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<!DOCTYPE html>   <html class="no-js" lang="en">  <head> <meta charset="utf-8"> <meta name="tdm-reservation" content="1"/> <meta name="tdm-policy" content="https://opg.optica.org/policies/opg-tdm-policy.json"/> <meta name="viewport" content="width=device-width" initial-scale="1"> <meta http-equiv="X-UA-Compatible" content="IE=Edge"> <meta name="format-detection" content="telephone=no"> <title>Coupling characterization and noise studies of the optical metrology system onboard the LISA Pathfinder mission</title> <link title="schema(DC)" rel="schema.dc" href="http://purl.org/dc/elements/1.1/" /> <meta name="twitter:card" content="summary"> <meta name="twitter:description" content="We describe the first investigations of the complete engineering model of the optical metrology system (OMS), a key subsystem of the LISA Pathfinder science mission to space. The latter itself is a technological precursor mission to LISA, a spaceborne gravitational wave detector. At its core, the OMS consists of four heterodyne Mach–Zehnder interferometers, a highly stable laser with an external modulator, and a phase meter. It is designed to monitor and track the longitudinal motion and attitude of two floating test masses in the optical reference frame with (relative) precision in the picometer and nanorad range, respectively. We analyze sensor signal correlations and determine a physical sensor noise limit. The coupling parameters between motional degrees of freedom and interferometer signals are analytically derived and compared to measurements. We also measure adverse cross-coupling effects originating from system imperfections and limitations and describe algorithmic mitigation techniques to overcome some of them. Their impact on system performance is analyzed within the context of the Pathfinder mission."> <meta name="twitter:image" content="https://opg.optica.org/getThumbnail.cfm?uri=ao-49-29-5665&o=y"> <meta name="twitter:site" content="@OpticaPubsGroup"> <meta name="twitter:title" content="Coupling characterization and noise studies of the optical metrology system onboard the LISA Pathfinder mission"> <meta name="dc.creator" content="Ulrich Johann"> <meta name="dc.creator" content="Frank Steier"> <meta name="dc.creator" content="Miquel Nofrarias"> <meta name="dc.creator" content="Gerald Hechenblaikner"> <meta name="dc.creator" content="Gerhard Heinzel"> <meta name="dc.creator" content="Rüdiger Gerndt"> <meta name="dc.creator" content="Peter Luetzow-Wentzky"> <meta name="dc.creator" content="Karsten Danzmann"> <meta name="dc.creator" content="Vinzenz Wand"> <meta name="dc.creator" content="Heather Audley"> <meta name="dc.creator" content="Antonio Garcia-Marin"> <meta name="dc.date" content="2010-10-10"> <meta name="dc.description" content="We describe the first investigations of the complete engineering model of the optical metrology system (OMS), a key subsystem of the LISA Pathfinder science mission to space. The latter itself is a technological precursor mission to LISA, a spaceborne gravitational wave detector. At its core, the OMS consists of four heterodyne Mach–Zehnder interferometers, a highly stable laser with an external modulator, and a phase meter. It is designed to monitor and track the longitudinal motion and attitude of two floating test masses in the optical reference frame with (relative) precision in the picometer and nanorad range, respectively. We analyze sensor signal correlations and determine a physical sensor noise limit. The coupling parameters between motional degrees of freedom and interferometer signals are analytically derived and compared to measurements. We also measure adverse cross-coupling effects originating from system imperfections and limitations and describe algorithmic mitigation techniques to overcome some of them. Their impact on system performance is analyzed within the context of the Pathfinder mission."> <meta name="dc.identifier" content="doi:10.1364/AO.49.005665"> <meta name="dc.language" content="EN"> <meta property="og:description" content="We describe the first investigations of the complete engineering model of the optical metrology system (OMS), a key subsystem of the LISA Pathfinder science mission to space. The latter itself is a technological precursor mission to LISA, a spaceborne gravitational wave detector. At its core, the OMS consists of four heterodyne Mach–Zehnder interferometers, a highly stable laser with an external modulator, and a phase meter. It is designed to monitor and track the longitudinal motion and attitude of two floating test masses in the optical reference frame with (relative) precision in the picometer and nanorad range, respectively. We analyze sensor signal correlations and determine a physical sensor noise limit. The coupling parameters between motional degrees of freedom and interferometer signals are analytically derived and compared to measurements. We also measure adverse cross-coupling effects originating from system imperfections and limitations and describe algorithmic mitigation techniques to overcome some of them. Their impact on system performance is analyzed within the context of the Pathfinder mission."> <meta property="og:sitename" content="Optica Publishing Group"> <meta property="og:title" content="Coupling characterization and noise studies of the optical metrology system onboard the LISA Pathfinder mission"> <meta property="og:type" content="Article"> <meta property="og:url" content="https://opg.optica.org/ao/abstract.cfm?uri=ao-49-29-5665"> <meta name="dc.publisher" content="Optica Publishing Group"> <meta name="dc.rights" content="&#169; 2010 Optical Society of America"> <meta name="dc.source" content="Applied Optics, Vol. 49, Issue 29, pp. 5665-5677"> <meta name="dc.subject" content="Fourier transforms"> <meta name="dc.subject" content="Laser beams"> <meta name="dc.subject" content="Optical systems"> <meta name="dc.subject" content="Optical testing"> <meta name="dc.subject" content="Phase noise"> <meta name="dc.subject" content="Phase shift"> <meta name="dc.title" content="Coupling characterization and noise studies of the optical metrology system onboard the LISA Pathfinder mission"> <meta name="citation_abstract_html_url" content="https://opg.optica.org/abstract.cfm?uri=ao-49-29-5665"> <meta name="citation_author" content="Gerald Hechenblaikner"> <meta name="citation_author_institution" content="EADS Astrium GmbH, Friedrichshafen, Germany"> <meta name="citation_author" content="Rüdiger Gerndt"> <meta name="citation_author_institution" content="EADS Astrium GmbH, Friedrichshafen, Germany"> <meta name="citation_author" content="Ulrich Johann"> <meta name="citation_author_institution" content="EADS Astrium GmbH, Friedrichshafen, Germany"> <meta name="citation_author" content="Peter Luetzow-Wentzky"> <meta name="citation_author_institution" content="EADS Astrium GmbH, Friedrichshafen, Germany"> <meta name="citation_author" content="Vinzenz Wand"> <meta name="citation_author_institution" content="EADS Astrium GmbH, Friedrichshafen, Germany"> <meta name="citation_author" content="Heather Audley"> <meta name="citation_author_institution" content="Albert Einstein Institut, Hannover, Germany"> <meta name="citation_author" content="Karsten Danzmann"> <meta name="citation_author_institution" content="Albert Einstein Institut, Hannover, Germany"> <meta name="citation_author" content="Antonio Garcia-Marin"> <meta name="citation_author_institution" content="Albert Einstein Institut, Hannover, Germany"> <meta name="citation_author" content="Gerhard Heinzel"> <meta name="citation_author_institution" content="Albert Einstein Institut, Hannover, Germany"> <meta name="citation_author" content="Miquel Nofrarias"> <meta name="citation_author_institution" content="Albert Einstein Institut, Hannover, Germany"> <meta name="citation_author" content="Frank Steier"> <meta name="citation_author_institution" content="Albert Einstein Institut, Hannover, Germany"> <meta name="citation_doi" content="10.1364/AO.49.005665"> <meta name="citation_firstpage" content="5665"> <meta name="citation_fulltext_html_url" content="https://opg.optica.org/viewmedia.cfm?uri=ao-49-29-5665&seq=0&html=true"> <meta name="citation_issn" content="2155-3165"> <meta name="citation_issue" content="29"> <meta name="citation_journal_abbrev" content="Appl. Opt., AO"> <meta name="citation_journal_title" content="Applied Optics"> <meta name="citation_keywords" content="Fourier transforms;Laser beams;Optical systems;Optical testing;Phase noise;Phase shift;"> <meta name="citation_language" content="EN"> <meta name="citation_lastpage" content="5677"> <meta name="citation_online_date" content="2010/10/07"> <meta name="citation_pdf_url" content="https://opg.optica.org/viewmedia.cfm?uri=ao-49-29-5665&seq=0"> <meta name="citation_publication_date" content="2010/10/10"> <meta name="citation_publisher" content="Optica Publishing Group"> <meta name="citation_title" content="Coupling characterization and noise studies of the optical metrology system onboard the LISA Pathfinder mission"> <meta name="citation_volume" content="49"> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content=""> <meta name="citation_reference" content="">  <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); 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id="articleContainer" style="padding-top:1em;"> <div class="col-md-12"> <div class="row"> <div class="article-parents"> <ul class="small list-inline article-journal-name"> <li><strong>Applied Optics</strong></li> <li>Vol. 49,</li> <li><a href="/ao/issue.cfm?volume=49&issue=29">Issue 29</a>,</li> <li>pp. 5665-5677</li> <li>(2010)</li> <li class="article-doi"><span class="separator-disc">•</span><a href="https://doi.org/10.1364/AO.49.005665">https://doi.org/10.1364/AO.49.005665</a></li> </ul> </div> </div> <div class="row"> <div class="article-header"> <div class="col-md-12 col-sm-12 pl-0"> <div class="col-md-2 col-sm-2 article-header__image p-0" style=""> <div class="w-100 text--left"> <div class="p-0 text--center" style="border:1px solid #ddd;"> <img src="/images/optica_general_thumbnail.jpg" width="168" height="170" alt="Optica Article" class="img-thumbnail hidden-xs article-thumbnail_img jcover"> </div> </div> </div> <div class="col-md-10 col-sm-10 pl-4 mb-1" style=""> <h1 class="article-title"> Coupling characterization and noise studies of the optical metrology system onboard the LISA Pathfinder mission </h1> <p class="article-authors"> Gerald Hechenblaikner, Rüdiger Gerndt, Ulrich Johann, Peter Luetzow-Wentzky, Vinzenz Wand, Heather Audley, Karsten Danzmann, Antonio Garcia-Marin, Gerhard Heinzel, Miquel Nofrarias, and Frank Steier </p> <div> <div class="btn-group article-affiliations-dropdown dropdown hidden-xs mr-2"> <a data-bs-toggle="dropdown" id="author-affiliations-dropdown"> Author Information <span class="caret"></span> </a> <div id="authorAffiliations" class="article-author-affiliations dropdown-menu"> <h5>Author Affiliations</h5> <p><strong> Gerald Hechenblaikner,<sup>1,</sup><sup>*</sup> Rüdiger Gerndt,<sup>1</sup> Ulrich Johann,<sup>1</sup> Peter Luetzow-Wentzky,<sup>1</sup> Vinzenz Wand,<sup>1</sup> Heather Audley,<sup>2</sup> Karsten Danzmann,<sup>2</sup> Antonio Garcia-Marin,<sup>2</sup> Gerhard Heinzel,<sup>2</sup> Miquel Nofrarias,<sup>2</sup> and Frank Steier<sup>2</sup> </strong></p> <p><em> <sup>1</sup>EADS Astrium GmbH, Friedrichshafen, Germany </em></p> <p><em> <sup>2</sup>Albert Einstein Institut, Hannover, Germany </em></p> <p> <sup>*</sup>Corresponding author: <a href="mailto:Gerald.Hechenblaikner@astrium.eads.net">Gerald.Hechenblaikner@astrium.eads.net</a> </p> </div> </div> <div class="btn-group hidden-xs hidden-sm"> <a data-bs-toggle="dropdown" id="search-by-author-dropdown"> <i class="fal fa-search p__1--sm"></i> Find other works by these authors <span class="caret"></span> </a> <ul class="dropdown-menu" id="search-by-author"> <li><a href="search.cfm?a=G Hechenblaikner">G Hechenblaikner</a></li> <li><a href="search.cfm?a=R Gerndt">R Gerndt</a></li> <li><a href="search.cfm?a=U Johann">U Johann</a></li> <li><a href="search.cfm?a=P Luetzow-Wentzky">P Luetzow-Wentzky</a></li> <li><a href="search.cfm?a=V Wand">V Wand</a></li> <li><a href="search.cfm?a=H Audley">H Audley</a></li> <li><a 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The latter itself is a technological precursor mission to LISA, a spaceborne gravitational wave detector. At its core, the OMS consists of four heterodyne Mach–Zehnder interferometers, a highly stable laser with an external modulator, and a phase meter. It is designed to monitor and track the longitudinal motion and attitude of two floating test masses in the optical reference frame with (relative) precision in the picometer and nanorad range, respectively. We analyze sensor signal correlations and determine a physical sensor noise limit. The coupling parameters between motional degrees of freedom and interferometer signals are analytically derived and compared to measurements. We also measure adverse cross-coupling effects originating from system imperfections and limitations and describe algorithmic mitigation techniques to overcome some of them. Their impact on system performance is analyzed within the context of the Pathfinder mission.</p></p> <p>© 2010 Optical Society of America</p> <a href="viewmedia.cfm?uri=ao-49-29-5665&seq=0&html=true" id="link-full">Full Article</a>  |  <a href="viewmedia.cfm?uri=ao-49-29-5665&seq=0" target="_blank" id="link-pdf">PDF Article</a> <hr style="margin-top:5em;"> <strong>More Like This</strong> <div class="content-item media-twbs"> <div class="media-twbs-left"> <img class="media-object" src="/getThumbnail.cfm?uri=ao-58-23-6346&o=y" width="50" height="50" aria-hidden="true" role="presentation"> </div> <div class="media-twbs-body"> <a class="js-relatedArticleLink" href="/ao/abstract.cfm?uri=ao-58-23-6346">Multi-axis heterodyne interferometry at MHz frequencies: a short-arm measurement demonstration for LISA with off-the-shelf hardware</a> <p>P. Fulda, R. T. DeRosa, E. DeMarco, M. Aitken, J. Livas, and J. I. Thorpe<br> <span class="muted">Appl. 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aria-hidden="true">×</button> <h4 class="modal-title" id="tablet1Label">Table 1</h4> </div> <div class="modal-body"> <h4>Correlation Matrix between the Relative Phases of the Quadrants of PDRA</h4> <div class="table-responsive"><?xml version="1.0" encoding="UTF-8"?><table CLASS="table" frame="hsides" rules="all"><colgroup span="1"><col id="t1col1" span="1"/><col id="t1col2" span="1"/><col id="t1col3" span="1"/><col id="t1col4" span="1"/><col id="t1col5" span="1"/></colgroup><thead><tr><th colspan="1" rowspan="1" valign="top"/><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml256"> <mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml257"> <mrow> <msub> <mi>Z</mi> <mn>2</mn> </msub> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml258"> <mrow> <msub> <mi>Z</mi> <mn>3</mn> </msub> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml259"> <mrow> <msub> <mi>Z</mi> <mn>4</mn> </msub> </mrow> </math> </inline-formula> </th></tr></thead><tbody><tr><td colspan="1" rowspan="1"> <inline-formula> <math display="inline" id="mml260"> <mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> </mrow> </math> </inline-formula> </td><td colspan="1" rowspan="1">1.00</td><td colspan="1" rowspan="1">0.45</td><td colspan="1" rowspan="1">0.49</td><td colspan="1" rowspan="1">0.48</td></tr><tr><td colspan="1" rowspan="1"> <inline-formula> <math display="inline" id="mml261"> <mrow> <msub> <mi>Z</mi> <mn>2</mn> </msub> </mrow> </math> </inline-formula> </td><td colspan="1" rowspan="1">0.45</td><td colspan="1" rowspan="1">1.00</td><td colspan="1" rowspan="1">0.46</td><td colspan="1" rowspan="1">0.43</td></tr><tr><td colspan="1" rowspan="1"> <inline-formula> <math display="inline" id="mml262"> <mrow> <msub> <mi>Z</mi> <mn>3</mn> </msub> </mrow> </math> </inline-formula> </td><td colspan="1" rowspan="1">0.49</td><td colspan="1" rowspan="1">0.46</td><td colspan="1" rowspan="1">1.00</td><td colspan="1" rowspan="1">0.47</td></tr><tr><td colspan="1" rowspan="1"> <inline-formula> <math display="inline" id="mml263"> <mrow> <msub> <mi>Z</mi> <mn>4</mn> </msub> </mrow> </math> </inline-formula> </td><td colspan="1" rowspan="1">0.48</td><td colspan="1" rowspan="1">0.43</td><td colspan="1" rowspan="1">0.47</td><td colspan="1" rowspan="1">1.00</td></tr></tbody></table></div> </div> <div class="modal-footer"> <button type="button" class="btn btn-default" data-bs-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="modal fade full" id="tablet2" tabindex="-1" role="dialog" aria-labelledby="tablet2Label" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-bs-dismiss="modal" aria-hidden="true">×</button> <h4 class="modal-title" id="tablet2Label">Table 2</h4> </div> <div class="modal-body"> <h4>Measured Coupling Coefficients, <inline-formula> <math display="inline" id="mml264"> <mrow> <mi mathvariant="sans-serif-italic">K</mi> <mn mathvariant="sans-serif">1</mn> <mi>–</mi> <mi mathvariant="sans-serif-italic">K</mi> <mn mathvariant="sans-serif">6</mn> </mrow> </math> </inline-formula> (DWS) and <inline-formula> <math display="inline" id="mml265"> <mrow> <mi mathvariant="sans-serif-italic">K</mi> <mn mathvariant="sans-serif">11</mn> <mi>–</mi> <mi mathvariant="sans-serif-italic">K</mi> <mn mathvariant="sans-serif">16</mn> </mrow> </math> </inline-formula> (DC)</h4> <div class="table-responsive"><?xml version="1.0" encoding="UTF-8"?><table CLASS="table" frame="hsides" rules="all"><colgroup span="1"><col id="t2col1" span="1"/><col id="t2col2" span="1"/><col id="t2col3" span="1"/><col id="t2col4" span="1"/><col id="t2col5" span="1"/><col id="t2col6" span="1"/><col id="t2col7" span="1"/><col id="t2col8" span="1"/><col id="t2col9" span="1"/><col id="t2col10" span="1"/><col id="t2col11" span="1"/><col id="t2col12" span="1"/></colgroup><thead><tr><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml266"> <mrow> <mi>K</mi> <mn>1</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml267"> <mrow> <mi>K</mi> <mn>2</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml268"> <mrow> <mi>K</mi> <mn>3</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml269"> <mrow> <mi>K</mi> <mn>4</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml270"> <mrow> <mi>K</mi> <mn>5</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml271"> <mrow> <mi>K</mi> <mn>6</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml272"> <mrow> <mi>K</mi> <mn>11</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml273"> <mrow> <mi>K</mi> <mn>12</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml274"> <mrow> <mi>K</mi> <mn>13</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml275"> <mrow> <mi>K</mi> <mn>14</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml276"> <mrow> <mi>K</mi> <mn>15</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml277"> <mrow> <mi>K</mi> <mn>16</mn> </mrow> </math> </inline-formula> </th></tr></thead><tbody><tr><td colspan="1" rowspan="1">5190</td><td colspan="1" rowspan="1">4963</td><td colspan="1" rowspan="1">5174</td><td colspan="1" rowspan="1">7281</td><td colspan="1" rowspan="1">4898</td><td colspan="1" rowspan="1">6793</td><td colspan="1" rowspan="1">510</td><td colspan="1" rowspan="1">595</td><td colspan="1" rowspan="1">615</td><td colspan="1" rowspan="1">191</td><td colspan="1" rowspan="1">718</td><td colspan="1" rowspan="1">228</td></tr></tbody></table></div> </div> <div class="modal-footer"> <button type="button" class="btn btn-default" data-bs-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="modal fade full" id="allTablesModal" tabindex="-1" role="dialog" aria-labelledby="allTablesLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-bs-dismiss="modal" aria-hidden="true">×</button> <h4 class="modal-title" id="allTablesLabel">Tables (2)</h4> </div> <div class="modal-body"> <h4>Table 1</h4> <p>Correlation Matrix between the Relative Phases of the Quadrants of PDRA</p> <div class="table-responsive"><?xml version="1.0" encoding="UTF-8"?><table CLASS="table" frame="hsides" rules="all"><colgroup span="1"><col id="t1col1" span="1"/><col id="t1col2" span="1"/><col id="t1col3" span="1"/><col id="t1col4" span="1"/><col id="t1col5" span="1"/></colgroup><thead><tr><th colspan="1" rowspan="1" valign="top"/><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml256"> <mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml257"> <mrow> <msub> <mi>Z</mi> <mn>2</mn> </msub> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml258"> <mrow> <msub> <mi>Z</mi> <mn>3</mn> </msub> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml259"> <mrow> <msub> <mi>Z</mi> <mn>4</mn> </msub> </mrow> </math> </inline-formula> </th></tr></thead><tbody><tr><td colspan="1" rowspan="1"> <inline-formula> <math display="inline" id="mml260"> <mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> </mrow> </math> </inline-formula> </td><td colspan="1" rowspan="1">1.00</td><td colspan="1" rowspan="1">0.45</td><td colspan="1" rowspan="1">0.49</td><td colspan="1" rowspan="1">0.48</td></tr><tr><td colspan="1" rowspan="1"> <inline-formula> <math display="inline" id="mml261"> <mrow> <msub> <mi>Z</mi> <mn>2</mn> </msub> </mrow> </math> </inline-formula> </td><td colspan="1" rowspan="1">0.45</td><td colspan="1" rowspan="1">1.00</td><td colspan="1" rowspan="1">0.46</td><td colspan="1" rowspan="1">0.43</td></tr><tr><td colspan="1" rowspan="1"> <inline-formula> <math display="inline" id="mml262"> <mrow> <msub> <mi>Z</mi> <mn>3</mn> </msub> </mrow> </math> </inline-formula> </td><td colspan="1" rowspan="1">0.49</td><td colspan="1" rowspan="1">0.46</td><td colspan="1" rowspan="1">1.00</td><td colspan="1" rowspan="1">0.47</td></tr><tr><td colspan="1" rowspan="1"> <inline-formula> <math display="inline" id="mml263"> <mrow> <msub> <mi>Z</mi> <mn>4</mn> </msub> </mrow> </math> </inline-formula> </td><td colspan="1" rowspan="1">0.48</td><td colspan="1" rowspan="1">0.43</td><td colspan="1" rowspan="1">0.47</td><td colspan="1" rowspan="1">1.00</td></tr></tbody></table></div> <h4>Table 2</h4> <p>Measured Coupling Coefficients, <inline-formula> <math display="inline" id="mml264"> <mrow> <mi mathvariant="sans-serif-italic">K</mi> <mn mathvariant="sans-serif">1</mn> <mi>–</mi> <mi mathvariant="sans-serif-italic">K</mi> <mn mathvariant="sans-serif">6</mn> </mrow> </math> </inline-formula> (DWS) and <inline-formula> <math display="inline" id="mml265"> <mrow> <mi mathvariant="sans-serif-italic">K</mi> <mn mathvariant="sans-serif">11</mn> <mi>–</mi> <mi mathvariant="sans-serif-italic">K</mi> <mn mathvariant="sans-serif">16</mn> </mrow> </math> </inline-formula> (DC)</p> <div class="table-responsive"><?xml version="1.0" encoding="UTF-8"?><table CLASS="table" frame="hsides" rules="all"><colgroup span="1"><col id="t2col1" span="1"/><col id="t2col2" span="1"/><col id="t2col3" span="1"/><col id="t2col4" span="1"/><col id="t2col5" span="1"/><col id="t2col6" span="1"/><col id="t2col7" span="1"/><col id="t2col8" span="1"/><col id="t2col9" span="1"/><col id="t2col10" span="1"/><col id="t2col11" span="1"/><col id="t2col12" span="1"/></colgroup><thead><tr><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml266"> <mrow> <mi>K</mi> <mn>1</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml267"> <mrow> <mi>K</mi> <mn>2</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml268"> <mrow> <mi>K</mi> <mn>3</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml269"> <mrow> <mi>K</mi> <mn>4</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml270"> <mrow> <mi>K</mi> <mn>5</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml271"> <mrow> <mi>K</mi> <mn>6</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml272"> <mrow> <mi>K</mi> <mn>11</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml273"> <mrow> <mi>K</mi> <mn>12</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml274"> <mrow> <mi>K</mi> <mn>13</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml275"> <mrow> <mi>K</mi> <mn>14</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml276"> <mrow> <mi>K</mi> <mn>15</mn> </mrow> </math> </inline-formula> </th><th colspan="1" rowspan="1" valign="top"> <inline-formula> <math display="inline" id="mml277"> <mrow> <mi>K</mi> <mn>16</mn> </mrow> </math> </inline-formula> </th></tr></thead><tbody><tr><td colspan="1" rowspan="1">5190</td><td colspan="1" rowspan="1">4963</td><td colspan="1" rowspan="1">5174</td><td colspan="1" rowspan="1">7281</td><td colspan="1" rowspan="1">4898</td><td colspan="1" 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id="facet-journal-values"> </div> </div> <div class="sf-module sf-proceedings"> <div class="row2"> <p id="facet-proceeding-show" class="sf-group-title collapsed" style="text-transform: none !important;">Conferences</p> <div id="sortProceeding" class="sf-sort"></div> </div> <div id="facet-proceeding-values"></div> </div> </script> <script type="text/template" id="search-result-facet-basics"> <ul class="sf-list"> <li class="sf-select-all"><input id="<%= allId %>" type="checkbox" checked="checked" disabled="disabled"/> <label for="<%= allId %>">All</label></li> <%= values %> <li class="sf-expanded"> <a href="#" id="more-<%= allId %>" class="search-panel_more-link" data-bs-toggle="modal" data-bs-target="#modal-<%= allId %>">more <%=name%> »</a> <div class="modal full fade" id="modal-<%= allId %>"> <div class="modal-dialog"> <div class="modal-content search"> <div class="row mbottom-20"> <div class="col-md-4"> <h3 class="modal-header search"><%= modalTitle %></h3> </div> <div class="col-md-6 col-md-offset-2"> <input id="input-<%= allId%>" type="text" class="form-control selectized" placeholder="(type names or look up list)" tabindex="-1" aria-label="type names or look up list"></input> <div class="selectize-control form-control multi"></div> </div> </div> <div class="modal_option-container mbottom-20 scrollable" id="moreUl-<%=allId%>"> </div> <hr> <div class="d-flex"> <a href="#" id="apply-<%= allId %>" class="btn btn-primary mr-1" data-bs-dismiss="modal">Apply Filters</a> <a href="#" id="cancel-<%= allId %>" class="btn btn-default" data-bs-dismiss="modal">Cancel</a> </div> </div> </div> </div> </li> </ul> </script> <script type="text/template" id="search-result-facet-terms"> <ul class="sf-list"> <li class="sf-select-all"> <input id="<%= allId %>" type="checkbox" checked="checked" disabled="disabled"/> <label for="<%= allId %>">Remove all topic filters</label> </li> <%= values %> <li class="sf-expanded"> <a href="#" id="more-<%= allId %>" class="search-panel_more-link hidden-xs" data-bs-toggle="modal" data-bs-target="#modal-<%= allId %>">include more topics »</a> <div class="modal full fade" id="modal-<%= allId %>"> <div class="modal-dialog"> <div class="modal-content search"> <div class="row mbottom-20"> <div class="col-md-4"> <h3 class="modal-header search">Optics & Photonics Topics</h3> </div> <div class="col-md-6 col-md-offset-2"> <input id="input-<%= allId%>" type="text" class="form-control" placeholder="Search for a specific topic" tabindex="-1" aria-label="Search for a specific topic"></input> </div> </div> <div class="row mbottom-20"> <div class="col-md-12"> <strong>Browse the topics:</strong> Click the <svg class="selection-list_arrow"><use xlink:href="#right-arrow" /></svg> to reveal subtopics. Use the checkbox to select a topic to filter your search. </div> </div> <div class="modal_option-container mbottom-20 scrollable" id="moreUl-<%=allId%>"> </div> <div class="row"> <div class="col-md-12"> <strong>Selected Topics</strong> </div> </div> <div id="moreSelectedList"></div> <div class="row"><div class="col-md-12"> </div></div> <div class="d-flex"> <a href="#" id="apply-<%= allId %>" class="btn btn-primary mr-1" data-bs-dismiss="modal">Add Selected Topic Filters</a> <a href="#" id="cancel-<%= allId %>" class="btn btn-default" data-bs-dismiss="modal">Cancel</a> </div> </div> </div> </div> </li> </ul> </script> <script type="text/template" id="search-result-facet-journal-proceedings"> <ul class="sf-list"> <li class="sf-select-all"><input id="<%= allId %>" type="checkbox" checked> <label for="<%= allId %>">All</label></li> <%= values %> <li class="sf-expanded"> <a href="#" id="more-<%= allId %>" class="search-panel_more-link" data-bs-toggle="modal" data-bs-target="#modal-<%= allId %>" class="sf-expanded-toggle">more <%=name%> »</a> <div class="modal full fade" id="modal-<%= allId %>"> <div class="modal-dialog"> <div class="modal-content search"> <div class="row mbottom-20"> <div class="col-md-4"> <h3 class="modal-header search"><%= modalTitle%></h3> </div> <div class="col-md-6 col-md-offset-2"> <input id="input-<%= allId%>" type="text" class="form-control selectized" placeholder="(type names or look up list)" tabindex="-1" aria-label="type names or look up list"></input> <div class="selectize-control form-control multi"></div> </div> </div> <div class="modal_option-container mbottom-20 scrollable" id="moreUl-<%=allId%>"> </div> <hr> <div class="d-flex"> <a href="#" id="apply-<%= allId %>" class="btn btn-primary mr-1" data-bs-dismiss="modal">Apply Filters</a> <a href="#" id="cancel-<%= allId %>" class="btn btn-default" data-bs-dismiss="modal">Cancel</a> </div> </div> </div> </div> </li> </ul> </script> <script type="text/template" id="search-result-facet-content"> <ul class="sf-list"> <%= values %> </ul> </script> <script type="text/template" id="facet-more-new-content"> <div class="more-columns_container"> <div class="more-columns_column"><ul class="selection-list"><%= val1%></ul></div> <div class="more-columns_column"><ul class="selection-list"><%= val2%></ul></div> <div class="more-columns_column"><ul class="selection-list"><%= val3%></ul></div> </div> </script> <script type="text/template" id="facet-more-terms-div"> <div class="more-columns_container"> <div class="more-columns_column" id="<%= name%>-col1"><%= val%></div> <div class="more-columns_column" id="<%= name%>-col2"></div> <div class="more-columns_column" id="<%= name%>-col3"></div> </div> </script> <script type="text/template" id="facet-more-terms-list"> <ul class="selection-list"><%= val%></ul> </script> <script type="text/template" id="search-result-facet-more"> <a id="more-<%= name %>" href="#" class="sidebar_more white">More</a> </script> <script type="text/template" id="search-result-facet-detail"> <a href="#" id="details-link-<%= id %>" class="sidebar_more black">details</a> <ul id="details-container-<%= id %>" class="list-unstyled" style="display:none;" data-value="<%= valName %>"></ul> </script> <script type="text/template" id="search-result-facet-value"> <li class="sf-list_list-item <%= rowclass %>" style="<%= display %>"> <input type="checkbox" class="sf-list_input <%= boxstyle %>" name="chkFacet-<%= name %>" value="<%= code %>" aria-label="<%= dataValue %>" data-value="<%= dataValue %>" id="<%= id %>" <%= checked %> acronym="<%= acronym %>" /> <% if (hasCloseButton === true) { %> <div <% if (isbold != '') { %> class="sf-list_label sf-authors-bold" <% } else { %> class="sf-list_label" style="margin-bottom:5px"<% } %>><%= valName %><span class="facet-count"><%= valCount %></span> <span class="fal fa-times-circle facet-value_toggle purple-color"></span></div> <%= detail%> <% } else { %> <label <%= title%> for="<%= id %>" <% if (isbold != '') { %> class="sf-list_label sf-authors-bold" <% } else { %> class="sf-list_label" <% } %>><%= valName %> <span class="facet-count"><%= valCount %></span></label> <%= detail%> <% } %> </li> </script> <script type="text/template" id="more-term-facet-value"> <li class="selection-list_list-item" style="<%= display %>"> <input id="<%= labelid %>" class="selection-list_checkbox" type="checkbox" name="<%= name %>" data-value="<%= dataValue %>" <%= checked %> <%= boxstyle %>/><div class="selection-list_link" name="text-<%= name %>" data-value="<%= dataValue %>" <%= clazz %>><label for="<%= labelid %>" style="font-weight:normal;margin-bottom:0px;"><%= valName %><% if (valCount != "") { %> <span class="more-facet-count"><%= valCount %></span><% } %></label></div><% if (isx === true) { %><a href="#" aria-label="selection expander" class="selection-list_expander <%= inputname%>-expandin"><svg class="selection-list_arrow"><use xlink:href="#right-arrow" /></svg></a><% } %> </li> </script> <script type="text/template" id="more-term-selected"> <div class="selected-facet" data-topic="<%= finalTopic %>"> <%= val %> <a href="#" name="selected-x" aria-label="<%= dataValue %>" data-value="<%= dataValue %>" count="<%= cnt %>" class="selected-facet_close" ><span class="fal fa-times-circle purple-color"></span></a> </div> </script> <script type="text/template" id="search-result-facet-class"> class="" </script> <script type="text/template" id="search-result-facet-style-normal"> style="font-weight:normal" </script> <script type="text/template" id="search-result-facet-sort-popup"> <p> <input type="radio" id='<%= name %>:item-order:ascending' name="facetSortBy" value='<%= name %>:item-order:ascending' > <label for='<%= name %>:item-order:ascending'><%= label %> ascending</label><br> <input type="radio" id='<%= name %>:item-order:descending' name="facetSortBy" value='<%= name %>:item-order:descending' > <label for='<%= name %>:item-order:descending'><%= label %> descending</label><br> <input type="radio" id='<%= name %>:frequency-order:ascending' name="facetSortBy" value='<%= name %>:frequency-order:ascending' > <label for='<%= name %>:frequency-order:ascending'>Frequency ascending</label><br> <input type="radio" id='<%= name %>:frequency-order:descending' name="facetSortBy" value='<%= name %>:frequency-order:descending'> <label for='<%= name %>:frequency-order:descending'>Frequency descending</label> </p> </script> <script type="text/template" id="filter-selected"> <li class="label filter-tag filter-tag--<%= filterType %>"> <%= filterValue %> <a class="inline-dismiss"><span name="filterSelected" id="<%= filterId %>" class="fal fa-times purple-color" data-value="<%= filterValue %>"></span></a></li> </script> <script type="text/template" id="filter-search"> <li class="filter-search label filter-tag filter-tag--<%= filterType %>"> <%= filterLabel %> <a class="inline-dismiss"><span name="filterSelected" id="<%= filterId %>" class="fal fa-times purple-color" data-value="<%= filterValue %>"></span></a></li> </script> <script type="text/template" id="publication-sort-template"> <button class="sf-sort-toggle"><i class="fas fa-sort"></i><span class="sr-only">sort</span></button> <div class="sf-sort-popup"> <ul> <li class="active"><a href="#" name="sort-<%= type%>" data-value="<%= type%>:frequency-order:descending">Article Count</a></li> <li><a href="#" name="sort-<%= type%>" data-value="<%= type%>:item-order:ascending">Alphabetical A>Z</a></li> <li><a href="#" name="sort-<%= type%>" data-value="<%= type%>:item-order:descending">Alphabetical Z>A</a></li> </ul> </div> </script> <script type="text/template" id="author-topic-sort-template"> <button class="sf-sort-toggle"><i class="fas fa-sort"></i><span class="sr-only">sort</span></button> <div class="sf-sort-popup"> <ul> <li class="active"><a href="#" name="sort-<%= type%>" data-value="<%= type%>:frequency-order:descending">Article Count</a></li> <li><a href="#" name="sort-<%= type%>" data-value="<%= type%>:item-order:ascending">Alphabetical A>Z</a></li> <li><a href="#" name="sort-<%= type%>" data-value="<%= type%>:item-order:descending">Alphabetical Z>A</a></li> </ul> </div> </script> <script type="text/template" id="year-sort-template"> <button class="sf-sort-toggle"><i class="fas fa-sort"></i><span class="sr-only">sort</span></button> <div class="sf-sort-popup"> <ul> <li class="active"><a href="#" name="sort-year" data-value="year:item-order:descending">Newest date first</a></li> <li><a href="#" name="sort-year" data-value="year:item-order:ascending">Oldest date first</a></li> <li><a href="#" name="sort-year" data-value="year:frequency-order:descending">Article Count</a></li> </ul> </div> </script> <script type="text/template" id="more-pop-up-template"> <%= values%> </script> <script type="text/template" id="loading-gif-template"> <li><img style="position:center; display:none;" src="../images/ajax-loader.gif"/></li> </script> <script type="text/template" id="all-plus-separator-template"> <li class="sf-select-all"><input id="<%= allId %>" type="checkbox" > <label for="<%= allId %>">All</label></li> </script> <script type="text/template" id="more-topic-column-header"> <div class="selection-list_header"><%= name %></div> </script> <script type="text/template" id="loader"> <div class="progress"> <div class="progress-bar progress-bar-striped active" role="progress-bar" id="progress-<%= allId %>"></div> </div> </script> <script type="text/javascript"> $(document).ready(function() { if (location.hash.indexOf("figanchor") != -1) { let figHash = location.hash; $("#figurestablink").click(); window.location.hash = figHash; $(location.hash).get(0).scrollIntoView({behavior: "smooth"}); } $.get('/checkjs.cfm?s=DF4J6P5'); populateRecentPages(); $("img").removeClass("lazyimg").unveil(100); }); </script> <script type="text/javascript"> var gaAcct = "UA-1200622-15"; function downloadJSAtOnload() { var element = document.createElement("script"); 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