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Accordingly, two novel optical biosensor configurations for cancer cell detections have been proposed in this paper. These structures are composed of one-dimensional photonic crystal (PC) lattices coupled to two metal–insulator–metal (MIM) plasmonic waveguides. Also, the tapering method is used to improve the matching between the MIM plasmonic waveguides and PC structure in the second proposed topology. The PC lattices at the central part of the structures generate photonic bandgaps (PBGs) with sharp edges in the transmission spectra of the biosensors. These sharp edges are suitable candidates for sensing applications. On the other hand, the long distance between two PBG edges causes that when the low PBG edge is used for sensing mechanism, it does not have an overlapping with the high PBG edge by changing the refractive index of the analyte. Therefore, the proposed biosensors can be used for a wide wavelength range. The maximum obtained sensitivities and FOM values of the designed biosensors are equal to 718.6, 714.3 nm/RIU, and 156.217, 60.1 RIU−1, respectively. The metal and insulator materials which are used in the designed structures are silver, air, and GaAs, respectively. The finite-difference time-domain (FDTD) method is used for the numerical investigation of the proposed structures. Furthermore, the initial structure of the proposed biosensors is analyzed using the transmission line method to verify the FDTD simulations. The attractive and simple topologies of the proposed biosensors and their high sensitivities make them suitable candidates for biosensing applications.","datePublished":"2022-03-28T00:00:00Z","dateModified":"2022-03-28T00:00:00Z","pageStart":"1","pageEnd":"19","license":"http://creativecommons.org/licenses/by/4.0/","sameAs":"https://doi.org/10.1038/s41598-022-09213-w","keywords":["Optics and photonics","Physics","Science","Humanities and Social Sciences","multidisciplinary"],"image":["https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig1_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig2_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig3_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig4_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig5_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig6_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig7_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig8_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig9_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig10_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig11_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig12_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig13_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig14_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig15_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig16_HTML.png","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig17_HTML.png"],"isPartOf":{"name":"Scientific Reports","issn":["2045-2322"],"volumeNumber":"12","@type":["Periodical","PublicationVolume"]},"publisher":{"name":"Nature Publishing Group UK","logo":{"url":"https://www.springernature.com/app-sn/public/images/logo-springernature.png","@type":"ImageObject"},"@type":"Organization"},"author":[{"name":"Shiva Khani","affiliation":[{"name":"Razi University","address":{"name":"Electrical Engineering Department, Faculty of Engineering, Razi University, Kermanshah, Iran","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"},{"name":"Mohsen Hayati","affiliation":[{"name":"Razi University","address":{"name":"Electrical Engineering Department, Faculty of Engineering, Razi University, Kermanshah, Iran","@type":"PostalAddress"},"@type":"Organization"}],"email":"mohsen_hayati@yahoo.com","@type":"Person"}],"isAccessibleForFree":true,"@type":"ScholarlyArticle"},"@context":"https://schema.org","@type":"WebPage"}</script> <link rel="canonical" href="https://www.nature.com/articles/s41598-022-09213-w"> <meta name="journal_id" content="41598"/> <meta name="dc.title" content="Optical biosensors using plasmonic and photonic crystal band-gap structures for the detection of basal cell cancer"/> <meta name="dc.source" content="Scientific Reports 2022 12:1"/> <meta name="dc.format" content="text/html"/> <meta name="dc.publisher" content="Nature Publishing Group"/> <meta name="dc.date" content="2022-03-28"/> <meta name="dc.type" content="OriginalPaper"/> <meta name="dc.language" content="En"/> <meta name="dc.copyright" content="2022 The Author(s)"/> <meta name="dc.rights" content="2022 The Author(s)"/> <meta name="dc.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="dc.description" content="One of the most interesting topics in bio-optics is measuring the refractive index of tissues. Accordingly, two novel optical biosensor configurations for cancer cell detections have been proposed in this paper. These structures are composed of one-dimensional photonic crystal (PC) lattices coupled to two metal–insulator–metal (MIM) plasmonic waveguides. Also, the tapering method is used to improve the matching between the MIM plasmonic waveguides and PC structure in the second proposed topology. The PC lattices at the central part of the structures generate photonic bandgaps (PBGs) with sharp edges in the transmission spectra of the biosensors. These sharp edges are suitable candidates for sensing applications. On the other hand, the long distance between two PBG edges causes that when the low PBG edge is used for sensing mechanism, it does not have an overlapping with the high PBG edge by changing the refractive index of the analyte. Therefore, the proposed biosensors can be used for a wide wavelength range. The maximum obtained sensitivities and FOM&nbsp;values of the designed biosensors are equal to 718.6, 714.3&nbsp;nm/RIU, and 156.217, 60.1&nbsp;RIU−1, respectively. The metal and insulator materials which are used in the designed structures are silver, air, and GaAs, respectively. The finite-difference time-domain (FDTD) method is used for the numerical investigation of the proposed structures. Furthermore, the initial structure of the proposed biosensors is analyzed using the transmission line method to verify the FDTD simulations. The attractive and simple topologies of the proposed biosensors and their high sensitivities make them suitable candidates for biosensing applications."/> <meta name="prism.issn" content="2045-2322"/> <meta name="prism.publicationName" content="Scientific Reports"/> <meta name="prism.publicationDate" content="2022-03-28"/> <meta name="prism.volume" content="12"/> <meta name="prism.number" content="1"/> <meta name="prism.section" content="OriginalPaper"/> <meta name="prism.startingPage" content="1"/> <meta name="prism.endingPage" content="19"/> <meta name="prism.copyright" content="2022 The Author(s)"/> <meta name="prism.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="prism.url" content="https://www.nature.com/articles/s41598-022-09213-w"/> <meta name="prism.doi" content="doi:10.1038/s41598-022-09213-w"/> <meta name="citation_pdf_url" content="https://www.nature.com/articles/s41598-022-09213-w.pdf"/> <meta name="citation_fulltext_html_url" content="https://www.nature.com/articles/s41598-022-09213-w"/> <meta name="citation_journal_title" content="Scientific Reports"/> <meta name="citation_journal_abbrev" content="Sci Rep"/> <meta name="citation_publisher" content="Nature Publishing Group"/> <meta name="citation_issn" content="2045-2322"/> <meta name="citation_title" content="Optical biosensors using plasmonic and photonic crystal band-gap structures for the detection of basal cell cancer"/> <meta name="citation_volume" content="12"/> <meta name="citation_issue" content="1"/> <meta name="citation_online_date" content="2022/03/28"/> <meta name="citation_firstpage" content="1"/> <meta name="citation_lastpage" content="19"/> <meta name="citation_article_type" content="Article"/> <meta name="citation_fulltext_world_readable" content=""/> <meta name="citation_language" content="en"/> <meta name="dc.identifier" content="doi:10.1038/s41598-022-09213-w"/> <meta name="DOI" content="10.1038/s41598-022-09213-w"/> <meta name="size" content="287327"/> <meta name="citation_doi" content="10.1038/s41598-022-09213-w"/> <meta name="citation_springer_api_url" content="http://api.springer.com/xmldata/jats?q=doi:10.1038/s41598-022-09213-w&api_key="/> <meta name="description" content="One of the most interesting topics in bio-optics is measuring the refractive index of tissues. Accordingly, two novel optical biosensor configurations for cancer cell detections have been proposed in this paper. These structures are composed of one-dimensional photonic crystal (PC) lattices coupled to two metal–insulator–metal (MIM) plasmonic waveguides. Also, the tapering method is used to improve the matching between the MIM plasmonic waveguides and PC structure in the second proposed topology. The PC lattices at the central part of the structures generate photonic bandgaps (PBGs) with sharp edges in the transmission spectra of the biosensors. These sharp edges are suitable candidates for sensing applications. On the other hand, the long distance between two PBG edges causes that when the low PBG edge is used for sensing mechanism, it does not have an overlapping with the high PBG edge by changing the refractive index of the analyte. Therefore, the proposed biosensors can be used for a wide wavelength range. The maximum obtained sensitivities and FOM&nbsp;values of the designed biosensors are equal to 718.6, 714.3&nbsp;nm/RIU, and 156.217, 60.1&nbsp;RIU−1, respectively. The metal and insulator materials which are used in the designed structures are silver, air, and GaAs, respectively. The finite-difference time-domain (FDTD) method is used for the numerical investigation of the proposed structures. Furthermore, the initial structure of the proposed biosensors is analyzed using the transmission line method to verify the FDTD simulations. 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u-hide" data-test="context-bar" data-context-bar aria-hidden="true"> <div class="c-context-bar__container u-container" data-track-context="sticky banner"> <div class="c-context-bar__title"> Optical biosensors using plasmonic and photonic crystal band-gap structures for the detection of basal cell cancer </div> <div class="c-pdf-download u-clear-both js-pdf-download"> <a href="/articles/s41598-022-09213-w.pdf" class="u-button u-button--full-width u-button--primary u-justify-content-space-between c-pdf-download__link" data-article-pdf="true" data-readcube-pdf-url="true" data-test="download-pdf" data-draft-ignore="true" data-track="content_download" data-track-type="article pdf download" data-track-action="download pdf" data-track-label="link" data-track-external download> <span class="c-pdf-download__text">Download PDF</span> <svg aria-hidden="true" focusable="false" width="16" height="16" class="u-icon"><use xlink:href="#icon-download"/></svg> </a> </div> </div> </div> <article 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data-test="article-category">Article</li> <li class="c-article-identifiers__item"> <a href="https://www.springernature.com/gp/open-research/about/the-fundamentals-of-open-access-and-open-research" data-track="click" data-track-action="open access" data-track-label="link" class="u-color-open-access" data-test="open-access">Open access</a> </li> <li class="c-article-identifiers__item">Published: <time datetime="2022-03-28">28 March 2022</time></li> </ul> <h1 class="c-article-title" data-test="article-title" data-article-title="">Optical biosensors using plasmonic and photonic crystal band-gap structures for the detection of basal cell cancer</h1> <ul class="c-article-author-list c-article-author-list--short" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Shiva-Khani-Aff1" data-author-popup="auth-Shiva-Khani-Aff1" data-author-search="Khani, Shiva">Shiva Khani</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup> & </li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Mohsen-Hayati-Aff1" data-author-popup="auth-Mohsen-Hayati-Aff1" data-author-search="Hayati, Mohsen" data-corresp-id="c1">Mohsen Hayati<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-mail-medium"></use></svg></a><sup class="u-js-hide"><a href="#Aff1">1</a></sup> </li></ul> <p class="c-article-info-details" data-container-section="info"> <a data-test="journal-link" href="/srep" data-track="click" data-track-action="journal homepage" data-track-category="article body" data-track-label="link"><i data-test="journal-title">Scientific Reports</i></a> <b data-test="journal-volume"><span class="u-visually-hidden">volume</span> 12</b>, Article number: <span data-test="article-number">5246</span> (<span data-test="article-publication-year">2022</span>) <a href="#citeas" class="c-article-info-details__cite-as u-hide-print" data-track="click" data-track-action="cite this article" data-track-label="link">Cite this article</a> </p> <div class="c-article-metrics-bar__wrapper u-clear-both"> <ul class="c-article-metrics-bar u-list-reset"> <li class=" c-article-metrics-bar__item" data-test="access-count"> <p class="c-article-metrics-bar__count">4839 <span class="c-article-metrics-bar__label">Accesses</span></p> </li> <li class="c-article-metrics-bar__item" data-test="citation-count"> <p class="c-article-metrics-bar__count">59 <span class="c-article-metrics-bar__label">Citations</span></p> </li> <li class="c-article-metrics-bar__item" data-test="altmetric-score"> <p class="c-article-metrics-bar__count">7 <span class="c-article-metrics-bar__label">Altmetric</span></p> </li> <li class="c-article-metrics-bar__item"> <p class="c-article-metrics-bar__details"><a href="/articles/s41598-022-09213-w/metrics" data-track="click" data-track-action="view metrics" data-track-label="link" rel="nofollow">Metrics <span class="u-visually-hidden">details</span></a></p> </li> </ul> </div> </header> <div class="u-js-hide" data-component="article-subject-links"> <h3 class="c-article__sub-heading">Subjects</h3> <ul class="c-article-subject-list"> <li class="c-article-subject-list__subject"><a href="/subjects/optics-and-photonics" data-track="click" data-track-action="view subject" data-track-label="link">Optics and photonics</a></li><li class="c-article-subject-list__subject"><a href="/subjects/physics" data-track="click" data-track-action="view subject" data-track-label="link">Physics</a></li> </ul> </div> </div> <div class="c-article-body"> <section aria-labelledby="Abs1" data-title="Abstract" lang="en"><div class="c-article-section" id="Abs1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Abs1">Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>One of the most interesting topics in bio-optics is measuring the refractive index of tissues. Accordingly, two novel optical biosensor configurations for cancer cell detections have been proposed in this paper. These structures are composed of one-dimensional photonic crystal (PC) lattices coupled to two metal–insulator–metal (MIM) plasmonic waveguides. Also, the tapering method is used to improve the matching between the MIM plasmonic waveguides and PC structure in the second proposed topology. The PC lattices at the central part of the structures generate photonic bandgaps (PBGs) with sharp edges in the transmission spectra of the biosensors. These sharp edges are suitable candidates for sensing applications. On the other hand, the long distance between two PBG edges causes that when the low PBG edge is used for sensing mechanism, it does not have an overlapping with the high PBG edge by changing the refractive index of the analyte. Therefore, the proposed biosensors can be used for a wide wavelength range. The maximum obtained sensitivities and FOM values of the designed biosensors are equal to 718.6, 714.3 nm/RIU, and 156.217, 60.1 RIU<sup>−1</sup>, respectively. The metal and insulator materials which are used in the designed structures are silver, air, and GaAs, respectively. The finite-difference time-domain (FDTD) method is used for the numerical investigation of the proposed structures. Furthermore, the initial structure of the proposed biosensors is analyzed using the transmission line method to verify the FDTD simulations. The attractive and simple topologies of the proposed biosensors and their high sensitivities make them suitable candidates for biosensing applications.