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finite element model (fem) using comsol multiphysics® software  (COMSOL Inc)

 
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    COMSOL Inc finite element model (fem) using comsol multiphysics® software
    Angular interrogation analysis of grating coupled surface plasmons. ( a ) Schematic illustration of the proposed geometry for grating coupled surface plasmons (GC-SPR) in angle interrogation mode. ( a ) Cross-sectional view of the sinusoidal metal-dielectric grating, with the inset highlighting the key geometric parameters: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t$$\end{document} (film thickness), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:d$$\end{document} (grating depth), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varLambda\:$$\end{document} (grating period), and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\theta\:}_{i}$$\end{document} (angle of incidence). ( b ) Illustration of the unit cell containing the sinusoidal grating geometry used in the finite element method (FEM) computations, along with the associated material domains: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{n}_{d}$$\end{document} (dielectric material) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{n}_{a}$$\end{document} (incident medium). ( c ) Magnetic field intensity distribution at the SPR condition for a sinusoidal grating metasurface \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:(\varLambda\:=320\:nm)$$\end{document} . (Microsoft PowerPoint, