.p15.10.m10.10.10.5.cmml">,</mo><msub id="Sx4.p15.10.m10.8.8.2.2" xref="Sx4.p15.10.m10.8.8.2.2.cmml"><mi id="Sx4.p15.10.m10.8.8.2.2.2" xref="Sx4.p15.10.m10.8.8.2.2.2.cmml">ω</mi><mrow id="Sx4.p15.10.m10.2.2.2.4" xref="Sx4.p15.10.m10.2.2.2.3.cmml"><mn id="Sx4.p15.10.m10.1.1.1.1" xref="Sx4.p15.10.m10.1.1.1.1.cmml">0</mn><mo id="Sx4.p15.10.m10.2.2.2.4.1" 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id="Sx4.p15.10.m10.10.10.4.4.2.cmml" xref="Sx4.p15.10.m10.10.10.4.4.2">𝛾</ci><list id="Sx4.p15.10.m10.6.6.2.3.cmml" xref="Sx4.p15.10.m10.6.6.2.4"><ci id="Sx4.p15.10.m10.5.5.1.1a.cmml" xref="Sx4.p15.10.m10.5.5.1.1"><mtext id="Sx4.p15.10.m10.5.5.1.1.cmml" mathsize="70%" xref="Sx4.p15.10.m10.5.5.1.1">G</mtext></ci><ci id="Sx4.p15.10.m10.6.6.2.2.cmml" xref="Sx4.p15.10.m10.6.6.2.2">𝑛</ci></list></apply></list></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p15.10.m10.10c">A_{n},\omega_{0,n},\gamma_{\textrm{L},n},\gamma_{\textrm{G},n}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p15.10.m10.10d">italic_A start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT , italic_ω start_POSTSUBSCRIPT 0 , italic_n end_POSTSUBSCRIPT , italic_γ start_POSTSUBSCRIPT L , italic_n end_POSTSUBSCRIPT , italic_γ start_POSTSUBSCRIPT G , italic_n end_POSTSUBSCRIPT</annotation></semantics></math>, <math alttext="n=1-5" class="ltx_Math" display="inline" id="Sx4.p15.11.m11.1"><semantics id="Sx4.p15.11.m11.1a"><mrow id="Sx4.p15.11.m11.1.1" xref="Sx4.p15.11.m11.1.1.cmml"><mi id="Sx4.p15.11.m11.1.1.2" xref="Sx4.p15.11.m11.1.1.2.cmml">n</mi><mo id="Sx4.p15.11.m11.1.1.1" xref="Sx4.p15.11.m11.1.1.1.cmml">=</mo><mrow id="Sx4.p15.11.m11.1.1.3" xref="Sx4.p15.11.m11.1.1.3.cmml"><mn id="Sx4.p15.11.m11.1.1.3.2" xref="Sx4.p15.11.m11.1.1.3.2.cmml">1</mn><mo id="Sx4.p15.11.m11.1.1.3.1" xref="Sx4.p15.11.m11.1.1.3.1.cmml">−</mo><mn id="Sx4.p15.11.m11.1.1.3.3" xref="Sx4.p15.11.m11.1.1.3.3.cmml">5</mn></mrow></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p15.11.m11.1b"><apply id="Sx4.p15.11.m11.1.1.cmml" xref="Sx4.p15.11.m11.1.1"><eq id="Sx4.p15.11.m11.1.1.1.cmml" xref="Sx4.p15.11.m11.1.1.1"></eq><ci id="Sx4.p15.11.m11.1.1.2.cmml" xref="Sx4.p15.11.m11.1.1.2">𝑛</ci><apply id="Sx4.p15.11.m11.1.1.3.cmml" xref="Sx4.p15.11.m11.1.1.3"><minus id="Sx4.p15.11.m11.1.1.3.1.cmml" xref="Sx4.p15.11.m11.1.1.3.1"></minus><cn id="Sx4.p15.11.m11.1.1.3.2.cmml" type="integer" 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xref="Sx4.p15.12.m12.1.1.2">italic-ϵ</ci><infinity id="Sx4.p15.12.m12.1.1.3.cmml" xref="Sx4.p15.12.m12.1.1.3"></infinity></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p15.12.m12.1c">\epsilon_{\infty}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p15.12.m12.1d">italic_ϵ start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT</annotation></semantics></math>, and 42 fitting parameters in total for both polarizations. These fitting parameters were uniquely determined by simultaneously fit six experimentally measured spectra, including linear-polarization absorption spectra for one-layer aligned CNT film, and averaged absorption of LCP and RCP light and CD spectra of twisted two-layer and three-layer stacks with a twist angle of 30<sup class="ltx_sup" id="Sx4.p15.13.1"><span class="ltx_text ltx_font_italic" id="Sx4.p15.13.1.1">∘</span></sup>, as shown in Supplementary Fig. 4. The fitting wavelength range was from 600 nm to 800 nm wavelength.</p> </div> <div class="ltx_para ltx_noindent" id="Sx4.p16"> <p class="ltx_p" id="Sx4.p16.10"><span class="ltx_text ltx_font_bold" id="Sx4.p16.10.1">Measurement of dielectric functions of GST films</span> – The film thickness and optical constants (refractive index <math alttext="n" class="ltx_Math" display="inline" id="Sx4.p16.1.m1.1"><semantics id="Sx4.p16.1.m1.1a"><mi id="Sx4.p16.1.m1.1.1" xref="Sx4.p16.1.m1.1.1.cmml">n</mi><annotation-xml encoding="MathML-Content" id="Sx4.p16.1.m1.1b"><ci id="Sx4.p16.1.m1.1.1.cmml" xref="Sx4.p16.1.m1.1.1">𝑛</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p16.1.m1.1c">n</annotation><annotation encoding="application/x-llamapun" id="Sx4.p16.1.m1.1d">italic_n</annotation></semantics></math> and extinction coefficient <math alttext="k" class="ltx_Math" display="inline" id="Sx4.p16.2.m2.1"><semantics id="Sx4.p16.2.m2.1a"><mi id="Sx4.p16.2.m2.1.1" xref="Sx4.p16.2.m2.1.1.cmml">k</mi><annotation-xml encoding="MathML-Content" id="Sx4.p16.2.m2.1b"><ci id="Sx4.p16.2.m2.1.1.cmml" xref="Sx4.p16.2.m2.1.1">𝑘</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p16.2.m2.1c">k</annotation><annotation encoding="application/x-llamapun" id="Sx4.p16.2.m2.1d">italic_k</annotation></semantics></math>) of GST films were measured using a J.A. Woollam RC2 Spectroscopic Ellipsometer over a wavelength range of <math alttext="190-1700" class="ltx_Math" display="inline" id="Sx4.p16.3.m3.1"><semantics id="Sx4.p16.3.m3.1a"><mrow id="Sx4.p16.3.m3.1.1" xref="Sx4.p16.3.m3.1.1.cmml"><mn id="Sx4.p16.3.m3.1.1.2" xref="Sx4.p16.3.m3.1.1.2.cmml">190</mn><mo id="Sx4.p16.3.m3.1.1.1" xref="Sx4.p16.3.m3.1.1.1.cmml">−</mo><mn id="Sx4.p16.3.m3.1.1.3" xref="Sx4.p16.3.m3.1.1.3.cmml">1700</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p16.3.m3.1b"><apply id="Sx4.p16.3.m3.1.1.cmml" xref="Sx4.p16.3.m3.1.1"><minus id="Sx4.p16.3.m3.1.1.1.cmml" xref="Sx4.p16.3.m3.1.1.1"></minus><cn id="Sx4.p16.3.m3.1.1.2.cmml" type="integer" xref="Sx4.p16.3.m3.1.1.2">190</cn><cn id="Sx4.p16.3.m3.1.1.3.cmml" type="integer" xref="Sx4.p16.3.m3.1.1.3">1700</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p16.3.m3.1c">190-1700</annotation><annotation encoding="application/x-llamapun" id="Sx4.p16.3.m3.1d">190 - 1700</annotation></semantics></math> nm. The measurements were conducted over a wide spectral range from UV to NIR and were analyzed using CompleteEASE software. In this procedure, polarized light was reflected off the sample surface, and the change in polarization was measured as two quantities: <math alttext="\Psi" class="ltx_Math" display="inline" id="Sx4.p16.4.m4.1"><semantics id="Sx4.p16.4.m4.1a"><mi id="Sx4.p16.4.m4.1.1" mathvariant="normal" xref="Sx4.p16.4.m4.1.1.cmml">Ψ</mi><annotation-xml encoding="MathML-Content" id="Sx4.p16.4.m4.1b"><ci id="Sx4.p16.4.m4.1.1.cmml" xref="Sx4.p16.4.m4.1.1">Ψ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p16.4.m4.1c">\Psi</annotation><annotation encoding="application/x-llamapun" id="Sx4.p16.4.m4.1d">roman_Ψ</annotation></semantics></math> and <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx4.p16.5.m5.1"><semantics id="Sx4.p16.5.m5.1a"><mi id="Sx4.p16.5.m5.1.1" mathvariant="normal" xref="Sx4.p16.5.m5.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx4.p16.5.m5.1b"><ci id="Sx4.p16.5.m5.1.1.cmml" xref="Sx4.p16.5.m5.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p16.5.m5.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx4.p16.5.m5.1d">roman_Δ</annotation></semantics></math>. <math alttext="\Psi" class="ltx_Math" display="inline" id="Sx4.p16.6.m6.1"><semantics id="Sx4.p16.6.m6.1a"><mi id="Sx4.p16.6.m6.1.1" mathvariant="normal" xref="Sx4.p16.6.m6.1.1.cmml">Ψ</mi><annotation-xml encoding="MathML-Content" id="Sx4.p16.6.m6.1b"><ci id="Sx4.p16.6.m6.1.1.cmml" xref="Sx4.p16.6.m6.1.1">Ψ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p16.6.m6.1c">\Psi</annotation><annotation encoding="application/x-llamapun" id="Sx4.p16.6.m6.1d">roman_Ψ</annotation></semantics></math> represents the amplitude ratio and <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx4.p16.7.m7.1"><semantics id="Sx4.p16.7.m7.1a"><mi id="Sx4.p16.7.m7.1.1" mathvariant="normal" xref="Sx4.p16.7.m7.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx4.p16.7.m7.1b"><ci id="Sx4.p16.7.m7.1.1.cmml" xref="Sx4.p16.7.m7.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p16.7.m7.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx4.p16.7.m7.1d">roman_Δ</annotation></semantics></math> represents the phase difference. A model describing the sample’s physical structure (layers and materials) was created and adjusted to fit the measured <math alttext="\Psi" class="ltx_Math" display="inline" id="Sx4.p16.8.m8.1"><semantics id="Sx4.p16.8.m8.1a"><mi id="Sx4.p16.8.m8.1.1" mathvariant="normal" xref="Sx4.p16.8.m8.1.1.cmml">Ψ</mi><annotation-xml encoding="MathML-Content" id="Sx4.p16.8.m8.1b"><ci id="Sx4.p16.8.m8.1.1.cmml" xref="Sx4.p16.8.m8.1.1">Ψ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p16.8.m8.1c">\Psi</annotation><annotation encoding="application/x-llamapun" id="Sx4.p16.8.m8.1d">roman_Ψ</annotation></semantics></math> and <math alttext="\Delta" class="ltx_Math" display="inline" id="Sx4.p16.9.m9.1"><semantics id="Sx4.p16.9.m9.1a"><mi id="Sx4.p16.9.m9.1.1" mathvariant="normal" xref="Sx4.p16.9.m9.1.1.cmml">Δ</mi><annotation-xml encoding="MathML-Content" id="Sx4.p16.9.m9.1b"><ci id="Sx4.p16.9.m9.1.1.cmml" xref="Sx4.p16.9.m9.1.1">Δ</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p16.9.m9.1c">\Delta</annotation><annotation encoding="application/x-llamapun" id="Sx4.p16.9.m9.1d">roman_Δ</annotation></semantics></math> values through regression analysis. The software calculated results based on the model, and the model parameters (e.g., layer thicknesses, optical constants) were varied to minimize the mean-squared error between experimental and calculation results. The fitting process yielded the film thickness and the optical constants of the material. These optical constants include the real and imaginary parts of refractive indices, or alternatively, the real and imaginary parts of the dielectric function <math alttext="\varepsilon" class="ltx_Math" display="inline" id="Sx4.p16.10.m10.1"><semantics id="Sx4.p16.10.m10.1a"><mi id="Sx4.p16.10.m10.1.1" xref="Sx4.p16.10.m10.1.1.cmml">ε</mi><annotation-xml encoding="MathML-Content" id="Sx4.p16.10.m10.1b"><ci id="Sx4.p16.10.m10.1.1.cmml" xref="Sx4.p16.10.m10.1.1">𝜀</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p16.10.m10.1c">\varepsilon</annotation><annotation encoding="application/x-llamapun" id="Sx4.p16.10.m10.1d">italic_ε</annotation></semantics></math>.</p> </div> <div class="ltx_para ltx_noindent" id="Sx4.p17"> <p class="ltx_p" id="Sx4.p17.1"><span class="ltx_text ltx_font_bold" id="Sx4.p17.1.1">Backpropagation and Bayesian optimization algorithms</span> – The Adam optimizer in <span class="ltx_text ltx_font_typewriter" id="Sx4.p17.1.2">PyTorch</span> was employed for the backpropagation algorithm. The learning rate was set at 0.01. For Bayesian optimization, the results shown in Fig. <a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#Sx2.F3" title="Figure 3 ‣ Experimental demonstration ‣ Results ‣ A Programmable Wafer-scale Chiroptical Heterostructure of Twisted Aligned Carbon Nanotubes and Phase Change Materials"><span class="ltx_text ltx_ref_tag">3</span></a>c were obtained without the bound of the twist angle between aligned CNT films. For the results shown in Supplementary Fig. 5, the twist angle was bounded in a range of <math alttext="22.5-67.5^{\circ}" class="ltx_Math" display="inline" id="Sx4.p17.1.m1.1"><semantics id="Sx4.p17.1.m1.1a"><mrow id="Sx4.p17.1.m1.1.1" xref="Sx4.p17.1.m1.1.1.cmml"><mn id="Sx4.p17.1.m1.1.1.2" xref="Sx4.p17.1.m1.1.1.2.cmml">22.5</mn><mo id="Sx4.p17.1.m1.1.1.1" xref="Sx4.p17.1.m1.1.1.1.cmml">−</mo><msup id="Sx4.p17.1.m1.1.1.3" xref="Sx4.p17.1.m1.1.1.3.cmml"><mn id="Sx4.p17.1.m1.1.1.3.2" xref="Sx4.p17.1.m1.1.1.3.2.cmml">67.5</mn><mo id="Sx4.p17.1.m1.1.1.3.3" xref="Sx4.p17.1.m1.1.1.3.3.cmml">∘</mo></msup></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p17.1.m1.1b"><apply id="Sx4.p17.1.m1.1.1.cmml" xref="Sx4.p17.1.m1.1.1"><minus id="Sx4.p17.1.m1.1.1.1.cmml" xref="Sx4.p17.1.m1.1.1.1"></minus><cn id="Sx4.p17.1.m1.1.1.2.cmml" type="float" xref="Sx4.p17.1.m1.1.1.2">22.5</cn><apply id="Sx4.p17.1.m1.1.1.3.cmml" xref="Sx4.p17.1.m1.1.1.3"><csymbol cd="ambiguous" id="Sx4.p17.1.m1.1.1.3.1.cmml" xref="Sx4.p17.1.m1.1.1.3">superscript</csymbol><cn id="Sx4.p17.1.m1.1.1.3.2.cmml" type="float" xref="Sx4.p17.1.m1.1.1.3.2">67.5</cn><compose id="Sx4.p17.1.m1.1.1.3.3.cmml" xref="Sx4.p17.1.m1.1.1.3.3"></compose></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p17.1.m1.1c">22.5-67.5^{\circ}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p17.1.m1.1d">22.5 - 67.5 start_POSTSUPERSCRIPT ∘ end_POSTSUPERSCRIPT</annotation></semantics></math>. The accumulated average over all epochs was plotted.</p> </div> <div class="ltx_para ltx_noindent" id="Sx4.p18"> <p class="ltx_p" id="Sx4.p18.1"><span class="ltx_text ltx_font_bold" id="Sx4.p18.1.1">Heterostructure fabrication</span> – The heterostructure fabrication process consists of (i) transfer of aligned CNT films, (ii) deposition of GST and other dielectrics, and (iii) twist-stacking of aligned CNT films. The substrate was fused silica for broadband transparency. For (i), aligned CNT films were produced through the SAVF method as described before. The alignment direction was determined by the linear shaking direction. The produced film was typically cut into multiple pieces for twist-stacking and transferred onto the substrate or heterostructure using the wet transfer process as described before. For (ii), SiO<sub class="ltx_sub" id="Sx4.p18.1.2"><span class="ltx_text ltx_font_italic" id="Sx4.p18.1.2.1">2</span></sub> films were deposited using a Denton Discovery 18 Sputtering System at an argon pressure of 6 mTorr with a power setting of 100 W. GST films were deposited using the same system at an argon pressure of 4.5 mTorr and a power setting of 35 W. For (iii), to facilitate twist-stacking, the heterostructure was put onto a transparent protractor, which was back-illuminated by a light-emitting-diode panel. An aligned CNT film was placed on top of the heterostructure and the orientation was rotated to a specific angle relative to transferred aligned CNT films before. The film was then transferred using the same wet transfer process. To induce the phase transition in GST films, the heterostructure was placed on a hotplate (Corning hotplate and stirrer with digital display) at set temperatures and left for a few minutes for a complete phase transition.</p> </div> <div class="ltx_para ltx_noindent" id="Sx4.p19"> <p class="ltx_p" id="Sx4.p19.14"><span class="ltx_text ltx_font_bold" id="Sx4.p19.14.1">Finite element simulation</span> – A 2D finite element simulation using COMSOL Multiphysics was conducted to analyze the temperature distribution of the heterostructure under applied voltage and current. Because of the limited computer memory resource and wafer-scale sample sizes, the finite element model and thermal excitation were simultaneously scaled down. Specifically, the thickness or vertical dimension of the heterostructure was kept unchanged, while the lateral dimension was scaled down to <math alttext="500\times 500" class="ltx_Math" display="inline" id="Sx4.p19.1.m1.1"><semantics id="Sx4.p19.1.m1.1a"><mrow id="Sx4.p19.1.m1.1.1" xref="Sx4.p19.1.m1.1.1.cmml"><mn id="Sx4.p19.1.m1.1.1.2" xref="Sx4.p19.1.m1.1.1.2.cmml">500</mn><mo id="Sx4.p19.1.m1.1.1.1" lspace="0.222em" rspace="0.222em" xref="Sx4.p19.1.m1.1.1.1.cmml">×</mo><mn id="Sx4.p19.1.m1.1.1.3" xref="Sx4.p19.1.m1.1.1.3.cmml">500</mn></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p19.1.m1.1b"><apply id="Sx4.p19.1.m1.1.1.cmml" xref="Sx4.p19.1.m1.1.1"><times id="Sx4.p19.1.m1.1.1.1.cmml" xref="Sx4.p19.1.m1.1.1.1"></times><cn id="Sx4.p19.1.m1.1.1.2.cmml" type="integer" xref="Sx4.p19.1.m1.1.1.2">500</cn><cn id="Sx4.p19.1.m1.1.1.3.cmml" type="integer" xref="Sx4.p19.1.m1.1.1.3">500</cn></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p19.1.m1.1c">500\times 500</annotation><annotation encoding="application/x-llamapun" id="Sx4.p19.1.m1.1d">500 × 500</annotation></semantics></math> nm<sup class="ltx_sup" id="Sx4.p19.14.2">2</sup>. The thicknesses of the layers from top to bottom were 20 nm for the top CNT film, 71 nm for SiO<sub class="ltx_sub" id="Sx4.p19.14.3">2</sub>, 11 nm for GST, 68 nm for SiO<sub class="ltx_sub" id="Sx4.p19.14.4">2</sub>, and 20 nm for the bottom CNT film. The thermal conductivity of CNTs along the tube axis was set as 43 W m<sup class="ltx_sup" id="Sx4.p19.14.5"><span class="ltx_text ltx_font_italic" id="Sx4.p19.14.5.1">-1</span></sup> K<sup class="ltx_sup" id="Sx4.p19.14.6"><span class="ltx_text ltx_font_italic" id="Sx4.p19.14.6.1">-1</span></sup> <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib49" title="">49</a>]</cite>, and the GST thermal conductivity was set as 0.27 W m<sup class="ltx_sup" id="Sx4.p19.14.7"><span class="ltx_text ltx_font_italic" id="Sx4.p19.14.7.1">-1</span></sup> K<sup class="ltx_sup" id="Sx4.p19.14.8"><span class="ltx_text ltx_font_italic" id="Sx4.p19.14.8.1">-1</span></sup> <cite class="ltx_cite ltx_citemacro_cite">[<a class="ltx_ref" href="https://arxiv.org/html/2406.13190v1#bib.bib50" title="">50</a>]</cite>. The heat source was a square wave with a duration of 5 <math alttext="\mu" class="ltx_Math" display="inline" id="Sx4.p19.9.m9.1"><semantics id="Sx4.p19.9.m9.1a"><mi id="Sx4.p19.9.m9.1.1" xref="Sx4.p19.9.m9.1.1.cmml">μ</mi><annotation-xml encoding="MathML-Content" id="Sx4.p19.9.m9.1b"><ci id="Sx4.p19.9.m9.1.1.cmml" xref="Sx4.p19.9.m9.1.1">𝜇</ci></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p19.9.m9.1c">\mu</annotation><annotation encoding="application/x-llamapun" id="Sx4.p19.9.m9.1d">italic_μ</annotation></semantics></math>s and a power of <math alttext="3\times 10^{-5}" class="ltx_Math" display="inline" id="Sx4.p19.10.m10.1"><semantics id="Sx4.p19.10.m10.1a"><mrow id="Sx4.p19.10.m10.1.1" xref="Sx4.p19.10.m10.1.1.cmml"><mn id="Sx4.p19.10.m10.1.1.2" xref="Sx4.p19.10.m10.1.1.2.cmml">3</mn><mo id="Sx4.p19.10.m10.1.1.1" lspace="0.222em" rspace="0.222em" xref="Sx4.p19.10.m10.1.1.1.cmml">×</mo><msup id="Sx4.p19.10.m10.1.1.3" xref="Sx4.p19.10.m10.1.1.3.cmml"><mn id="Sx4.p19.10.m10.1.1.3.2" xref="Sx4.p19.10.m10.1.1.3.2.cmml">10</mn><mrow id="Sx4.p19.10.m10.1.1.3.3" xref="Sx4.p19.10.m10.1.1.3.3.cmml"><mo id="Sx4.p19.10.m10.1.1.3.3a" xref="Sx4.p19.10.m10.1.1.3.3.cmml">−</mo><mn id="Sx4.p19.10.m10.1.1.3.3.2" xref="Sx4.p19.10.m10.1.1.3.3.2.cmml">5</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p19.10.m10.1b"><apply id="Sx4.p19.10.m10.1.1.cmml" xref="Sx4.p19.10.m10.1.1"><times id="Sx4.p19.10.m10.1.1.1.cmml" xref="Sx4.p19.10.m10.1.1.1"></times><cn id="Sx4.p19.10.m10.1.1.2.cmml" type="integer" xref="Sx4.p19.10.m10.1.1.2">3</cn><apply id="Sx4.p19.10.m10.1.1.3.cmml" xref="Sx4.p19.10.m10.1.1.3"><csymbol cd="ambiguous" id="Sx4.p19.10.m10.1.1.3.1.cmml" xref="Sx4.p19.10.m10.1.1.3">superscript</csymbol><cn id="Sx4.p19.10.m10.1.1.3.2.cmml" type="integer" xref="Sx4.p19.10.m10.1.1.3.2">10</cn><apply id="Sx4.p19.10.m10.1.1.3.3.cmml" xref="Sx4.p19.10.m10.1.1.3.3"><minus id="Sx4.p19.10.m10.1.1.3.3.1.cmml" xref="Sx4.p19.10.m10.1.1.3.3"></minus><cn id="Sx4.p19.10.m10.1.1.3.3.2.cmml" type="integer" xref="Sx4.p19.10.m10.1.1.3.3.2">5</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p19.10.m10.1c">3\times 10^{-5}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p19.10.m10.1d">3 × 10 start_POSTSUPERSCRIPT - 5 end_POSTSUPERSCRIPT</annotation></semantics></math> W, resulting in a total heat energy of <math alttext="1.5\times 10^{-10}" class="ltx_Math" display="inline" id="Sx4.p19.11.m11.1"><semantics id="Sx4.p19.11.m11.1a"><mrow id="Sx4.p19.11.m11.1.1" xref="Sx4.p19.11.m11.1.1.cmml"><mn id="Sx4.p19.11.m11.1.1.2" xref="Sx4.p19.11.m11.1.1.2.cmml">1.5</mn><mo id="Sx4.p19.11.m11.1.1.1" lspace="0.222em" rspace="0.222em" xref="Sx4.p19.11.m11.1.1.1.cmml">×</mo><msup id="Sx4.p19.11.m11.1.1.3" xref="Sx4.p19.11.m11.1.1.3.cmml"><mn id="Sx4.p19.11.m11.1.1.3.2" xref="Sx4.p19.11.m11.1.1.3.2.cmml">10</mn><mrow id="Sx4.p19.11.m11.1.1.3.3" xref="Sx4.p19.11.m11.1.1.3.3.cmml"><mo id="Sx4.p19.11.m11.1.1.3.3a" xref="Sx4.p19.11.m11.1.1.3.3.cmml">−</mo><mn id="Sx4.p19.11.m11.1.1.3.3.2" xref="Sx4.p19.11.m11.1.1.3.3.2.cmml">10</mn></mrow></msup></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p19.11.m11.1b"><apply id="Sx4.p19.11.m11.1.1.cmml" xref="Sx4.p19.11.m11.1.1"><times id="Sx4.p19.11.m11.1.1.1.cmml" xref="Sx4.p19.11.m11.1.1.1"></times><cn id="Sx4.p19.11.m11.1.1.2.cmml" type="float" xref="Sx4.p19.11.m11.1.1.2">1.5</cn><apply id="Sx4.p19.11.m11.1.1.3.cmml" xref="Sx4.p19.11.m11.1.1.3"><csymbol cd="ambiguous" id="Sx4.p19.11.m11.1.1.3.1.cmml" xref="Sx4.p19.11.m11.1.1.3">superscript</csymbol><cn id="Sx4.p19.11.m11.1.1.3.2.cmml" type="integer" xref="Sx4.p19.11.m11.1.1.3.2">10</cn><apply id="Sx4.p19.11.m11.1.1.3.3.cmml" xref="Sx4.p19.11.m11.1.1.3.3"><minus id="Sx4.p19.11.m11.1.1.3.3.1.cmml" xref="Sx4.p19.11.m11.1.1.3.3"></minus><cn id="Sx4.p19.11.m11.1.1.3.3.2.cmml" type="integer" xref="Sx4.p19.11.m11.1.1.3.3.2">10</cn></apply></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p19.11.m11.1c">1.5\times 10^{-10}</annotation><annotation encoding="application/x-llamapun" id="Sx4.p19.11.m11.1d">1.5 × 10 start_POSTSUPERSCRIPT - 10 end_POSTSUPERSCRIPT</annotation></semantics></math> J. This was scaled down from the injected heat energy into our fabricated device with a lateral size of of 5 mm<math alttext="\times" class="ltx_Math" display="inline" id="Sx4.p19.12.m12.1"><semantics id="Sx4.p19.12.m12.1a"><mo id="Sx4.p19.12.m12.1.1" xref="Sx4.p19.12.m12.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="Sx4.p19.12.m12.1b"><times id="Sx4.p19.12.m12.1.1.cmml" xref="Sx4.p19.12.m12.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p19.12.m12.1c">\times</annotation><annotation encoding="application/x-llamapun" id="Sx4.p19.12.m12.1d">×</annotation></semantics></math>5 mm, which was estimated with a power <math alttext="1.1" class="ltx_Math" display="inline" id="Sx4.p19.13.m13.1"><semantics id="Sx4.p19.13.m13.1a"><mn id="Sx4.p19.13.m13.1.1" xref="Sx4.p19.13.m13.1.1.cmml">1.1</mn><annotation-xml encoding="MathML-Content" id="Sx4.p19.13.m13.1b"><cn id="Sx4.p19.13.m13.1.1.cmml" type="float" xref="Sx4.p19.13.m13.1.1">1.1</cn></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p19.13.m13.1c">1.1</annotation><annotation encoding="application/x-llamapun" id="Sx4.p19.13.m13.1d">1.1</annotation></semantics></math> W and phase transition time <math alttext="\sim 1-2" class="ltx_Math" display="inline" id="Sx4.p19.14.m14.1"><semantics id="Sx4.p19.14.m14.1a"><mrow id="Sx4.p19.14.m14.1.1" xref="Sx4.p19.14.m14.1.1.cmml"><mi id="Sx4.p19.14.m14.1.1.2" xref="Sx4.p19.14.m14.1.1.2.cmml"></mi><mo id="Sx4.p19.14.m14.1.1.1" xref="Sx4.p19.14.m14.1.1.1.cmml">∼</mo><mrow id="Sx4.p19.14.m14.1.1.3" xref="Sx4.p19.14.m14.1.1.3.cmml"><mn id="Sx4.p19.14.m14.1.1.3.2" xref="Sx4.p19.14.m14.1.1.3.2.cmml">1</mn><mo id="Sx4.p19.14.m14.1.1.3.1" xref="Sx4.p19.14.m14.1.1.3.1.cmml">−</mo><mn id="Sx4.p19.14.m14.1.1.3.3" xref="Sx4.p19.14.m14.1.1.3.3.cmml">2</mn></mrow></mrow><annotation-xml encoding="MathML-Content" id="Sx4.p19.14.m14.1b"><apply id="Sx4.p19.14.m14.1.1.cmml" xref="Sx4.p19.14.m14.1.1"><csymbol cd="latexml" id="Sx4.p19.14.m14.1.1.1.cmml" xref="Sx4.p19.14.m14.1.1.1">similar-to</csymbol><csymbol cd="latexml" id="Sx4.p19.14.m14.1.1.2.cmml" xref="Sx4.p19.14.m14.1.1.2">absent</csymbol><apply id="Sx4.p19.14.m14.1.1.3.cmml" xref="Sx4.p19.14.m14.1.1.3"><minus id="Sx4.p19.14.m14.1.1.3.1.cmml" xref="Sx4.p19.14.m14.1.1.3.1"></minus><cn id="Sx4.p19.14.m14.1.1.3.2.cmml" type="integer" xref="Sx4.p19.14.m14.1.1.3.2">1</cn><cn id="Sx4.p19.14.m14.1.1.3.3.cmml" type="integer" xref="Sx4.p19.14.m14.1.1.3.3">2</cn></apply></apply></annotation-xml><annotation encoding="application/x-tex" id="Sx4.p19.14.m14.1c">\sim 1-2</annotation><annotation encoding="application/x-llamapun" id="Sx4.p19.14.m14.1d">∼ 1 - 2</annotation></semantics></math> ms.</p> </div> </section> <section class="ltx_section" id="Sx5"> <h2 class="ltx_title ltx_title_section">Data availability</h2> <div class="ltx_para" id="Sx5.p1"> <p class="ltx_p" id="Sx5.p1.1">The data that support the findings of this study are available from the corresponding author upon request.</p> </div> </section> <section class="ltx_section" id="Sx6"> <h2 class="ltx_title ltx_title_section">Acknowledgements</h2> <div class="ltx_para" id="Sx6.p1"> <p class="ltx_p" id="Sx6.p1.1">J.F., R.C., H.X., and W.G. acknowledge support from the National Science Foundation through Grants No. 2230727, No. 2235276, No. 2316627 and No. 2321366.</p> </div> </section> <section class="ltx_section" id="Sx7"> <h2 class="ltx_title ltx_title_section">Author Contributions Statement</h2> <div class="ltx_para" id="Sx7.p1"> <p class="ltx_p" id="Sx7.p1.1">W.G. conceived the idea, designed experiments, and supervised the project. J.F. performed the experiments with the help of R.C. and H.X. and under the support and guidance W.G. J.F. and M.L. conducted theoretical modeling and calculations with the help of Y.T. and under the support and guidance of W.G. N.H. performed spectroscopic ellipsometry measurements. All authors discussed the results and contributed to the manuscript.</p> </div> </section> <section class="ltx_section" id="Sx8"> <h2 class="ltx_title ltx_title_section">Competing Interests Statement</h2> <div class="ltx_para" id="Sx8.p1"> <p class="ltx_p" id="Sx8.p1.1">The authors declare no competing interests.</p> </div> </section> <section class="ltx_bibliography" id="bib"> <h2 class="ltx_title ltx_title_bibliography">References</h2> <ul class="ltx_biblist"> <li class="ltx_bibitem" id="bib.1.1"> <span class="ltx_bibblock"><span class="ltx_ERROR undefined" id="bib.1.1.1.1">\bibcommenthead</span> </span> </li> <li class="ltx_bibitem" id="bib.bib1"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Liu et al. [2023]</span> <span class="ltx_bibblock"> Liu, Y., Wu, Z., Armstrong, D.W., Wolosker, H., Zheng, Y.: Detection and analysis of chiral molecules as disease biomarkers. Nat. Rev. Chem. <span class="ltx_text ltx_font_bold" id="bib.bib1.1.1">7</span>(5), 355–373 (2023) </span> </li> <li class="ltx_bibitem" id="bib.bib2"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Yoo and Park [2019]</span> <span class="ltx_bibblock"> Yoo, S., Park, Q.-H.: Metamaterials and chiral sensing: a review of fundamentals and applications. Nanophotonics <span class="ltx_text ltx_font_bold" id="bib.bib2.1.1">8</span>(2), 249–261 (2019) </span> </li> <li class="ltx_bibitem" id="bib.bib3"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Warning et al. [2021]</span> <span class="ltx_bibblock"> Warning, L.A., Miandashti, A.R., McCarthy, L.A., Zhang, Q., Landes, C.F., Link, S.: Nanophotonic approaches for chirality sensing. ACS Nano <span class="ltx_text ltx_font_bold" id="bib.bib3.1.1">15</span>(10), 15538–15566 (2021) </span> </li> <li class="ltx_bibitem" id="bib.bib4"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Zhan et al. [2021]</span> <span class="ltx_bibblock"> Zhan, X., Xu, F.-F., Zhou, Z., Yan, Y., Yao, J., Zhao, Y.S.: 3d laser displays based on circularly polarized lasing from cholesteric liquid crystal arrays. Adv. Mater. <span class="ltx_text ltx_font_bold" id="bib.bib4.1.1">33</span>(37), 2104418 (2021) </span> </li> <li class="ltx_bibitem" id="bib.bib5"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Khaliq et al. [2022]</span> <span class="ltx_bibblock"> Khaliq, H.S., Kim, J., Naeem, T., Riaz, K., Badloe, T., Seong, J., Akbar, J., Zubair, M., Mehmood, M.Q., Massoud, Y., <span class="ltx_text ltx_font_italic" id="bib.bib5.1.1">et al.</span>: Broadband chiro-optical effects for futuristic meta-holographic displays. Adv. Opt. Mater. <span class="ltx_text ltx_font_bold" id="bib.bib5.2.2">10</span>(22), 2201175 (2022) </span> </li> <li class="ltx_bibitem" id="bib.bib6"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Dan et al. [2024]</span> <span class="ltx_bibblock"> Dan, S., Paramanik, S., Pal, A.J.: Introducing chiro-optical activities in photonic synapses for neuromorphic computing and in-memory logic operations. ACS Nano (2024) </span> </li> <li class="ltx_bibitem" id="bib.bib7"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Kim et al. [2019]</span> <span class="ltx_bibblock"> Kim, J.-Y., Yeom, J., Zhao, G., Calcaterra, H., Munn, J., Zhang, P., Kotov, N.: Assembly of gold nanoparticles into chiral superstructures driven by circularly polarized light. J. Am. Chem. Soc. <span class="ltx_text ltx_font_bold" id="bib.bib7.1.1">141</span>(30), 11739–11744 (2019) </span> </li> <li class="ltx_bibitem" id="bib.bib8"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Genet [2022]</span> <span class="ltx_bibblock"> Genet, C.: Chiral light–chiral matter interactions: an optical force perspective. ACS Photonics <span class="ltx_text ltx_font_bold" id="bib.bib8.1.1">9</span>(2), 319–332 (2022) </span> </li> <li class="ltx_bibitem" id="bib.bib9"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Lodahl et al. [2017]</span> <span class="ltx_bibblock"> Lodahl, P., Mahmoodian, S., Stobbe, S., Rauschenbeutel, A., Schneeweiss, P., Volz, J., Pichler, H., Zoller, P.: Chiral quantum optics. Nature <span class="ltx_text ltx_font_bold" id="bib.bib9.1.1">541</span>(7638), 473–480 (2017) </span> </li> <li class="ltx_bibitem" id="bib.bib10"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Hübener et al. [2021]</span> <span class="ltx_bibblock"> Hübener, H., De Giovannini, U., Schäfer, C., Andberger, J., Ruggenthaler, M., Faist, J., Rubio, A.: Engineering quantum materials with chiral optical cavities. Nat. Mater. <span class="ltx_text ltx_font_bold" id="bib.bib10.1.1">20</span>(4), 438–442 (2021) </span> </li> <li class="ltx_bibitem" id="bib.bib11"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Chen et al. [2021]</span> <span class="ltx_bibblock"> Chen, D., He, R., Cai, H., Liu, X., Gao, W.: Chiral single-photon generators. ACS Nano <span class="ltx_text ltx_font_bold" id="bib.bib11.1.1">15</span>(2), 1912–1916 (2021) </span> </li> <li class="ltx_bibitem" id="bib.bib12"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Aiello et al. [2022]</span> <span class="ltx_bibblock"> Aiello, C.D., Abendroth, J.M., Abbas, M., Afanasev, A., Agarwal, S., Banerjee, A.S., Beratan, D.N., Belling, J.N., Berche, B., Botana, A., <span class="ltx_text ltx_font_italic" id="bib.bib12.1.1">et al.</span>: A chirality-based quantum leap. ACS Nano <span class="ltx_text ltx_font_bold" id="bib.bib12.2.2">16</span>(4), 4989–5035 (2022) </span> </li> <li class="ltx_bibitem" id="bib.bib13"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Li et al. [2023]</span> <span class="ltx_bibblock"> Li, X., Jones, A.C., Choi, J., Zhao, H., Chandrasekaran, V., Pettes, M.T., Piryatinski, A., Tschudin, M.A., Reiser, P., Broadway, D.A., <span class="ltx_text ltx_font_italic" id="bib.bib13.1.1">et al.</span>: Proximity-induced chiral quantum light generation in strain-engineered wse2/nips3 heterostructures. Nat. Mater. <span class="ltx_text ltx_font_bold" id="bib.bib13.2.2">22</span>(11), 1311–1316 (2023) </span> </li> <li class="ltx_bibitem" id="bib.bib14"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Albano et al. [2020]</span> <span class="ltx_bibblock"> Albano, G., Pescitelli, G., Di Bari, L.: Chiroptical properties in thin films of <math alttext="\pi" class="ltx_Math" display="inline" id="bib.bib14.1.m1.1"><semantics id="bib.bib14.1.m1.1a"><mi id="bib.bib14.1.m1.1.1" xref="bib.bib14.1.m1.1.1.cmml">π</mi><annotation-xml encoding="MathML-Content" id="bib.bib14.1.m1.1b"><ci id="bib.bib14.1.m1.1.1.cmml" xref="bib.bib14.1.m1.1.1">𝜋</ci></annotation-xml><annotation encoding="application/x-tex" id="bib.bib14.1.m1.1c">\pi</annotation><annotation encoding="application/x-llamapun" id="bib.bib14.1.m1.1d">italic_π</annotation></semantics></math>-conjugated systems. Chem. Rev. <span class="ltx_text ltx_font_bold" id="bib.bib14.2.1">120</span>(18), 10145–10243 (2020) </span> </li> <li class="ltx_bibitem" id="bib.bib15"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Albano et al. [2022]</span> <span class="ltx_bibblock"> Albano, G., Pescitelli, G., Di Bari, L.: Reciprocal and non-reciprocal chiroptical features in thin films of organic dyes. ChemNanoMat <span class="ltx_text ltx_font_bold" id="bib.bib15.1.1">8</span>(8), 202200219 (2022) </span> </li> <li class="ltx_bibitem" id="bib.bib16"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Furlan et al. [2024]</span> <span class="ltx_bibblock"> Furlan, F., Moreno-Naranjo, J.M., Gasparini, N., Feldmann, S., Wade, J., Fuchter, M.J.: Chiral materials and mechanisms for circularly polarized light-emitting diodes. Nat. Photonics, 1–11 (2024) </span> </li> <li class="ltx_bibitem" id="bib.bib17"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Doumani et al. [2023]</span> <span class="ltx_bibblock"> Doumani, J., Lou, M., Dewey, O., Hong, N., Fan, J., Baydin, A., Zahn, K., Yomogida, Y., Yanagi, K., Pasquali, M., <span class="ltx_text ltx_font_italic" id="bib.bib17.1.1">et al.</span>: Engineering chirality at wafer scale with ordered carbon nanotube architectures. Nat. Commun. <span class="ltx_text ltx_font_bold" id="bib.bib17.2.2">14</span>(1), 7380 (2023) </span> </li> <li class="ltx_bibitem" id="bib.bib18"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Dresselhaus et al. [2001]</span> <span class="ltx_bibblock"> Dresselhaus, M.S., Dresselhaus, G., Avouris, P. (eds.): Carbon Nanotubes: Synthesis, Structure, Properties, and Applications. Topics in Applied Physics, vol. 18. Springer, Berlin (2001) </span> </li> <li class="ltx_bibitem" id="bib.bib19"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Avouris et al. [2008]</span> <span class="ltx_bibblock"> Avouris, P., Freitag, M., Perebeinos, V.: Carbon-nanotube photonics and optoelectronics. Nat. Photonics <span class="ltx_text ltx_font_bold" id="bib.bib19.1.1">2</span>(6), 341 (2008) </span> </li> <li class="ltx_bibitem" id="bib.bib20"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Lv et al. [2022]</span> <span class="ltx_bibblock"> Lv, J., Gao, X., Han, B., Zhu, Y., Hou, K., Tang, Z.: Self-assembled inorganic chiral superstructures. Nat. Rev. Chem. <span class="ltx_text ltx_font_bold" id="bib.bib20.1.1">6</span>(2), 125–145 (2022) </span> </li> <li class="ltx_bibitem" id="bib.bib21"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Kaschke and Wegener [2016]</span> <span class="ltx_bibblock"> Kaschke, J., Wegener, M.: Optical and infrared helical metamaterials. Nanophotonics <span class="ltx_text ltx_font_bold" id="bib.bib21.1.1">5</span>(4), 510–523 (2016) </span> </li> <li class="ltx_bibitem" id="bib.bib22"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Wang et al. [2016]</span> <span class="ltx_bibblock"> Wang, Z., Cheng, F., Winsor, T., Liu, Y.: Optical chiral metamaterials: a review of the fundamentals, fabrication methods and applications. Nanotechnology <span class="ltx_text ltx_font_bold" id="bib.bib22.1.1">27</span>(41), 412001 (2016) </span> </li> <li class="ltx_bibitem" id="bib.bib23"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Mun et al. [2020]</span> <span class="ltx_bibblock"> Mun, J., Kim, M., Yang, Y., Badloe, T., Ni, J., Chen, Y., Qiu, C.-W., Rho, J.: Electromagnetic chirality: from fundamentals to nontraditional chiroptical phenomena. Light Sci. Appl. <span class="ltx_text ltx_font_bold" id="bib.bib23.1.1">9</span>(1), 139 (2020) </span> </li> <li class="ltx_bibitem" id="bib.bib24"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Zhao et al. [2024]</span> <span class="ltx_bibblock"> Zhao, L., Fan, J., Gong, C., Dyke, A., Gao, W., Li, B.: A critical review on recent progress of solution-processed monolayer assembly of nanomaterials and applications. Small, 2312268 (2024) </span> </li> <li class="ltx_bibitem" id="bib.bib25"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Yin et al. [2015]</span> <span class="ltx_bibblock"> Yin, X., Schäferling, M., Michel, A.-K.U., Tittl, A., Wuttig, M., Taubner, T., Giessen, H.: Active chiral plasmonics. Nano Lett. <span class="ltx_text ltx_font_bold" id="bib.bib25.1.1">15</span>(7), 4255–4260 (2015) </span> </li> <li class="ltx_bibitem" id="bib.bib26"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Kim et al. [2017]</span> <span class="ltx_bibblock"> Kim, T.-T., Oh, S.S., Kim, H.-D., Park, H.S., Hess, O., Min, B., Zhang, S.: Electrical access to critical coupling of circularly polarized waves in graphene chiral metamaterials. Sci. Adv. <span class="ltx_text ltx_font_bold" id="bib.bib26.1.1">3</span>(9), 1701377 (2017) </span> </li> <li class="ltx_bibitem" id="bib.bib27"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Kindness et al. [2020]</span> <span class="ltx_bibblock"> Kindness, S.J., Almond, N.W., Michailow, W., Wei, B., Delfanazari, K., Braeuninger-Weimer, P., Hofmann, S., Beere, H.E., Ritchie, D.A., Degl’Innocenti, R.: A terahertz chiral metamaterial modulator. Adv. Opt. Mater. <span class="ltx_text ltx_font_bold" id="bib.bib27.1.1">8</span>(21), 2000581 (2020) </span> </li> <li class="ltx_bibitem" id="bib.bib28"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Kwon and Faraon [2021]</span> <span class="ltx_bibblock"> Kwon, H., Faraon, A.: Nems-tunable dielectric chiral metasurfaces. ACS Photonics <span class="ltx_text ltx_font_bold" id="bib.bib28.1.1">8</span>(10), 2980–2986 (2021) </span> </li> <li class="ltx_bibitem" id="bib.bib29"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Rodrigues et al. [2022]</span> <span class="ltx_bibblock"> Rodrigues, S.P., Cunha, P., Kudtarkar, K., Dede, E.M., Lan, S.: Review of optically active and nonlinear chiral metamaterials. J. Nanophotonics <span class="ltx_text ltx_font_bold" id="bib.bib29.1.1">16</span>(2), 020901–020901 (2022) </span> </li> <li class="ltx_bibitem" id="bib.bib30"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Jiang et al. [2020]</span> <span class="ltx_bibblock"> Jiang, J., Chen, M., Fan, J.A.: Deep neural networks for the evaluation and design of photonic devices. Nat. Rev. Mater., 1–22 (2020) </span> </li> <li class="ltx_bibitem" id="bib.bib31"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Wuttig et al. [2017]</span> <span class="ltx_bibblock"> Wuttig, M., Bhaskaran, H., Taubner, T.: Phase-change materials for non-volatile photonic applications. Nat. Photonics <span class="ltx_text ltx_font_bold" id="bib.bib31.1.1">11</span>(8), 465 (2017) <a class="ltx_ref ltx_url ltx_font_typewriter" href="https://doi.org/10.1038/nphoton.2017.126" title="">https://doi.org/10.1038/nphoton.2017.126</a> </span> </li> <li class="ltx_bibitem" id="bib.bib32"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Zhang et al. [2019]</span> <span class="ltx_bibblock"> Zhang, Y., Chou, J.B., Li, J., Li, H., Du, Q., Yadav, A., Zhou, S., Shalaginov, M.Y., Fang, Z., Zhong, H., <span class="ltx_text ltx_font_italic" id="bib.bib32.1.1">et al.</span>: Broadband transparent optical phase change materials for high-performance nonvolatile photonics. Nat. Commun. <span class="ltx_text ltx_font_bold" id="bib.bib32.2.2">10</span>, 4279 (2019) </span> </li> <li class="ltx_bibitem" id="bib.bib33"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Yomogida et al. [2018]</span> <span class="ltx_bibblock"> Yomogida, Y., Liu, Z., Ichinose, Y., Yanagi, K.: Sorting transition-metal dichalcogenide nanotubes by centrifugation. ACS omega <span class="ltx_text ltx_font_bold" id="bib.bib33.1.1">3</span>(8), 8932–8936 (2018) </span> </li> <li class="ltx_bibitem" id="bib.bib34"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Xu et al. [2022]</span> <span class="ltx_bibblock"> Xu, T., Zhang, K., Cai, Q., Wang, N., Wu, L., He, Q., Wang, H., Zhang, Y., Xie, Y., Yao, Y., <span class="ltx_text ltx_font_italic" id="bib.bib34.1.1">et al.</span>: Advances in synthesis and applications of boron nitride nanotubes: A review. Chem. Eng. J. <span class="ltx_text ltx_font_bold" id="bib.bib34.2.2">431</span>, 134118 (2022) </span> </li> <li class="ltx_bibitem" id="bib.bib35"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Xiang et al. [2020]</span> <span class="ltx_bibblock"> Xiang, R., Inoue, T., Zheng, Y., Kumamoto, A., Qian, Y., Sato, Y., Liu, M., Tang, D., Gokhale, D., Guo, J., <span class="ltx_text ltx_font_italic" id="bib.bib35.1.1">et al.</span>: One-dimensional van der waals heterostructures. Science <span class="ltx_text ltx_font_bold" id="bib.bib35.2.2">367</span>(6477), 537–542 (2020) </span> </li> <li class="ltx_bibitem" id="bib.bib36"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Balandin et al. [2022]</span> <span class="ltx_bibblock"> Balandin, A.A., Kargar, F., Salguero, T.T., Lake, R.K.: One-dimensional van der waals quantum materials. Mater. Today <span class="ltx_text ltx_font_bold" id="bib.bib36.1.1">55</span>, 74–91 (2022) </span> </li> <li class="ltx_bibitem" id="bib.bib37"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Benea-Chelmus et al. [2021]</span> <span class="ltx_bibblock"> Benea-Chelmus, I.-C., Meretska, M.L., Elder, D.L., Tamagnone, M., Dalton, L.R., Capasso, F.: Electro-optic spatial light modulator from an engineered organic layer. Nat. Commun. <span class="ltx_text ltx_font_bold" id="bib.bib37.1.1">12</span>(1), 5928 (2021) </span> </li> <li class="ltx_bibitem" id="bib.bib38"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Prabhathan et al. [2023]</span> <span class="ltx_bibblock"> Prabhathan, P., Sreekanth, K.V., Teng, J., Ko, J.H., Yoo, Y.J., Jeong, H.-H., Lee, Y., Zhang, S., Cao, T., Popescu, C.