</p></div></div></section> <noscript> </noscript> <section aria-labelledby="inline-recommendations" data-title="Inline Recommendations" class="c-article-recommendations" data-track-component="inline-recommendations"> <h3 class="c-article-recommendations-title" id="inline-recommendations">Similar content being viewed by others</h3> <div class="c-article-recommendations-list"> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs41598-023-41193-3/MediaObjects/41598_2023_41193_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://www.nature.com/articles/s41598-023-41193-3?fromPaywallRec=false" data-track="select_recommendations_1" data-track-context="inline recommendations" data-track-action="click recommendations inline - 1" data-track-label="10.1038/s41598-023-41193-3">A single-mode tunable plasmonic sensor based on an 8-shaped resonator for cancer cell detection </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">26 August 2023</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs41598-023-46667-y/MediaObjects/41598_2023_46667_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://www.nature.com/articles/s41598-023-46667-y?fromPaywallRec=false" data-track="select_recommendations_2" data-track-context="inline recommendations" data-track-action="click recommendations inline - 2" data-track-label="10.1038/s41598-023-46667-y">Ultra-high sensitive cancerous cells detection and sensing capabilities of photonic biosensor </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">09 November 2023</span> </div> </div> </article> </div> <div class="c-article-recommendations-list__item"> <article class="c-article-recommendations-card" itemscope itemtype="http://schema.org/ScholarlyArticle"> <div class="c-article-recommendations-card__img"><img src="https://media.springernature.com/w215h120/springer-static/image/art%3A10.1038%2Fs41598-020-63459-w/MediaObjects/41598_2020_63459_Fig1_HTML.png" loading="lazy" alt=""></div> <div class="c-article-recommendations-card__main"> <h3 class="c-article-recommendations-card__heading" itemprop="name headline"> <a class="c-article-recommendations-card__link" itemprop="url" href="https://www.nature.com/articles/s41598-020-63459-w?fromPaywallRec=false" data-track="select_recommendations_3" data-track-context="inline recommendations" data-track-action="click recommendations inline - 3" data-track-label="10.1038/s41598-020-63459-w">Multi-band MIM refractive index biosensor based on Ag-air grating with equivalent circuit and T-matrix methods in near-infrared region </a> </h3> <div class="c-article-meta-recommendations" data-test="recommendation-info"> <span class="c-article-meta-recommendations__item-type">Article</span> <span class="c-article-meta-recommendations__access-type">Open access</span> <span class="c-article-meta-recommendations__date">14 April 2020</span> </div> </div> </article> </div> </div> </section> <script> window.dataLayer = window.dataLayer || []; window.dataLayer.push({ recommendations: { recommender: 'semantic', model: 'specter', policy_id: 'NA', timestamp: 1732383414, embedded_user: 'null' } }); </script> <div class="main-content"> <section data-title="Introduction"><div class="c-article-section" id="Sec1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec1">Introduction</h2><div class="c-article-section__content" id="Sec1-content"><p>Electronic devices<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 1" title="Abbasi, H., Hayati, M., Kazimierczuk, M. K. & Sekiya, H. Design of class-E M amplifier with consideration of parasitic non-linear capacitances and on-state resistance. IET Power Electron. 13, 3065–3071 (2020)." href="/articles/s41598-022-09213-w#ref-CR1" id="ref-link-section-d121634187e297">1</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 2" title="Foo, C. Y., Lim, H. N., Mahdi, M. A., Wahid, M. H. & Huang, N. M. Three-dimensional printed electrode and its novel applications in electronic devices. Sci. Rep. 8, 1–11 (2018)." href="/articles/s41598-022-09213-w#ref-CR2" id="ref-link-section-d121634187e300">2</a></sup> are unable to fulfill all of the future’s expanding needs such as increasing the speed and reducing power dissipation. As a result, photonic integrated circuits such as photonic crystals (PCs)<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 3" title="Farmani, A., Mir, A. & Irannejad, M. 2D-FDTD simulation of ultra-compact multifunctional logic gates with nonlinear photonic crystal. JOSA B 36, 811–818 (2019)." href="/articles/s41598-022-09213-w#ref-CR3" id="ref-link-section-d121634187e304">3</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 4" title="Zaky, Z. A., Ahmed, A. M., Shalaby, A. S. & Aly, A. H. Refractive index gas sensor based on the Tamm state in a one-dimensional photonic crystal: Theoretical optimisation. Sci. Rep. 10, 1–9 (2020)." href="/articles/s41598-022-09213-w#ref-CR4" id="ref-link-section-d121634187e307">4</a></sup> can be suitable candidates to replace electronic integrated circuits due to their higher computational speeds, higher information densities, and less noise. One-dimensional PC structures consist of a multilayer stack of insulator materials<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="Khani, S., Danaie, M. & Rezaei, P. Hybrid all-optical infrared metal-insulator-metal plasmonic switch incorporating photonic crystal bandgap structures. Photonics Nanostruct. Fundam. Appl. 40, 100802 (2020)." href="/articles/s41598-022-09213-w#ref-CR5" id="ref-link-section-d121634187e311">5</a></sup>. Appearance of photonic band-gap (PBG) is one of the most significant properties of these structures<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 6" title="Joannopoulos, J. D., Villeneuve, P. R. & Fan, S. Photonic crystals: Putting a new twist on light. Nature 386, 143–149 (1997)." href="/articles/s41598-022-09213-w#ref-CR6" id="ref-link-section-d121634187e315">6</a></sup>. The dynamic shift of the PBG edge in PCs can be used to design various structures such as optical sensors<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 7" title="Aly, A. H., Zaky, Z. A., Shalaby, A. S., Ahmed, A. M. & Vigneswaran, D. Theoretical study of hybrid multifunctional one-dimensional photonic crystal as a flexible blood sugar sensor. Phys. Scr. 95, 035510 (2020)." href="/articles/s41598-022-09213-w#ref-CR7" id="ref-link-section-d121634187e319">7</a></sup>, switches<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="Khani, S., Danaie, M. & Rezaei, P. Hybrid all-optical infrared metal-insulator-metal plasmonic switch incorporating photonic crystal bandgap structures. Photonics Nanostruct. Fundam. Appl. 40, 100802 (2020)." href="/articles/s41598-022-09213-w#ref-CR5" id="ref-link-section-d121634187e324">5</a></sup>, and modulators<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 8" title="Yan, H. et al. One-dimensional photonic crystal slot waveguide for silicon-organic hybrid electro-optic modulators. Opt. Lett. 41, 5466–5469 (2016)." href="/articles/s41598-022-09213-w#ref-CR8" id="ref-link-section-d121634187e328">8</a></sup>. Unfortunately, due to the diffraction limit of light, PC devices are not suitable structures for the realization of highly integrated optical circuits<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="Khani, S., Danaie, M. & Rezaei, P. Hybrid all-optical infrared metal-insulator-metal plasmonic switch incorporating photonic crystal bandgap structures. Photonics Nanostruct. Fundam. Appl. 40, 100802 (2020)." href="/articles/s41598-022-09213-w#ref-CR5" id="ref-link-section-d121634187e332">5</a></sup>.</p><p>Surface plasmon polaritons (SPPs) can be used to overcome the footprint problem<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 9" title="Khani, S., Danaie, M. & Rezaei, P. 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 (2010)." href="/articles/s41598-022-09213-w#ref-CR11" id="ref-link-section-d121634187e347">11</a></sup>. SPPs are the electromagnetic surface waves that propagate at the surface of the metal and insulator materials. In the low-frequency range, metal is treated as a perfect conductor. In the UV and visible region, metal can no longer be treated as a perfect conductor. It is because of its collective electrons excitation, which is called the plasmon. In this frequency range, metal can still be used to build a low-loss metal waveguide or metal–insulator waveguide. In these cases, the electromagnetic field takes the form of an evanescent field. Furthermore, the complex permittivity of noble metals such as gold and silver has a relatively larger real part than its imaginary part. Also, its real part is usually a large negative number in the near infrared region (NIR) and visible region. This optical property of metal causes the surface plasmon wave can propagate at the surface of the metal and insulator.</p><p>In addition, plasmonic structures have the integration capability with other electrical and microwave components<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Kiani, S., Rezaei, P. & Fakhr, M. An overview of interdigitated microwave resonance sensors for liquid samples permittivity detection. Interdigit. Sens. Prog. Last Two Decades. 153–197. 
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Compact microstrip lowpass filter with wide stopband and sharp roll-off. Microw. J. 60, 86–92 (2017)." href="/articles/s41598-022-09213-w#ref-CR15" id="ref-link-section-d121634187e357">15</a></sup>. Therefore, different metal–insulator–metal (MIM) plasmonic devices have been designed so far. Such devices include plasmonic filters<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Kamari, M., Hayati, M. & Khosravi, S. Tunable infrared wide band-stop plasmonic filter using T-shaped resonators. Mater. Sci. Semicond. Process. 133, 105983 (2021)." href="#ref-CR16" id="ref-link-section-d121634187e361">16</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Wang, A. & Dan, Y. Mid-infrared plasmonic multispectral filters. Sci. 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Plasmonics 15, 2213–2221 (2020)." href="/articles/s41598-022-09213-w#ref-CR19" id="ref-link-section-d121634187e368">19</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 20" title="Chang, K.-W. & Huang, C.-C. Ultrashort broadband polarization beam splitter based on a combined hybrid plasmonic waveguide. Sci. Rep. 6, 1–11 (2016)." href="/articles/s41598-022-09213-w#ref-CR20" id="ref-link-section-d121634187e371">20</a></sup>, sensors<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Omidniaee, A., Karimi, S. & Farmani, A. Surface plasmon resonance-based SiO2 kretschmann configuration biosensor for the detection of blood glucose. SILICON 10, 1–10 (2021)." href="#ref-CR21" id="ref-link-section-d121634187e375">21</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Khani, S. & Hayati, M. An ultra-high sensitive plasmonic refractive index sensor using an elliptical resonator and MIM waveguide. Superlattices Microstruct. 156, 106970 (2021)." href="#ref-CR22" id="ref-link-section-d121634187e375_1">22</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 23" title="Amoosoltani, N., Mehrabi, K., Zarifkar, A., Farmani, A. & Yasrebi, N. Double-ring resonator plasmonic refractive index sensor utilizing dual-band unidirectional reflectionless propagation effect. Plasmonics 16, 1–9 (2021)." href="/articles/s41598-022-09213-w#ref-CR23" id="ref-link-section-d121634187e378">23</a></sup>, demultiplexers<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 24" title="Khani, S., Farmani, A. & Mir, A. Reconfigurable and scalable 2, 4-and 6-channel plasmonics demultiplexer utilizing symmetrical rectangular resonators containing silver nano-rod defects with FDTD method. Sci. Rep. 11, 1–13 (2021)." href="/articles/s41598-022-09213-w#ref-CR24" id="ref-link-section-d121634187e382">24</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 25" title="Asgari, S. & Fabritius, T. Tunable mid-infrared graphene plasmonic cross-shaped resonator for demultiplexing application. Appl. Sci. 10, 1193 (2020)." href="/articles/s41598-022-09213-w#ref-CR25" id="ref-link-section-d121634187e385">25</a></sup>, slow light waveguides<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 26" title="Liang, S. et al. Plasmonic slow light waveguide with hyperbolic metamaterials claddings. J. Opt. 20, 065001 (2018)." href="/articles/s41598-022-09213-w#ref-CR26" id="ref-link-section-d121634187e390">26</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 27" title="Akhavan, A., Ghafoorifard, H., Abdolhosseini, S. & Habibiyan, H. Metal–insulator–metal waveguide-coupled asymmetric resonators for sensing and slow light applications. IET Optoelectron. 12, 220–227 (2018)." href="/articles/s41598-022-09213-w#ref-CR27" id="ref-link-section-d121634187e393">27</a></sup>, switches<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Jafari, D., Danaie, M., Rezaei, P. & Nurmohammadi, T. A novel variable-length header extraction scheme based on ring laser for all-optical packet switching network. Opt. Quantum Electron. 2021(53), 1–9 (2021)." href="#ref-CR28" id="ref-link-section-d121634187e397">28</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Mbarak, H., Ghahrizjani, R. T., Hamidi, S., Mohajerani, E. & Zaatar, Y. Reversible and tunable photochemical switch based on plasmonic structure. Sci. 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Commun. 477, 126359 (2020)." href="/articles/s41598-022-09213-w#ref-CR31" id="ref-link-section-d121634187e400">31</a></sup>, logic gates<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 32" title="Rezaei, M. H., Zarifkar, A. & Miri, M. Ultra-compact electro-optical graphene-based plasmonic multi-logic gate with high extinction ratio. Opt. Mater. 84, 572–578 (2018)." href="/articles/s41598-022-09213-w#ref-CR32" id="ref-link-section-d121634187e404">32</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 33" title="Kewes, G. et al. A realistic fabrication and design concept for quantum gates based on single emitters integrated in plasmonic-dielectric waveguide structures. Sci. Rep. 6, 1–10 (2016)." href="/articles/s41598-022-09213-w#ref-CR33" id="ref-link-section-d121634187e407">33</a></sup>, converters<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 34" title="Jafari, D., Danaie, M. & Orouji, A. A. Ultra-fast two-bit all-optical analog to digital convertor based on surface plasmons and kerr-type nonlinear cavity. Plasmonics 16, 1–8 (2021)." href="/articles/s41598-022-09213-w#ref-CR34" id="ref-link-section-d121634187e411">34</a></sup>, modulators<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 35" title="Khani, S., Danaie, M. & Rezaei, P. Fano Resonance using surface plasmon polaritons in a nano-disk resonator coupled to perpendicular waveguides for amplitude modulation applications. Plasmonics 16, 1–18 (2021)." href="/articles/s41598-022-09213-w#ref-CR35" id="ref-link-section-d121634187e415">35</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 36" title="Melikyan, A. et al. High-speed plasmonic phase modulators. Nat. Photonics 8, 229–233 (2014)." href="/articles/s41598-022-09213-w#ref-CR36" id="ref-link-section-d121634187e418">36</a></sup> and so on. It is worth mentioning that the main disadvantage of plasmonic structures<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 37" title="Khosravi, S. & Hayati, M. Dual-wide band plasmonic filter based on nanocomposite media. Opt. Eng. 59, 095107 (2020)." href="/articles/s41598-022-09213-w#ref-CR37" id="ref-link-section-d121634187e422">37</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 38" title="Khani, S., Danaie, M. & Rezaei, P. All-optical plasmonic switches based on asymmetric directional couplers incorporating Bragg gratings. Plasmonics 15, 869–879 (2020)." href="/articles/s41598-022-09213-w#ref-CR38" id="ref-link-section-d121634187e425">38</a></sup> compared to PCs<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 39" title="Khatami, S. A., Rezaei, P., Danaie, M. & Daroonkola, A. H. Photonic crystal 180° ring-shaped hybrid: From microwave to optics. IEEE Photonics Technol. Lett. 33, 1165–1168 (2021)." href="/articles/s41598-022-09213-w#ref-CR39" id="ref-link-section-d121634187e430">39</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 40" title="Tavousi, A., Rakhshani, M. & Mansouri-Birjandi, M. High sensitivity label-free refractometer based biosensor applicable to glycated hemoglobin detection in human blood using all-circular photonic crystal ring resonators. Opt. Commun. 429, 166–174 (2018)." href="/articles/s41598-022-09213-w#ref-CR40" id="ref-link-section-d121634187e433">40</a></sup> is their higher absorption value which results in lower Q-factor. As a result, the combination of plasmonic and PC structures has been used to obtain a trade-off between various designing parameters in this paper.</p><p>Optical sensors<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Hajshahvaladi, L., Kaatuzian, H. & Danaie, M. A high-sensitivity refractive index biosensor based on Si nanorings coupled to plasmonic nanohole arrays for glucose detection in water solution. Opt. Commun. 502, 127421 (2022)." href="#ref-CR41" id="ref-link-section-d121634187e440">41</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Khani, S. & Hayati, M. Optical sensing in single-mode filters base on surface plasmon H-shaped cavities. Opt. Commun. 505, 127534 (2021)." href="#ref-CR42" id="ref-link-section-d121634187e440_1">42</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 43" title="Hajshahvaladi, L., Kaatuzian, H. & Danaie, M. Design of a hybrid photonic-plasmonic crystal refractive index sensor for highly sensitive and high-resolution sensing applications. Phys. Lett. A 420, 127754 (2021)." href="/articles/s41598-022-09213-w#ref-CR43" id="ref-link-section-d121634187e443">43</a></sup> are attracted important interest as their wide range of applications. One of the most significant applications of optical sensors is in the biomedical field. For example, such sensors can be used for cancer cell detections<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="Khani, S. & Hayati, M. Optical sensing in single-mode filters base on surface plasmon H-shaped cavities. Opt. Commun. 505, 127534 (2021)." href="/articles/s41598-022-09213-w#ref-CR42" id="ref-link-section-d121634187e447">42</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 44" title="Rakhshani, M. R. Wide-angle perfect absorber using a 3D nanorod metasurface as a plasmonic sensor for detecting cancerous cells and its tuning with a graphene layer. Photonics Nanostruct. Fundam. Appl. 43, 100883 (2021)." href="/articles/s41598-022-09213-w#ref-CR44" id="ref-link-section-d121634187e450">44</a></sup>, health care applications<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 45" title="Sharma, A. K. Plasmonic biosensor for detection of hemoglobin concentration in human blood: Design considerations. J. Appl. Phys. 114, 044701 (2013)." href="/articles/s41598-022-09213-w#ref-CR45" id="ref-link-section-d121634187e454">45</a></sup>, and blood component measurements<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 46" title="Dinish, U., Balasundaram, G., Chang, Y. T. & Olivo, M. Sensitive multiplex detection of serological liver cancer biomarkers using SERS-active photonic crystal fiber probe. J. Biophotonics 7, 956–965 (2014)." href="/articles/s41598-022-09213-w#ref-CR46" id="ref-link-section-d121634187e458">46</a></sup>. Up to now, different approaches based on various configurations such as plasmonic<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 47" title="Chen, J. et al. High-quality temperature sensor based on the plasmonic resonant absorber. Plasmonics 14, 279–283 (2019)." href="/articles/s41598-022-09213-w#ref-CR47" id="ref-link-section-d121634187e462">47</a></sup>, PC<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 48" title="Liu, C. et al. Symmetrical dual D-shape photonic crystal fibers for surface plasmon resonance sensing. Opt. Express 26, 9039–9049 (2018)." href="/articles/s41598-022-09213-w#ref-CR48" id="ref-link-section-d121634187e467">48</a></sup>, graphene<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 49" title="Nickpay, M.-R., Danaie, M. & Shahzadi, A. Highly sensitive THz refractive index sensor based on folded split-ring metamaterial graphene resonators. Plasmonics. 17(1), 237–248 (2021)." href="/articles/s41598-022-09213-w#ref-CR49" id="ref-link-section-d121634187e471">49</a></sup>, optical fiber topologies<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 50" title="Nasirifar, R., Danaie, M. & Dideban, A. Surface plasmon resonance biosensor using inverted graded index optical fiber. Photonics Nanostruct. Fundam. Appl. 44, 100916 (2021)." href="/articles/s41598-022-09213-w#ref-CR50" id="ref-link-section-d121634187e475">50</a></sup>, etc. have been adopted to design optical sensors. Since surface plasmons are sensitive to changes in the refractive index of the metal surface, this phenomenon can be used as a tool for optical sensing. Sensors designed using plasmonic structures are sensitive to refractive index changes so that by connecting the particle to the surface, refractive index changes will be detectable. In this method, the particle-to-surface connection is converted directly into a signal and does not require labeling, while in conventional optical sensors, chromophore colors are required. Recent progress in plasmon-based sensors has overcome the limitations of conventional optical sensors so that using such structures will enhance the sensitivity, optical stability, tunability, and usability of these sensors in the living environment.</p><p>The conventional configurations to design optical sensors are based on plasmonic Mach–Zehnder interferometer<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 51" title="El Shamy, R. S., Khalil, D. & Swillam, M. A. Mid infrared optical gas sensor using plasmonic Mach-Zehnder interferometer. Sci. Rep. 10, 1–9 (2020)." href="/articles/s41598-022-09213-w#ref-CR51" id="ref-link-section-d121634187e483">51</a></sup>, plasmonic square ring resonator<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 52" title="Khonina, S., Kazanskiy, N., Butt, M., Kaźmierczak, A. & Piramidowicz, R. Plasmonic sensor based on metal-insulator-metal waveguide square ring cavity filled with functional material for the detection of CO2 gas. Opt. Express 29, 16584–16594 (2021)." href="/articles/s41598-022-09213-w#ref-CR52" id="ref-link-section-d121634187e487">52</a></sup>, plasmonic cross resonator<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 53" title="Pang, S., Huo, Y., Xie, Y. & Hao, L. Tunable electromagnetically induced transparency-like in plasmonic stub waveguide with cross resonator. Plasmonics 12, 1161–1168 (2017)." href="/articles/s41598-022-09213-w#ref-CR53" id="ref-link-section-d121634187e491">53</a></sup>, rectangular plasmonic interferometer<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 54" title="Khajemiri, Z., Lee, D., Hamidi, S. M. & Kim, D.-S. Rectangular plasmonic interferometer for high sensitive glycerol sensor. Sci. Rep. 9, 1–7 (2019)." href="/articles/s41598-022-09213-w#ref-CR54" id="ref-link-section-d121634187e495">54</a></sup>, plasmonic triangular resonator<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 55" title="Al Mahmud, R., Faruque, M. O. & Sagor, R. H. A highly sensitive plasmonic refractive index sensor based on triangular resonator. Opt. Commun. 483, 126634 (2021)." href="/articles/s41598-022-09213-w#ref-CR55" id="ref-link-section-d121634187e499">55</a></sup>, one dimensional porous silicon PC sensor<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 56" title="Ahmed, A. M. & Mehaney, A. Ultra-high sensitive 1D porous silicon photonic crystal sensor based on the coupling of Tamm/Fano resonances in the mid-infrared region. Sci. Rep. 9, 1–9 (2019)." href="/articles/s41598-022-09213-w#ref-CR56" id="ref-link-section-d121634187e504">56</a></sup>, armchair graphene nano-ribbon<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 57" title="Salih, E. & Ayesh, A. I. Pt-doped armchair graphene nanoribbon as a promising gas sensor for CO and CO2: DFT study. Phys. E Low Dimens. Syst. Nanostruct. 125, 114418 (2021)." href="/articles/s41598-022-09213-w#ref-CR57" id="ref-link-section-d121634187e508">57</a></sup>, and so on. All aforementioned sensor structures in the literature create conventional spectra like Lorentzian, Fano resonance, and electromagnetically induced transparency (EIT) spectra for sensing applications.</p><p>In this paper, two novel topologies have been proposed based on the combination of one-dimensional (1D) PC and MIM plasmonic configurations. In these structures, the PC topologies have been used at the central part of the sensor structures (between two MIM plasmonic waveguides) to create PBGs in the transmission spectra with sharp transient edges. These sharp edges increase the sensitivity of the proposed sensors. Accordingly, this spectrum type is a suitable choice for sensing mechanisms. Also, the tapering technique has been used in the second proposed topology to improve the matching between the plasmonic and PC sections. It is worth mentioning that the designed sensors can be used for the detection of the basal cell cancer. Today, cancer has spread worldwide in a way that has attracted the serious attention of researchers. Prompt and timely diagnosis of cancer is one way to determine the best treatment option. Cancer seems to be on the rise today due to environmental pollution, lifestyle, and nutrition. On the other hand, due to the high cost, lengthy and difficult treatment of cancer, early detection of cancer is very important for treatment.</p><p>The metal material of the substrate area in these structures is assumed to be silver, which is characterized by a well-known Drude model<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 58" title="Khani, S., Danaie, M. & Rezaei, P. Tunable single-mode bandpass filter based on metal–insulator–metal plasmonic coupled U-shaped cavities. IET Optoelectron. 13, 161–171 (2019)." href="/articles/s41598-022-09213-w#ref-CR58" id="ref-link-section-d121634187e518">58</a></sup>. Meanwhile, the used insulator materials are air (<span class="mathjax-tex">$\varepsilon =1$</span>) and GaAs (Palik model). The finite-difference time-domain (FDTD) method has been used for the numerical investigation of the designed structures. To verify the FDTD simulations, analytical formulas based on the transmission line method (TLM) have also been proposed for the initial structure.</p><p>The rest of this paper is organized as follows: The initial structure which is used to design the proposed biosensor structures is introduced in “Initial structure and its formulation”. Also, an analytical model is presented in this section to calculate the transmission spectrum of the initial structure. “Design of the proposed biosensor I” and “Design of the proposed biosensor II” introduce the first and second proposed biosensors. Biosensors application is explained in “Biosensors application”. The obtained results are summarized and compared with other works in “Discussions and comparisons”. Finally, the last section is devoted to conclusions.</p></div></div></section><section data-title="Initial structure and its formulation"><div class="c-article-section" id="Sec2-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec2">Initial structure and its formulation</h2><div class="c-article-section__content" id="Sec2-content"><p>As shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig1">1</a>, a rectangular resonator connected to two MIM plasmonic waveguides is used to design the initial structure of the proposed sensors. The geometrical parameters of the initial structure include the length (L = 3980 nm) and width (W<sub>2</sub> = 250 nm) of the rectangular resonator and the width of the MIM waveguide (W<sub>1</sub> = 100 nm). The insulator layer is air with <span class="mathjax-tex">${\varepsilon }_{d1}=1$</span>, and the metal layers are silver. The complex relative permittivity of silver is characterized by the Drude model<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 59" title="Khani, S., Danaie, M. & Rezaei, P. Double and triple-wavelength plasmonic demultiplexers based on improved circular nanodisk resonators. Opt. Eng. 57, 107102 (2018)." href="/articles/s41598-022-09213-w#ref-CR59" id="ref-link-section-d121634187e598">59</a></sup>:</p><div id="Equ1" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${\upvarepsilon }_{\mathrm{m}}\left(\upomega \right)= {\upvarepsilon }_{\infty }-\frac{{\upomega }_{\mathrm{p}}^{2}}{\upomega \left(\upomega +\mathrm{j \gamma }\right)},$$</span></div><div class="c-article-equation__number"> (1) </div></div><p>where ε<sub>∞</sub> = 3.7 is the medium dielectric constant for the infinite frequency, ω<sub>p</sub> = 1.38 × 1016 Hz presents the bulk plasma frequency, ɤ = 2.73 × 1013 Hz denotes the electron collision frequency, and ω is the angular frequency of incident light.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-1" data-title="Figure 1"><figure><figcaption><b id="Fig1" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 1</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/1" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig1_HTML.png?as=webp"><img aria-describedby="Fig1" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig1_HTML.png" alt="figure 1" loading="lazy" width="685" height="553"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-1-desc"><p>3D topology of the initial structure.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/1" data-track-dest="link:Figure1 Full size image" aria-label="Full size image figure 1" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>The FDTD method is commonly used to model the MIM waveguide-based plasmonic structures<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 60" title="Nasirifar, R., Danaie, M. & Dideban, A. Highly sensitive surface plasmon resonance sensor using perforated optical fiber for biomedical applications. Optik 250, 168051 (2022)." href="/articles/s41598-022-09213-w#ref-CR60" id="ref-link-section-d121634187e716">60</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 61" title="Khani, S., Danaie, M. & Rezaei, P. Size reduction of MIM surface plasmon based optical bandpass filters by the introduction of arrays of silver nano-rods. Phys. E 113, 25–34 (2019)." href="/articles/s41598-022-09213-w#ref-CR61" id="ref-link-section-d121634187e719">61</a></sup>. Another method to model such structures is the TLM<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 62" title="Farahani, M., Granpayeh, N. & Rezvani, M. Broadband zero reflection plasmonic junctions. JOSA B 29, 1722–1730 (2012)." href="/articles/s41598-022-09213-w#ref-CR62" id="ref-link-section-d121634187e723">62</a></sup>. The second model, which is an analytical method, is usually used for the plasmonic structures with linear insulator materials. On the other hand, the FDTD method is more time-consuming than the TLM. Consequently, in addition to the FDTD method, the TLM has also been investigated for the initial structure.</p><p>After introducing the initial structure, the analytical model is presented to describe the behavior of this structure. Since the width of the rectangular resonator (W<sub>2</sub>) is close to the width of the MIM waveguides (W<sub>1</sub>) and <span class="mathjax-tex">$L\gg {W}_{2}$</span>, the proposed initial structure can be considered as a combination of three cascaded waveguides with widths of W<sub>1</sub>, W<sub>2</sub>, and W<sub>1</sub>, respectively. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig2">2</a>a shows the 2D topology of the initial structure. Also, the schematic of MIM junctions between three serial waveguides and the equivalent circuit of the initial structure are shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig2">2</a>b,c, respectively<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 9" title="Khani, S., Danaie, M. & Rezaei, P. Plasmonic all-optical metal–insulator–metal switches based on silver nano-rods, comprehensive theoretical analysis and design guidelines. J. Comput. Electron. 20, 442–457 (2021)." href="/articles/s41598-022-09213-w#ref-CR9" id="ref-link-section-d121634187e776">9</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 30" title="Khani, S., Danaie, M. & Rezaei, P. Compact and low-power all-optical surface plasmon switches with isolated pump and data waveguides and a rectangular cavity containing nano-silver strips. Superlattices Microstruct. 141, 106481 (2020)." href="/articles/s41598-022-09213-w#ref-CR30" id="ref-link-section-d121634187e779">30</a></sup>. As seen in the equivalent transmission-line circuit (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig2">2</a>c), the MIM waveguides are modeled by semi-infinite transmission lines. In this model, the characteristic impedances of Z<sub>1</sub> and Z<sub>2</sub> are assigned to the waveguides with widths of W<sub>1</sub> and W<sub>2</sub>, respectively. The microwave circuit theories can be used to obtain the values of characteristic impedances<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 63" title="Veronis, G. & Fan, S. Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides. Appl. Phys. Lett. 87, 131102 (2005)." href="/articles/s41598-022-09213-w#ref-CR63" id="ref-link-section-d121634187e795">63</a></sup>. Accordingly, they are approximated by the ratio of the voltage to the current (Eq. <a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ2">2</a>):</p><div id="Equ2" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${Z}_{j}=\frac{{V}_{j}}{{I}_{j}}=\frac{\beta ({W}_{j}){W}_{j}}{\omega {\varepsilon }_{0}{\varepsilon }_{1}} j=1, 2,$$</span></div><div class="c-article-equation__number"> (2) </div></div><p>where <span class="mathjax-tex">${W}_{j}$</span> is the width of the waveguides, <span class="mathjax-tex">$\omega$</span> is the frequency of incident light, <span class="mathjax-tex">${\varepsilon }_{0}$</span> is the linear dielectric constant, <span class="mathjax-tex">${\varepsilon }_{1}$</span> the relative permittivity of the insulator, and <span class="mathjax-tex">$\beta$</span> is the propagation constant, calculated by Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ3">3</a>)<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 64" title="Pannipitiya, A., Rukhlenko, I. D., Premaratne, M., Hattori, H. T. & Agrawal, G. P. Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure. Opt. Express 18, 6191–6204 (2010)." href="/articles/s41598-022-09213-w#ref-CR64" id="ref-link-section-d121634187e1018">64</a></sup>:</p><div id="Equ3" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\beta \left({W}_{j}\right)=k\bullet {n}_{eff}\left({W}_{j}\right) j=1, 2,$$</span></div><div class="c-article-equation__number"> (3) </div></div><p>where <span class="mathjax-tex">$k$</span> can be given by Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ4">4</a>)<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 64" title="Pannipitiya, A., Rukhlenko, I. D., Premaratne, M., Hattori, H. T. & Agrawal, G. P. Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure. Opt. Express 18, 6191–6204 (2010)." href="/articles/s41598-022-09213-w#ref-CR64" id="ref-link-section-d121634187e1115">64</a></sup>:</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-2" data-title="Figure 2"><figure><figcaption><b id="Fig2" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 2</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/2" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig2_HTML.png?as=webp"><img aria-describedby="Fig2" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig2_HTML.png" alt="figure 2" loading="lazy" width="685" height="507"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-2-desc"><p>(<b>a</b>) 2D topology of the initial structure. (<b>b</b>) Schematic of MIM junctions between three waveguides, (<b>c</b>) Equivalent transmission line circuit of the initial structure.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/2" data-track-dest="link:Figure2 Full size image" aria-label="Full size image figure 2" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div id="Equ4" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$k=\frac{2\pi }{\lambda }.$$</span></div><div class="c-article-equation__number"> (4) </div></div><p>Here, the wavelength of λ is obtained by Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ5">5</a>):</p><div id="Equ5" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\lambda =\frac{2\pi c}{\omega },$$</span></div><div class="c-article-equation__number"> (5) </div></div><p>where c is the light speed in vacuum. It is worth mentioning that <span class="mathjax-tex">${n}_{eff}$</span> in Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ3">3</a>) can be approximated by Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ6">6</a>)<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 65" title="Taheri, A. N. & Kaatuzian, H. Design and simulation of a nanoscale electro-plasmonic 1× 2 switch based on asymmetric metal–insulator–metal stub filters. Appl. Opt. 53, 6546–6553 (2014)." href="/articles/s41598-022-09213-w#ref-CR65" id="ref-link-section-d121634187e1263">65</a></sup>:</p><div id="Equ6" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${n}_{eff}=\sqrt{{\varepsilon }_{1}}{\left(1+\frac{\lambda }{\pi h\sqrt{{-\varepsilon }_{2}}}\sqrt{1+\frac{{\varepsilon }_{1}}{{-\varepsilon }_{2}}}\right)}^\frac{1}{2}.$$</span></div><div class="c-article-equation__number"> (6) </div></div><p>The transfer matrix method is used to calculate the transfer function of the transmission line circuit (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig2">2</a>c). Therefore, the scattering matrix of a plasmonic MIM junction is introduced (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig3">3</a>). The input and output voltages of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig3">3</a> (<span class="mathjax-tex">${V}_{1}^{+}$</span>, <span class="mathjax-tex">${V}_{2}^{+}$</span>, <span class="mathjax-tex">${V}_{1}^{-}$</span>, <span class="mathjax-tex">${V}_{2}^{-}$</span>) are given by Eqs. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ7">7</a> and <a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ8">8</a>) <sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 66" title="Collin, R. E. Foundations for Microwave Engineering. (Wiley, 2007)." href="/articles/s41598-022-09213-w#ref-CR66" id="ref-link-section-d121634187e1518">66</a></sup>:</p><div id="Equ7" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${V}_{1}\left(x\right)={V}_{1}^{+}{e}^{i\beta x}+{V}_{1}^{-}{e}^{-i\beta x},$$</span></div><div class="c-article-equation__number"> (7) </div></div><div id="Equ8" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${V}_{2}\left(x\right)={V}_{2}^{+}{e}^{i\beta {x}^{^{\prime}}}+{V}_{2}^{-}{e}^{-i\beta {x}^{^{\prime}}},$$</span></div><div class="c-article-equation__number"> (8) </div></div><p>where <span class="mathjax-tex">$x$</span> is the distance from the input port and <span class="mathjax-tex">${x}^{^{\prime}}$</span> is the distance from the output port. Also, <span class="mathjax-tex">${x+x}^{^{\prime}}$</span> presents the total distance from the input port to the output port. The voltages at the input and output ports of the line are related to each other by the scattering matrix of <b>S</b><sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 66" title="Collin, R. E. Foundations for Microwave Engineering. (Wiley, 2007)." href="/articles/s41598-022-09213-w#ref-CR66" id="ref-link-section-d121634187e1829">66</a></sup>:</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-3" data-title="Figure 3"><figure><figcaption><b id="Fig3" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 3</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/3" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig3_HTML.png?as=webp"><img aria-describedby="Fig3" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig3_HTML.png" alt="figure 3" loading="lazy" width="685" height="144"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-3-desc"><p>Schematic of relations between circuit input and outputs through (<b>a</b>) Scattering matrix. (<b>b</b>) Transfer matrix.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/3" data-track-dest="link:Figure3 Full size image" aria-label="Full size image figure 3" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div id="Equ9" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\left[\begin{array}{c}{\mathrm{V}}_{1}^{-}\\ {\mathrm{V}}_{2}^{-}\end{array}\right]=\mathbf{S}\left[\begin{array}{c}{\mathrm{V}}_{1}^{+}\\ {\mathrm{V}}_{2}^{+}\end{array}\right].$$</span></div><div class="c-article-equation__number"> (9) </div></div><p>In this formula, the scattering matrix of a straight waveguide is given by<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 66" title="Collin, R. E. Foundations for Microwave Engineering. (Wiley, 2007)." href="/articles/s41598-022-09213-w#ref-CR66" id="ref-link-section-d121634187e1991">66</a></sup>:</p><div id="Equ10" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${\mathbf{S}}_{MIM}=\left[\begin{array}{cc}0& {\mathrm{e}}^{-\mathrm{i\beta L}}\\ {\mathrm{e}}^{\mathrm{i\beta L}}& 0\end{array}\right].$$</span></div><div class="c-article-equation__number"> (10) </div></div><p>Here, <span class="mathjax-tex">$L$</span> is the length of the straight waveguide. Furthermore, the scattering matrix of the direct junction of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig2">2</a>c is defined as<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 66" title="Collin, R. E. Foundations for Microwave Engineering. (Wiley, 2007)." href="/articles/s41598-022-09213-w#ref-CR66" id="ref-link-section-d121634187e2134">66</a></sup>:</p><div id="Equ11" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${\mathbf{S}}_{jun}=\left[\begin{array}{cc}\Gamma & 1-\Gamma \\ 1+\Gamma & -\Gamma \end{array}\right].$$</span></div><div class="c-article-equation__number"> (11) </div></div><p>In this formula, <span class="mathjax-tex">$\Gamma$</span> is calculated by:</p><div id="Equ12" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\Gamma =\frac{{\mathrm{Z}}_{2}-{\mathrm{Z}}_{1}}{{\mathrm{Z}}_{2}+{\mathrm{Z}}_{1}}.$$</span></div><div class="c-article-equation__number"> (12) </div></div><p>By introducing <span class="mathjax-tex">${V}_{1}^{+,-}=\sqrt{{Z}_{1}}{ {\tilde{\text{V}}} }_{1}^{+,-}$</span> and <span class="mathjax-tex">${V}_{2}^{+,-}=\sqrt{{Z}_{2}}{ {\tilde{\text{V}}} }_{2}^{+,-}$</span>, the normalized scattering matrix can be given by:</p><div id="Equ13" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${\mathrm{S}}_{11}=-{\mathrm{S}}_{22}=\Gamma , {\mathrm{S}}_{12}={\mathrm{S}}_{21}=\frac{2\sqrt{{\mathrm{Z}}_{1}{\mathrm{Z}}_{2}}}{{\mathrm{Z}}_{1}+{\mathrm{Z}}_{2}}.$$</span></div><div class="c-article-equation__number"> (13) </div></div><p>Here, <span class="mathjax-tex">${{\tilde{\text{V}}}}_{1}^{+,-}$</span> and <span class="mathjax-tex">${{\tilde{\text{V}}}}_{2}^{+,-}$</span> are the normalized input and output voltages, respectively. Thereafter, the transfer matrix of Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig3">3</a>b can be calculated using the obtained scattering parameters<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 66" title="Collin, R. E. Foundations for Microwave Engineering. (Wiley, 2007)." href="/articles/s41598-022-09213-w#ref-CR66" id="ref-link-section-d121634187e2683">66</a></sup>:</p><div id="Equ14" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\left[\begin{array}{c}{\mathrm{V}}_{1}^{+}\\ {\mathrm{V}}_{1}^{-}\end{array}\right]=\mathbf{T}\left[\begin{array}{c}{\mathrm{V}}_{2}^{+}\\ {\mathrm{V}}_{2}^{-}\end{array}\right],$$</span></div><div class="c-article-equation__number"> (14) </div></div><p>where <span class="mathjax-tex">$\mathbf{T}$</span> is given by:</p><div id="Equ15" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\mathbf{T}=\frac{1}{{\mathrm{S}}_{21}}\left[\begin{array}{cc}1& -{\mathrm{S}}_{22}\\ {\mathrm{S}}_{11}& -\mathrm{Det}(\mathbf{S})\end{array}\right]=\left[\begin{array}{cc}{\mathrm{t}}_{11}& {\mathrm{t}}_{12}\\ {\mathrm{t}}_{21}& {\mathrm{t}}_{22}\end{array}\right].$$</span></div><div class="c-article-equation__number"> (15) </div></div><p>In this formula, the matrix elements are defined as:</p><div id="Equ16" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${\mathrm{t}}_{11}=\frac{1}{2}\left(\sqrt{\frac{{Z}_{2}}{{Z}_{1}}}+\sqrt{\frac{{Z}_{1}}{{Z}_{2}}}\right) . {\mathrm{t}}_{12}=\frac{1}{2}\left(\sqrt{\frac{{Z}_{2}}{{Z}_{1}}}-\sqrt{\frac{{Z}_{1}}{{Z}_{2}}}\right).$$</span></div><div class="c-article-equation__number"> (16) </div></div><p>Now, there are all the factors to calculate the total transfer matrix of the equivalent circuit of the initial structure. This transfer function can be given by:</p><div id="Equ17" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\mathbf{T}={\mathbf{T}}_{1}\left({l}_{1}\right){\mathbf{T}}_{\mathrm{jun}\_1}{\mathbf{T}}_{2}\left({l}_{2}\right){\mathbf{T}}_{\mathrm{jun}\_2}{\mathbf{T}}_{1}\left({l}_{1}\right).$$</span></div><div class="c-article-equation__number"> (17) </div></div><p>Here, the transfer matrixes of <span class="mathjax-tex">${\mathbf{T}}_{j}\left({l}_{j}\right)$</span> and <span class="mathjax-tex">${\mathbf{T}}_{jun\_j}$</span> are defined as:</p><div id="Equ18" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${\mathbf{T}}_{j}\left({l}_{j}\right)=\left[\begin{array}{cc}{\mathrm{e}}^{-i{\beta }_{j}{l}_{j}}& 0\\ 0& {\mathrm{e}}^{i{\beta }_{j}{l}_{j}}\end{array}\right]; j=1, 2,$$</span></div><div class="c-article-equation__number"> (18) </div></div><div id="Equ19" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${\mathbf{T}}_{jun\_j}=\left[\begin{array}{cc}{\mathrm{t}}_{j}^{+}& {\mathrm{t}}_{j}^{-}\\ {\mathrm{t}}_{j}^{-}& {\mathrm{t}}_{j}^{+}\end{array}\right] , {\mathrm{t}}_{j}^{\pm }=\frac{\sqrt{\frac{{\mathrm{Z}}_{\mathrm{s}(\mathrm{i}+1)}}{{\mathrm{Z}}_{\mathrm{si}}}}\pm \sqrt{\frac{{\mathrm{Z}}_{\mathrm{si}}}{{\mathrm{Z}}_{\mathrm{s}(\mathrm{i}+1)}}}}{2}; j=1, 2.$$</span></div><div class="c-article-equation__number"> (19) </div></div><p>Finally, the transfer function can be calculated by realizing the total transfer matrix (Eq. <a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ20">20</a>):</p><div id="Equ20" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\mathrm{T}={\left|\frac{{\mathrm{V}}_{2}^{+}}{{\mathrm{V}}_{1}^{+}}\right|}^{2}.$$</span></div><div class="c-article-equation__number"> (20) </div></div><p>After presenting the analytical model, the transmission spectrum of the initial structure is obtained using this method and compared with the FDTD method. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig4">4</a> shows these transmission spectra. As seen in this figure, good agreement can generally be shown between two methods. It is worth mentioning that there is a reason why these two curves do not match completely. This small amount of error stems from the fact that the approximated formula is used for the calculation of n<sub>eff</sub> (Eq. <a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ6">6</a>).</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-4" data-title="Figure 4"><figure><figcaption><b id="Fig4" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 4</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/4" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig4_HTML.png?as=webp"><img aria-describedby="Fig4" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig4_HTML.png" alt="figure 4" loading="lazy" width="685" height="299"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-4-desc"><p>Transmission spectra of the initial structure using FDTD simulations and TLM.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/4" data-track-dest="link:Figure4 Full size image" aria-label="Full size image figure 4" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div></div></div></section><section data-title="Design of the proposed biosensor I"><div class="c-article-section" id="Sec3-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec3">Design of the proposed biosensor I</h2><div class="c-article-section__content" id="Sec3-content"><p>The initial structure of the proposed biosensors is presented in the previous section. The main problems of this structure are its multimode spectrum and low Q-factor modes. Accordingly, such a structure is not suitable for a sensor structure and it should be improved. In this section, the periodic GaAs (Palik model) insulator layers are inserted in the rectangular resonator to improve the initial structure. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig5">5</a>a shows this structure. In this figure, the values of the geometrical parameters of “a<sub>1</sub>” and “a<sub>2</sub>” are equal to 80 and 330 nm. It is worth mentioning that the geometrical parameter of “a” is the lattice constant of the structure and it is equal to a = a<sub>1</sub> + a<sub>2</sub>.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-5" data-title="Figure 5"><figure><figcaption><b id="Fig5" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 5</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/5" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig5_HTML.png?as=webp"><img aria-describedby="Fig5" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig5_HTML.png" alt="figure 5" loading="lazy" width="685" height="804"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-5-desc"><p>(<b>a</b>) 3D topology of the proposed biosensor I. (<b>b</b>) Its transmission and reflection spectra.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/5" data-track-dest="link:Figure5 Full size image" aria-label="Full size image figure 5" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>According to Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig5">5</a>a, inserting the GaAs layers generates a 1D PC structure in the central part of the topology. Consequently, it can be expected that a PBG is generated in the transmission spectrum of this structure. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig5">5</a>b shows the transmission and reflection spectra of the proposed biosensor I. As seen, this figure proves the claim of the existence of a PBG. The wavelength range of this PBG is extended from 954 to 2074 nm with sharp edges. The maximum transmission values of the PBG edges are equal to 33.8% and 56.1%, respectively. Therefore, the edges of this PBG can be used for sensing applications.</p><p>We also intend to provide a view of the operation mechanism of the proposed structure of biosensor I by its field profile. The field profile of <span class="mathjax-tex">$\left|{\mathrm{H}}_{\mathrm{z}}\right|$</span> for this structure is shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig6">6</a>. Figures <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig6">6</a>a–c show the field profile of the proposed biosensor I at the wavelengths of λ<sub>A</sub> = 954, λ<sub>B</sub> = 1500, and λ<sub>C</sub> = 2074 nm, respectively. As seen in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig5">5</a>a,c the wavelengths of λ<sub>A</sub> and λ<sub>C</sub> (wavelengths of the PBG’s edges) have appeared in the structure and are transmitted to the output port. Also, the proposed structure does not transmit the wavelength of λ<sub>B</sub> which is located at the PBG region (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig6">6</a>b). It is because PCs can act as a perfect mirror and confine light in the PBG region.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-6" data-title="Figure 6"><figure><figcaption><b id="Fig6" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 6</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/6" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig6_HTML.png?as=webp"><img aria-describedby="Fig6" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig6_HTML.png" alt="figure 6" loading="lazy" width="685" height="893"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-6-desc"><p>Field profile of <span class="mathjax-tex">$\left|{H}_{z}\right|$</span> for the proposed biosensor I at the wavelength of (<b>a</b>) λ<sub>A</sub>, (<b>b</b>) λ<sub>B</sub>, (<b>c</b>) λ<sub>C</sub>.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/6" data-track-dest="link:Figure6 Full size image" aria-label="Full size image figure 6" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>After designing the proposed biosensor I, the sensor operation has been investigated. The transmission spectrum variation of this structure for a 0.01 change in the refractive index of the analyte (air in this case) is shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig7">7</a>a. As seen, the transmission spectrum shifts to higher wavelengths by changing the refractive index of the analyte. Also, the zoomed views of the low and high PBG edges are shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig7">7</a>b,c, respectively. As seen in these figures, the wavelength shift of the low PBG is more than the high PBG. On the other hand, the sharpness of the low PBG edge is more the high PBG edge. It is also intended to design this structure for bio-optics applications whose wavelength is located at the NIR. As a result, the low PBG is more suitable for sensing applications.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-7" data-title="Figure 7"><figure><figcaption><b id="Fig7" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 7</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/7" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig7_HTML.png?as=webp"><img aria-describedby="Fig7" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig7_HTML.png" alt="figure 7" loading="lazy" width="685" height="618"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-7-desc"><p>Transmission spectra of the proposed biosensor I for n = 1 and n = 1.01 in different wavelength ranges.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/7" data-track-dest="link:Figure7 Full size image" aria-label="Full size image figure 7" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>To provide a better view into the performance of the designed biosensor I, this structure is once again simulated for RI changes of 0.001. This case is shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig8">8</a>a. As seen, the transmittance curve shifts for the refractive index change step of 0.001 are quite clear so that this variation can be enough for sensing. Also, a linear function is fitted on the data points, to quantify the relationship between the refractive index increasing and the resonance wavelength shifting (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig8">8</a>b). As seen in this figure, the slope value of this curve is a large value (equal to 718.6 nm/RIU). Since this value shows the sensitivity of the proposed sensor I, the proposed structure I is a high sensitive sensor. It should be noted that the sensitivity value can be calculated by<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 67" title="Islam, M. S. et al. Sensing of toxic chemicals using polarized photonic crystal fiber in the terahertz regime. Opt. Commun. 426, 341–347 (2018)." href="/articles/s41598-022-09213-w#ref-CR67" id="ref-link-section-d121634187e4057">67</a></sup>:</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-8" data-title="Figure 8"><figure><figcaption><b id="Fig8" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 8</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/8" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig8_HTML.png?as=webp"><img aria-describedby="Fig8" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig8_HTML.png" alt="figure 8" loading="lazy" width="685" height="283"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-8-desc"><p>(<b>a</b>) Transmission spectra of the proposed biosensor I for refractive index changes from 1 to 1.005 in steps of 0.001. (<b>b</b>) Relationship between the wavelength of the PBG’s low edge and different values of the refractive index.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/8" data-track-dest="link:Figure8 Full size image" aria-label="Full size image figure 8" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><div id="Equ21" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$${S}_{\lambda }\left(\lambda \right)=\frac{\Delta \lambda }{\Delta n} \left(\frac{nm}{RIU}\right).$$</span></div><div class="c-article-equation__number"> (21) </div></div><p>Based on the perturbation theory which is discussed in Refs.<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 22" title="Khani, S. & Hayati, M. An ultra-high sensitive plasmonic refractive index sensor using an elliptical resonator and MIM waveguide. Superlattices Microstruct. 156, 106970 (2021)." href="/articles/s41598-022-09213-w#ref-CR22" id="ref-link-section-d121634187e4161">22</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="Khani, S. & Hayati, M. Optical sensing in single-mode filters base on surface plasmon H-shaped cavities. Opt. Commun. 505, 127534 (2021)." href="/articles/s41598-022-09213-w#ref-CR42" id="ref-link-section-d121634187e4164">42</a></sup>, two parameters can increase the sensitivity of sensors. One of them is a high portion of the resonance mode energy (σ) and the other one is a high quality factor (Q-factor) value. The portion of the resonance mode energy for the proposed biosensor I has been studied in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig6">6</a>a by showing its field profile. As a result, it is desirable to calculate the Q-factor of the proposed structure. The Q-factor can be calculated by Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ22">22</a>)<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 68" title="Lu, H., Gan, X., Mao, D., Jia, B. & Zhao, J. Flexibly tunable high-quality-factor induced transparency in plasmonic systems. Sci. Rep. 8, 1–9 (2018)." href="/articles/s41598-022-09213-w#ref-CR68" id="ref-link-section-d121634187e4174">68</a></sup>:</p><div id="Equ22" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$Q=\frac{{\lambda }_{res}}{\Gamma },$$</span></div><div class="c-article-equation__number"> (22) </div></div><p>where <span class="mathjax-tex">${\uplambda }_{\mathrm{res}}$</span> is the resonance wavelength and <span class="mathjax-tex">$\Gamma$</span> is the resonance bandwidth. For the resonance wavelength of the low PBG edge in the proposed biosensor I, the calculated Q-factor is equal to 207.4. The most comprehensive parameter that can be used for the comparison of the sensors’ operations is the figure of merit (FOM). It is because both factors of σ and Q-factor have been considered in this parameter. The FOM parameter can be calculated by Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ23">23</a>)<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="Khani, S. & Hayati, M. Optical sensing in single-mode filters base on surface plasmon H-shaped cavities. Opt. Commun. 505, 127534 (2021)." href="/articles/s41598-022-09213-w#ref-CR42" id="ref-link-section-d121634187e4267">42</a></sup>:</p><div id="Equ23" class="c-article-equation"><div class="c-article-equation__content"><span class="mathjax-tex">$$\mathrm{FOM}=\frac{{\mathrm{S}}_{\uplambda }\left(\uplambda \right)}{\Gamma } \left({\mathrm{RIU}}^{-1}\right).$$</span></div><div class="c-article-equation__number"> (23) </div></div><p>Base on Eq. (<a data-track="click" data-track-label="link" data-track-action="equation anchor" href="/articles/s41598-022-09213-w#Equ23">23</a>), the calculated FOM value for the proposed biosensor I is 156.217 RIU<sup>−1</sup>.</p><p>After studying the sensing operation of biosensor I, some important issues such as the incident angle of the source light and the plasmonic effect on the sensor’s operation have been investigated. As shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig2">2</a>a (the initial structure), the incoming TM-polarized light irradiates one side of the sensor structure at an incidence angle θ = 0 degrees. In this part, we intend to investigate the effect of changing the incidence angle on the sensor’s performance. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig9">9</a>a shows the transmission spectra of the proposed biosensor I for different values of incident angle of the light source. As seen in this figure, by deviating the incident angle from zero degrees, the PBG region shifts to higher wavelengths. Also, this change reduces the transmittance value of the low PBG edge and the sensitivity value of the proposed sensor structure. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig9">9</a>b,c show these cases. Accordingly, the best choice for the incident angle is θ = 0 degrees.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-9" data-title="Figure 9"><figure><figcaption><b id="Fig9" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 9</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/9" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig9_HTML.png?as=webp"><img aria-describedby="Fig9" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig9_HTML.png" alt="figure 9" loading="lazy" width="685" height="607"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-9-desc"><p>(<b>a</b>) Transmission spectra of the proposed biosensor I for different incident angles. (<b>b</b>) Relationship between the maximum transmission value of the low PBG edge and different values of the incident angle. (<b>c</b>) Relationship between the sensitivity value and different values of the incident angle.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/9" data-track-dest="link:Figure9 Full size image" aria-label="Full size image figure 9" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>In order to investigate the plasmonic effect on the PBG and sensitivity of the proposed structure, the behavior of the PC structure without the plasmonic section has been investigated and compared to the proposed sensor structure. The 1D PC structure used in this paper is shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig10">10</a>a. The geometrical parameters of this topology have been already explained. In Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig10">10</a>b, the transmission spectrum of the 1D PC structure obtained using the FDTD method has been compared to the transmission spectrum of the total proposed sensor topology. As seen in this figure, the plasmonic structure causes the PBG to shift to higher wavelengths with higher transmission values at its PBG’s edges which are more desirable.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-10" data-title="Figure 10"><figure><figcaption><b id="Fig10" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 10</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/10" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig10_HTML.png?as=webp"><img aria-describedby="Fig10" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig10_HTML.png" alt="figure 10" loading="lazy" width="685" height="890"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-10-desc"><p>(<b>a</b>) 3D topology of the used PC structure in the proposed biosensor I. (<b>b</b>) Transmission spectra of the PC structure and biosensor I. (<b>c</b>,<b>d</b>) Transmission spectra of the proposed biosensor I for n = 1 and n = 1.01 in different wavelength ranges.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/10" data-track-dest="link:Figure10 Full size image" aria-label="Full size image figure 10" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>By changing the refractive index of air layers from 1 to 1.01, the shift of its transmittance curve has also been investigated. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig10">10</a>c,d show this case. As can be seen, the shift of the low PBG edge is equal to 6.1 nm. Based on the obtained results, the sensitivity value for the 1D PC is equal to 610 nm/RIU. Based on the obtained results, it can be concluded that the plasmonic structure also increases the sensitivity value of the proposed sensor. Accordingly, adding a plasmonic structure improves the sensing performance of the proposed structure.</p></div></div></section><section data-title="Design of the proposed biosensor II"><div class="c-article-section" id="Sec4-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec4">Design of the proposed biosensor II</h2><div class="c-article-section__content" id="Sec4-content"><p>To achieve higher transmittance values in the PBG’s edges, tapered resonators are added to the proposed biosensor I. The topology of the proposed biosensor II is shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig11">11</a>a. The value of the geometrical parameter of “d” is equal to 265 nm. Other parameters have been already explained. The transmission spectrum of the proposed biosensor II is shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig11">11</a>b and it is also compared with the transmission spectrum of the biosensor I. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig11">11</a>b shows that the transmittance value in the low edge of the PBG (952.4 nm) increases (from 33.8 to 60.6%). Increasing the transmittance value in this PBG edge provides a biosensor with more transmittance value. It is because of the more coupling strength between MIM plasmonic waveguides and the central PC structure in this topology. As known, there is a trade-off between designing parameters of sensor structures. Increasing the coupling effect between MIM plasmonic waveguides and PC leads to slower sharpness in transition from the maximum transmittance to the minimum transmittance. Accordingly, it can be caused that the sensitivity of biosensor II is slightly lower than the sensitivity of biosensor I.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-11" data-title="Figure 11"><figure><figcaption><b id="Fig11" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 11</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/11" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig11_HTML.png?as=webp"><img aria-describedby="Fig11" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig11_HTML.png" alt="figure 11" loading="lazy" width="685" height="793"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-11-desc"><p>(<b>a</b>) 3D topology of the proposed biosensor II. (<b>b</b>) Transmission spectra of the proposed biosensor I and biosensor II.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/11" data-track-dest="link:Figure11 Full size image" aria-label="Full size image figure 11" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>Due to the appropriate view of the magnitude of H<sub>z</sub>, the field profile of <span class="mathjax-tex">$\left|{\mathrm{H}}_{\mathrm{z}}\right|$</span> for the proposed biosensor II has also been investigated. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig12">12</a> shows this case. As seen in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig12">12</a>a,c, the incident light at the wavelengths of the PBG’s edges (λ<sub>A'</sub> = 952.4 and λ<sub>C'</sub> = 2074 nm) can pass through the structure. Also, Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig12">12</a>b shows the field profile of <span class="mathjax-tex">$\left|{\mathrm{H}}_{\mathrm{z}}\right|$</span> for λ<sub>B'</sub> = 1500 nm, which cannot be transmitted to the output port. It is because this wavelength is located at the PBG region.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-12" data-title="Figure 12"><figure><figcaption><b id="Fig12" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 12</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/12" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig12_HTML.png?as=webp"><img aria-describedby="Fig12" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig12_HTML.png" alt="figure 12" loading="lazy" width="685" height="988"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-12-desc"><p>Field profile of <span class="mathjax-tex">$\left|{H}_{z}\right|$</span> for the proposed biosensor II at the wavelength of (<b>a</b>) λ<sub>A'</sub>, (<b>b</b>) λ<sub>B'</sub>, (<b>c</b>) λ<sub>C'</sub>.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/12" data-track-dest="link:Figure12 Full size image" aria-label="Full size image figure 12" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>To verify the operation mechanism of the proposed biosensor II, the shift of its transmittance curve has also been investigated by changing the refractive index of the analyte from 1 to 1.01. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig13">13</a>a shows this change in the transmittance curve of biosensor II. As expected, a high-frequency shift occurs in the low PBG’s edge, while the high PBG’s edge experiences a little frequency shift. The zoomed view of the low PBG's edge is shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig13">13</a>b. As seen in this figure, the shift of the low PBG’s edge is equal to 7.143 nm. It is worth mentioning that the obtained sensitivity, Q-factor, and FOM values for the proposed biosensor II are 714.3 nm/RIU<sup>−1</sup>, 80.16, and 60.1 RIU<sup>−1</sup>, respectively.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-13" data-title="Figure 13"><figure><figcaption><b id="Fig13" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 13</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/13" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig13_HTML.png?as=webp"><img aria-describedby="Fig13" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig13_HTML.png" alt="figure 13" loading="lazy" width="685" height="263"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-13-desc"><p>Transmission spectra of the proposed biosensor II for n = 1 and n = 1.01 in different wavelength ranges.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/13" data-track-dest="link:Figure13 Full size image" aria-label="Full size image figure 13" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>Similar to the previous sensor structure (biosensor I), the shift of the transmittance curve for biosensor II is considered by changing the refractive index of its analyte from 1 to 1.01 in steps of 0.001. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig14">14</a>a shows these changes. The relationship between the refractive index increasing and the resonance wavelength shifting is also shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig14">14</a>b. The fitted linear function on the data points of this figure shows that the slope of this curve is lower than the previous case (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig8">8</a>b). This difference is not too much.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-14" data-title="Figure 14"><figure><figcaption><b id="Fig14" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 14</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/14" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig14_HTML.png?as=webp"><img aria-describedby="Fig14" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig14_HTML.png" alt="figure 14" loading="lazy" width="685" height="286"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-14-desc"><p>(<b>a</b>) Transmission spectra of the proposed biosensor II for refractive index changes from 1 to 1.005 in steps of 0.001. (<b>b</b>) Relationship between the wavelength of the PBG’s low edge and different values of the refractive index.