-C., et al.: Roadmap for phase change materials in photonics and beyond. Iscience <span class="ltx_text ltx_font_bold" id="bib.bib38.1.1">26</span>(10) (2023) </span> </li> <li class="ltx_bibitem" id="bib.bib39"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Boes et al. [2023]</span> <span class="ltx_bibblock"> Boes, A., Chang, L., Langrock, C., Yu, M., Zhang, M., Lin, Q., Lončar, M., Fejer, M., Bowers, J., Mitchell, A.: Lithium niobate photonics: Unlocking the electromagnetic spectrum. Science <span class="ltx_text ltx_font_bold" id="bib.bib39.1.1">379</span>(6627), 4396 (2023) </span> </li> <li class="ltx_bibitem" id="bib.bib40"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Bloom et al. [2024]</span> <span class="ltx_bibblock"> Bloom, B.P., Paltiel, Y., Naaman, R., Waldeck, D.H.: Chiral induced spin selectivity. Chem. Rev. (2024) </span> </li> <li class="ltx_bibitem" id="bib.bib41"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Mak et al. [2011]</span> <span class="ltx_bibblock"> Mak, K.F., Shan, J., Heinz, T.F.: Seeing many-body effects in single-and few-layer graphene: observation of two-dimensional saddle-point excitons. Phys. Rev. Lett. <span class="ltx_text ltx_font_bold" id="bib.bib41.1.1">106</span>(4), 046401 (2011) </span> </li> <li class="ltx_bibitem" id="bib.bib42"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Liu et al. [2011]</span> <span class="ltx_bibblock"> Liu, H., Nishide, D., Tanaka, T., Kataura, H.: Large-scale single-chirality separation of single-wall carbon nanotubes by simple gel chromatography. Nat. Commun. <span class="ltx_text ltx_font_bold" id="bib.bib42.1.1">2</span>, 309 (2011) </span> </li> <li class="ltx_bibitem" id="bib.bib43"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Takagi and Okada [2009]</span> <span class="ltx_bibblock"> Takagi, Y., Okada, S.: Theoretical calculation for the ultraviolet optical properties of single-walled carbon nanotubes. Phys. Rev. B <span class="ltx_text ltx_font_bold" id="bib.bib43.1.1">79</span>(23), 233406 (2009) </span> </li> <li class="ltx_bibitem" id="bib.bib44"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Yanagi et al. [2018]</span> <span class="ltx_bibblock"> Yanagi, K., Okada, R., Ichinose, Y., Yomogida, Y., Katsutani, F., Gao, W., Kono, J.: Intersubband plasmons in the quantum limit in gated and aligned carbon nanotubes. Nat. Commun. <span class="ltx_text ltx_font_bold" id="bib.bib44.1.1">9</span>(1), 1121 (2018) </span> </li> <li class="ltx_bibitem" id="bib.bib45"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Nordén et al. [2010]</span> <span class="ltx_bibblock"> Nordén, B., Rodger, A., Dafforn, T.: Linear Dichroism and Circular Dichroism: a Textbook on Polarized-light Spectroscopy. Royal Society of Chemistry, Cambridge, UK (2010) </span> </li> <li class="ltx_bibitem" id="bib.bib46"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">He et al. [2016]</span> <span class="ltx_bibblock"> He, X., Gao, W., Xie, L., Li, B., Zhang, Q., Lei, S., Robinson, J.M., Hároz, E.H., Doorn, S.K., Wang, W., Vajtai, R., Ajayan, P.M., Adams, W.W., Hauge, R.H., Kono, J.: Wafer-scale monodomain films of spontaneously aligned single-walled carbon nanotubes. Nat. Nanotechnol. <span class="ltx_text ltx_font_bold" id="bib.bib46.1.1">11</span>(7), 633–638 (2016) </span> </li> <li class="ltx_bibitem" id="bib.bib47"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Hao and Zhou [2008]</span> <span class="ltx_bibblock"> Hao, J., Zhou, L.: Electromagnetic wave scatterings by anisotropic metamaterials: Generalized 4<math alttext="\times" class="ltx_Math" display="inline" id="bib.bib47.1.m1.1"><semantics id="bib.bib47.1.m1.1a"><mo id="bib.bib47.1.m1.1.1" xref="bib.bib47.1.m1.1.1.cmml">×</mo><annotation-xml encoding="MathML-Content" id="bib.bib47.1.m1.1b"><times id="bib.bib47.1.m1.1.1.cmml" xref="bib.bib47.1.m1.1.1"></times></annotation-xml><annotation encoding="application/x-tex" id="bib.bib47.1.m1.1c">\times</annotation><annotation encoding="application/x-llamapun" id="bib.bib47.1.m1.1d">×</annotation></semantics></math> 4 transfer-matrix method. Physical Review B <span class="ltx_text ltx_font_bold" id="bib.bib47.2.1">77</span>(9), 094201 (2008) </span> </li> <li class="ltx_bibitem" id="bib.bib48"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Meneses et al. [2005]</span> <span class="ltx_bibblock"> Meneses, D.D.S., Gruener, G., Malki, M., Echegut, P.: Causal voigt profile for modeling reflectivity spectra of glasses. J. Non-Cryst. Solids <span class="ltx_text ltx_font_bold" id="bib.bib48.1.1">351</span>(2), 124–129 (2005) </span> </li> <li class="ltx_bibitem" id="bib.bib49"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Yamaguchi et al. [2019]</span> <span class="ltx_bibblock"> Yamaguchi, S., Tsunekawa, I., Komatsu, N., Gao, W., Shiga, T., Kodama, T., Kono, J., Shiomi, J.: One-directional thermal transport in densely aligned single-wall carbon nanotube films. Appl. Phys. Lett. <span class="ltx_text ltx_font_bold" id="bib.bib49.1.1">115</span>(22), 223104 (2019) </span> </li> <li class="ltx_bibitem" id="bib.bib50"> <span class="ltx_tag ltx_role_refnum ltx_tag_bibitem">Taghinejad et al. [2021]</span> <span class="ltx_bibblock"> Taghinejad, H., Abdollahramezani, S., Eftekhar, A.A., Fan, T., Hosseinnia, A.H., Hemmatyar, O., Dorche, A.E., Gallmon, A., Adibi, A.: Ito-based microheaters for reversible multi-stage switching of phase-change materials: towards miniaturized beyond-binary reconfigurable integrated photonics. Opt. Express <span class="ltx_text ltx_font_bold" id="bib.bib50.1.1">29</span>(13), 20449–20462 (2021) </span> </li> </ul> </section> </article> </div> <footer class="ltx_page_footer"> <div class="ltx_page_logo">Generated on Wed Jun 19 03:42:42 2024 by <a class="ltx_LaTeXML_logo" href="http://dlmf.nist.gov/LaTeXML/"><span style="letter-spacing:-0.2em; margin-right:0.1em;">L<span class="ltx_font_smallcaps" style="position:relative; bottom:2.2pt;">a</span>T<span class="ltx_font_smallcaps" style="font-size:120%;position:relative; bottom:-0.2ex;">e</span></span><span style="font-size:90%; position:relative; bottom:-0.2ex;">XML</span><img alt="Mascot Sammy" src="data:image/png;base64,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"/></a> </div></footer> </div> </body> </html>