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/14" data-track-dest="link:Figure14 Full size image" aria-label="Full size image figure 14" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>To investigate the effect of some geometrical parameters of the proposed biosensor II on its transmission spectrum, the “a<sub>1</sub>”, “W<sub>2</sub>”, “number of the GaAs layers (N)”, and “d” parameters have been swept. The first three parameters are related to the 1D PC structure, and the last parameter is related to tapered resonators. As seen in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig15">15</a>a, by increasing the “a<sub>1</sub>” value from 78 to 82 nm, the low PBG edge shifts to higher wavelengths. Consequently, by changing the geometrical parameter of “a<sub>1</sub>”, the wavelength of the low PBG edge can be tuned. The transmission spectra of the proposed biosensor II as a function of W<sub>2</sub> are also shown in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig15">15</a>b. As seen in this figure, increasing W<sub>2</sub> corresponds to a lower sensing wavelength (the wavelength of the low PBG edge). Thereafter, the number of the GaAs layers is changed from 7 to 11 layers (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig15">15</a>c). It can be seen that increasing “N” shifts the low PBG edge to higher wavelengths. Also, Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig15">15</a>d shows the transmission spectra of biosensor II for different values of “d”. As seen in this figure, when the value of “d” is increased, the location of the low PBG edge is almost constant.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-15" data-title="Figure 15"><figure><figcaption><b id="Fig15" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 15</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/15" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig15_HTML.png?as=webp"><img aria-describedby="Fig15" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig15_HTML.png" alt="figure 15" loading="lazy" width="685" height="535"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-15-desc"><p>Transmission spectra of the proposed biosensor II for different values of (<b>a</b>) a<sub>1</sub>, (<b>b</b>) W<sub>2</sub>, (<b>c</b>) N, and (<b>d</b>) d.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/15" data-track-dest="link:Figure15 Full size image" aria-label="Full size image figure 15" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>At the next step, the important characteristic values of the biosensor II (transmittance value of the low PBG edge and FOM) for different values of “a<sub>1</sub>”, “W<sub>2</sub>”, “N”, and “d” have also been investigated to provide a better view of how such geometrical parameters changes affect the operation of the biosensor II. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig16">16</a> shows these changes. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig16">16</a>a,e show that by increasing the “a<sub>1</sub>” value, the transmittance value increases initially and then decreases, and the FOM value is almost constant from a<sub>1</sub> = 78 to 80 nm and then decreases. Accordingly, the value of 80 nm (with the highest transmittance value and a relatively high FOM value) is the best choice. Another parameter whose variation has been investigated is the “W<sub>2</sub>” parameter (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig16">16</a>b,f). As seen, increasing the “W<sub>2</sub>” value corresponds to higher transmittance and FOM values. On the other hand, the total size of the biosensor II increases by increasing the “W<sub>2</sub>” value. It should be that there is a trade-off between designing parameters of a sensor structure. Consequently, the medium value of 250 nm has been selected for the “W<sub>2</sub>” parameter.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-16" data-title="Figure 16"><figure><figcaption><b id="Fig16" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 16</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/16" rel="nofollow"><picture><img aria-describedby="Fig16" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig16_HTML.png" alt="figure 16" loading="lazy" width="685" height="443"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-16-desc"><p>Relationship between the maximum transmission value of the low PBG edge and different values of (<b>a</b>) a<sub>1</sub>, (<b>b</b>) W<sub>2</sub>, (<b>c</b>) N, and (<b>d</b>) d. Relationship between the FOM value of the proposed biosensor II and different values of (<b>e</b>) a<sub>1</sub>, (<b>f</b>) W<sub>2</sub>, (<b>g</b>) N, and (<b>h</b>) d.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/16" data-track-dest="link:Figure16 Full size image" aria-label="Full size image figure 16" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>The next parameter is the number of GaAs layers (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig16">16</a>c,g). As seen, when the “N” parameter is increased, the transmittance and FOM values decrease and increase, respectively. Similar to the previous parameter (“W<sub>2</sub>” parameter), increasing “N” causes the total size of the biosensor II to increase. Accordingly, to create a trade-off between different design parameters, the value of N = 9 has been selected. Finally, the last parameter is “d” (Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig16">16</a>d,h). As seen in Fig. <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig16">16</a>d, by increasing “d”, the transmittance value increases initially and then decreases. The highest transmittance value occurs at d = 265 nm. On the other hand, such variations of the “d” parameter cause the FOM value to decrease initially and then increase. As discussed before, the purpose of adding tapered resonators is to increase the transmittance value. Because the proposed biosensor I has a high FOM value. Therefore, the value of 265 nm, which corresponds to the highest transmittance value, has been chosen to design the proposed biosensor II.</p></div></div></section><section data-title="Biosensors application"><div class="c-article-section" id="Sec5-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec5">Biosensors application</h2><div class="c-article-section__content" id="Sec5-content"><p>After reviewing the performance of the designed sensor structures using air as the insulator material of the analyte, their behavior is also investigated for a special application. One of the attractive subjects in bio-optics is measuring the tissues’ refractive index. In this section, it is shown that the proposed structures can be used for the detection of basal cell cancer. It is because the used wavelengths of the proposed sensors (the PBGs’ low edges) are located at the NIR. On the other hand, in Ref.<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 69" title="Mishchenko, M. I. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnostics, SPIE Press, Bellingham, WA (2007) Hardbound, ISBN 0-8194-6433-3, xl+ 841 pp. J. Quant. Spectrosc. Radiat. Transf. 110, 528 (2009)." href="/articles/s41598-022-09213-w#ref-CR69" id="ref-link-section-d121634187e4841">69</a></sup>, the refractive index of human cells has been comprehensively measured and reported at this frequency range. The human skin tissue can be modeled using a mixture of water and organic compounds. Because this tissue is composed of approximately 70% water and 30% protein<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 69" title="Mishchenko, M. I. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnostics, SPIE Press, Bellingham, WA (2007) Hardbound, ISBN 0-8194-6433-3, xl+ 841 pp. J. Quant. Spectrosc. Radiat. Transf. 110, 528 (2009)." href="/articles/s41598-022-09213-w#ref-CR69" id="ref-link-section-d121634187e4845">69</a></sup>. The refractive indices of different sections of a cell for NIR are estimated as follows: cytoplasm: 1.36–1.375, extracellular fluid: 1.35–1.36, nucleus: 1.38–1.41, and melanin: 1.6–1.7. Since cancerous cells have more protein in their cytoplasm, they have a higher refractive index value<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 70" title="Yaroslavsky, A. N. et al. High-contrast mapping of basal cell carcinomas. Opt. Lett. 37, 644–646 (2012)." href="/articles/s41598-022-09213-w#ref-CR70" id="ref-link-section-d121634187e4849">70</a></sup>. The refractive indices of the cytoplasm for normal and cancerous basal cells are equal to 1.36 and 1.38, respectively<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 70" title="Yaroslavsky, A. N. et al. High-contrast mapping of basal cell carcinomas. Opt. Lett. 37, 644–646 (2012)." href="/articles/s41598-022-09213-w#ref-CR70" id="ref-link-section-d121634187e4853">70</a></sup>. Figure <a data-track="click" data-track-label="link" data-track-action="figure anchor" href="/articles/s41598-022-09213-w#Fig17">17</a> shows the transmission spectra of the proposed biosensors for these refractive indices (refractive indices of normal and cancerous cells). As seen in this figure, the wavelengths of low PBGs’ edges are steel located at the NIR for the refractive indices of normal and cancerous cells. Consequently, the proposed structures can be easily used for the detection of basal cell cancer. Also, enough contrast between normal and cancerous cells in both cases causes the proposed sensors can be good candidates for this application.</p><div class="c-article-section__figure js-c-reading-companion-figures-item" data-test="figure" data-container-section="figure" id="figure-17" data-title="Figure 17"><figure><figcaption><b id="Fig17" class="c-article-section__figure-caption" data-test="figure-caption-text">Figure 17</b></figcaption><div class="c-article-section__figure-content"><div class="c-article-section__figure-item"><a class="c-article-section__figure-link" data-test="img-link" data-track="click" data-track-label="image" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/17" rel="nofollow"><picture><source type="image/webp" srcset="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig17_HTML.png?as=webp"><img aria-describedby="Fig17" src="//media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-022-09213-w/MediaObjects/41598_2022_9213_Fig17_HTML.png" alt="figure 17" loading="lazy" width="685" height="494"></picture></a></div><div class="c-article-section__figure-description" data-test="bottom-caption" id="figure-17-desc"><p>(<b>a</b>,<b>b</b>) Transmission spectra of the proposed biosensor I for normal (n = 1.36) and cancerous (n = 1.38) cells in different wavelength ranges. (<b>c</b>,<b>d</b>) Transmission spectra of the proposed biosensor II for normal (n = 1.36) and cancerous (n = 1.38) cells in different wavelength ranges.</p></div></div><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="article-link" data-track="click" data-track-label="button" data-track-action="view figure" href="/articles/s41598-022-09213-w/figures/17" data-track-dest="link:Figure17 Full size image" aria-label="Full size image figure 17" rel="nofollow"><span>Full size image</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div></div></div></section><section data-title="Discussions and comparisons"><div class="c-article-section" id="Sec6-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec6">Discussions and comparisons</h2><div class="c-article-section__content" id="Sec6-content"><p>As mentioned before, the FDTD method has been used to design the proposed structures. Also, the fabrication procedure of the proposed structures is similar to what is discussed in Ref.<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 71" title="Aparna, U., Mruthyunjaya, H. & Kumar, M. S. Plasmonic wavelength demultiplexer with mode conversion capabilities. Plasmonics 13, 511–517 (2018)." href="/articles/s41598-022-09213-w#ref-CR71" id="ref-link-section-d121634187e4900">71</a></sup>. It is worth mentioning that there are some potential challenges in their fabrication process. The first one is the efficient coupling of light to the plasmonic waveguides. Using gratings or the Kretschmann prism configurations is usually suggested for this challenge. The tarnishing of silver which changes its refractive index is the second challenge. Accordingly, the fabrication procedure should be performed in a chamber emptied from air.</p><p>To provide a better view of the obtained results, the proposed biosensors have been compared with other reported works in recent years. Table <a data-track="click" data-track-label="link" data-track-action="table anchor" href="/articles/s41598-022-09213-w#Tab1">1</a> shows some main characteristics of sensors for comparison. In this table, the year of the papers’ publication, the topology type of the sensors, the spectrum type of their transmission spectra, sensing wavelengths (<span class="mathjax-tex">${\lambda }_{r}$</span>), the Q-factor, sensitivity, and FOM have been compared.</p><div class="c-article-table" data-test="inline-table" data-container-section="table" id="table-1"><figure><figcaption class="c-article-table__figcaption"><b id="Tab1" data-test="table-caption">Table 1 Performance comparisons between the proposed sensors and other works.</b></figcaption><div class="u-text-right u-hide-print"><a class="c-article__pill-button" data-test="table-link" data-track="click" data-track-action="view table" data-track-label="button" rel="nofollow" href="/articles/s41598-022-09213-w/tables/1" aria-label="Full size table 1"><span>Full size table</span><svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-chevron-right-small"></use></svg></a></div></figure></div><p>As seen in this table, the topology type of some published works is plasmonic structure<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 22" title="Khani, S. & Hayati, M. An ultra-high sensitive plasmonic refractive index sensor using an elliptical resonator and MIM waveguide. Superlattices Microstruct. 156, 106970 (2021)." href="/articles/s41598-022-09213-w#ref-CR22" id="ref-link-section-d121634187e5544">22</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 23" title="Amoosoltani, N., Mehrabi, K., Zarifkar, A., Farmani, A. & Yasrebi, N. Double-ring resonator plasmonic refractive index sensor utilizing dual-band unidirectional reflectionless propagation effect. Plasmonics 16, 1–9 (2021)." href="/articles/s41598-022-09213-w#ref-CR23" id="ref-link-section-d121634187e5547">23</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="Khani, S. & Hayati, M. Optical sensing in single-mode filters base on surface plasmon H-shaped cavities. Opt. Commun. 505, 127534 (2021)." href="/articles/s41598-022-09213-w#ref-CR42" id="ref-link-section-d121634187e5550">42</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 44" title="Rakhshani, M. R. Wide-angle perfect absorber using a 3D nanorod metasurface as a plasmonic sensor for detecting cancerous cells and its tuning with a graphene layer. Photonics Nanostruct. Fundam. Appl. 43, 100883 (2021)." href="/articles/s41598-022-09213-w#ref-CR44" id="ref-link-section-d121634187e5553">44</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Su, C. & Zhu, J. Novel SPR sensor based on MIM-based waveguide and an asymmetric cross-shaped resonator. Plasmonics 16, 769–775 (2021)." href="#ref-CR72" id="ref-link-section-d121634187e5556">72</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" title="Danaie, M. & Shahzadi, A. Design of a high-resolution metal–insulator–metal plasmonic refractive index sensor based on a ring-shaped Si resonator. Plasmonics 14, 1453–1465 (2019)." href="#ref-CR73" id="ref-link-section-d121634187e5556_1">73</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 74" title="Wu, C. et al. Plasmon-induced transparency and refractive index sensing in side-coupled stub-hexagon resonators. Plasmonics 13, 251–257 (2018)." href="/articles/s41598-022-09213-w#ref-CR74" id="ref-link-section-d121634187e5559">74</a></sup> and the topology type of some others is PC<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 75" title="Danaie, M. & Kiani, B. Design of a label-free photonic crystal refractive index sensor for biomedical applications. Photonics Nanostruct. Fundam. Appl. 31, 89–98 (2018)." href="/articles/s41598-022-09213-w#ref-CR75" id="ref-link-section-d121634187e5563">75</a></sup>. As discussed before, each of these topologies has some advantages and some disadvantages. In this paper, in order to benefit from the advantages of both topologies, the combination of them has been used. Another comparison parameter is the spectrum type of the transmission spectra. As seen, most of them have a Lorentzian spectrum<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 22" title="Khani, S. & Hayati, M. An ultra-high sensitive plasmonic refractive index sensor using an elliptical resonator and MIM waveguide. Superlattices Microstruct. 156, 106970 (2021)." href="/articles/s41598-022-09213-w#ref-CR22" id="ref-link-section-d121634187e5567">22</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 23" title="Amoosoltani, N., Mehrabi, K., Zarifkar, A., Farmani, A. & Yasrebi, N. Double-ring resonator plasmonic refractive index sensor utilizing dual-band unidirectional reflectionless propagation effect. Plasmonics 16, 1–9 (2021)." href="/articles/s41598-022-09213-w#ref-CR23" id="ref-link-section-d121634187e5570">23</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="Khani, S. & Hayati, M. Optical sensing in single-mode filters base on surface plasmon H-shaped cavities. Opt. Commun. 505, 127534 (2021)." href="/articles/s41598-022-09213-w#ref-CR42" id="ref-link-section-d121634187e5573">42</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 44" title="Rakhshani, M. R. Wide-angle perfect absorber using a 3D nanorod metasurface as a plasmonic sensor for detecting cancerous cells and its tuning with a graphene layer. Photonics Nanostruct. Fundam. Appl. 43, 100883 (2021)." href="/articles/s41598-022-09213-w#ref-CR44" id="ref-link-section-d121634187e5576">44</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 73" title="Danaie, M. & Shahzadi, A. Design of a high-resolution metal–insulator–metal plasmonic refractive index sensor based on a ring-shaped Si resonator. Plasmonics 14, 1453–1465 (2019)." href="/articles/s41598-022-09213-w#ref-CR73" id="ref-link-section-d121634187e5579">73</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 75" title="Danaie, M. & Kiani, B. Design of a label-free photonic crystal refractive index sensor for biomedical applications. Photonics Nanostruct. Fundam. Appl. 31, 89–98 (2018)." href="/articles/s41598-022-09213-w#ref-CR75" id="ref-link-section-d121634187e5582">75</a></sup>. Although such a spectrum has some advantages such as symmetrical shape, it has some drawbacks for sensing applications. The first one is that their edges cannot be very sharp. It is because this issue may lead to fabrication errors in real experimental situations. On the other hand, most of these spectra are multi-mode, while using multi-mode spectra for designing sensors is not desirable. It is because these modes may interfere with each other by changing the refractive index of their analytes. Other types of spectra that have been used for sensing applications are Fano-resonance<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 72" title="Su, C. & Zhu, J. Novel SPR sensor based on MIM-based waveguide and an asymmetric cross-shaped resonator. Plasmonics 16, 769–775 (2021)." href="/articles/s41598-022-09213-w#ref-CR72" id="ref-link-section-d121634187e5586">72</a></sup> and EIT-like resonance<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 74" title="Wu, C. et al. Plasmon-induced transparency and refractive index sensing in side-coupled stub-hexagon resonators. Plasmonics 13, 251–257 (2018)." href="/articles/s41598-022-09213-w#ref-CR74" id="ref-link-section-d121634187e5590">74</a></sup>. In this paper, the PBG transmission spectrum, which is less common in other published works, is used for sensing applications. This type of spectrum has different advantages. First, the sharp edges of PBGs are good candidates for sensing. The second one is that there is a long distance between two PBG edges. This causes that when the low PBG is used for sensing, it does not have an overlapping with the high PBG edge by changing the refractive index of the analyte. For this reason, the proposed structure can be used for a wide wavelength range. The other parameter is the sensing wavelength. As seen, the sensing wavelengths of the proposed sensors are located in the NIR which are suitable to use for biosensing applications. The other parameter is Q-factor. As seen, the Q-factors of the proposed structures are neither very low nor very high. It is because the low Q-factor decreases the FOM and the high Q-factor increases the effect of lithography error in the fabrication process. The last parameters are sensitivity and FOM. As discussed before, the most comprehensive parameter for the comparison of sensors’ operation is the FOM parameter. For example, the sensor designed in Ref.<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 42" title="Khani, S. & Hayati, M. Optical sensing in single-mode filters base on surface plasmon H-shaped cavities. Opt. Commun. 505, 127534 (2021)." href="/articles/s41598-022-09213-w#ref-CR42" id="ref-link-section-d121634187e5595">42</a></sup> has the most sensitivity in the comparison table, while its FOM value is low. As seen, the proposed biosensor I is among the highest FOM sensors.</p></div></div></section><section data-title="Conclusion"><div class="c-article-section" id="Sec7-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Sec7">Conclusion</h2><div class="c-article-section__content" id="Sec7-content"><p>In this paper, two novel biosensors based on a 1D PC and plasmonic structures were proposed. The combination of PC and plasmonic structures causes a suitable balance between different designing parameters can be obtained. The FDTD simulation has been used for numerical investigation of the designed structures. The obtained results show that the sensitivity values of 718.6 and 714.3 nm/RIU have been achieved for the designed biosensors I and II, respectively. The sharp PBG edges of the biosensors’ transmission spectra result in high sensitivity detections. The proposed structures could find potential for bio-optical sensing applications such as cancer cell detection.</p></div></div></section> </div> <div> <section data-title="Data availability"><div class="c-article-section" id="data-availability-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="data-availability">Data availability</h2><div class="c-article-section__content" id="data-availability-content"> <p>The calculated results during the current study are available from the corresponding author on reasonable request.</p> </div></div></section><div id="MagazineFulltextArticleBodySuffix"><section aria-labelledby="Bib1" data-title="References"><div class="c-article-section" id="Bib1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Bib1">References</h2><div class="c-article-section__content" id="Bib1-content"><div data-container-section="references"><ol class="c-article-references" data-track-component="outbound reference" data-track-context="references section"><li class="c-article-references__item js-c-reading-companion-references-item" data-counter="1."><p class="c-article-references__text" id="ref-CR1">Abbasi, H., Hayati, M., Kazimierczuk, M. 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All authors discussed the results and contributed to the final manuscript.</p><h3 class="c-article__sub-heading" id="corresponding-author">Corresponding author</h3><p id="corresponding-author-list">Correspondence to <a id="corresp-c1" href="mailto:mohsen_hayati@yahoo.com">Mohsen Hayati</a>.</p></div></div></section><section data-title="Ethics declarations"><div class="c-article-section" id="ethics-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="ethics">Ethics declarations</h2><div class="c-article-section__content" id="ethics-content"> <h3 class="c-article__sub-heading" id="FPar1">Competing interests</h3> <p>The authors declare no competing interests.</p> </div></div></section><section data-title="Additional information"><div class="c-article-section" id="additional-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="additional-information">Additional information</h2><div class="c-article-section__content" id="additional-information-content"><h3 class="c-article__sub-heading">Publisher's note</h3><p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p></div></div></section><section data-title="Rights and permissions"><div class="c-article-section" id="rightslink-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="rightslink">Rights and permissions</h2><div class="c-article-section__content" id="rightslink-content"> <p><b>Open Access</b> This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. 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id="citeas">Cite this article</h3><p class="c-bibliographic-information__citation">Khani, S., Hayati, M. Optical biosensors using plasmonic and photonic crystal band-gap structures for the detection of basal cell cancer. <i>Sci Rep</i> <b>12</b>, 5246 (2022). https://doi.org/10.1038/s41598-022-09213-w</p><p class="c-bibliographic-information__download-citation u-hide-print"><a data-test="citation-link" data-track="click" data-track-action="download article citation" data-track-label="link" data-track-external="" rel="nofollow" href="https://citation-needed.springer.com/v2/references/10.1038/s41598-022-09213-w?format=refman&flavour=citation">Download citation<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-download-medium"></use></svg></a></p><ul class="c-bibliographic-information__list" data-test="publication-history"><li class="c-bibliographic-information__list-item"><p>Received<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2021-12-04">04 December 2021</time></span></p></li><li class="c-bibliographic-information__list-item"><p>Accepted<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2022-03-09">09 March 2022</time></span></p></li><li class="c-bibliographic-information__list-item"><p>Published<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="2022-03-28">28 March 2022</time></span></p></li><li class="c-bibliographic-information__list-item c-bibliographic-information__list-item--full-width"><p><abbr title="Digital Object Identifier">DOI</abbr><span class="u-hide">: </span><span class="c-bibliographic-information__value">https://doi.org/10.1038/s41598-022-09213-w</span></p></li></ul><div data-component="share-box"><div class="c-article-share-box u-display-none" hidden=""><h3 class="c-article__sub-heading">Share this article</h3><p class="c-article-share-box__description">Anyone you share the following link with will be able to read this content:</p><button class="js-get-share-url c-article-share-box__button" type="button" id="get-share-url" data-track="click" data-track-label="button" data-track-external="" data-track-action="get shareable link">Get shareable link</button><div class="js-no-share-url-container u-display-none" hidden=""><p class="js-c-article-share-box__no-sharelink-info c-article-share-box__no-sharelink-info">Sorry, a shareable link is not currently available for this article.</p></div><div class="js-share-url-container u-display-none" hidden=""><p class="js-share-url c-article-share-box__only-read-input" id="share-url" data-track="click" data-track-label="button" data-track-action="select share url"></p><button class="js-copy-share-url c-article-share-box__button--link-like" type="button" id="copy-share-url" data-track="click" data-track-label="button" data-track-action="copy share url" data-track-external="">Copy to clipboard</button></div><p class="js-c-article-share-box__additional-info c-article-share-box__additional-info"> Provided by the Springer Nature SharedIt content-sharing initiative </p></div></div><div data-component="article-info-list"></div></div></div></div></div></section> </div> <section> <div class="c-article-section js-article-section" id="further-reading-section" data-test="further-reading-section"> <h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="further-reading">This article is cited by</h2> <div class="c-article-section__content js-collapsible-section" id="further-reading-content"> <ul class="c-article-further-reading__list" id="further-reading-list"> <li class="c-article-further-reading__item js-ref-item"> <h3 class="c-article-further-reading__title" data-test="article-title"> <a class="print-link" data-track="click" data-track-action="view further reading article" data-track-label="link:Photonic Crystal–Based Nanoscale Multipurpose Biosensor for Detection of Brain Tumours, HIV, and Anaemia with High Sensitivity" href="https://doi.org/10.1007/s11468-024-02199-3"> Photonic Crystal–Based Nanoscale Multipurpose Biosensor for Detection of Brain Tumours, HIV, and Anaemia with High Sensitivity </a> </h3> <ul data-test="author-list" class="c-author-list c-author-list--compact c-author-list--truncated u-sans-serif u-mb-4 u-mt-auto"> <li>Elizabeth Caroline Britto</li><li>Bhuvaneshwari Krishnamoorthi</li><li>S. 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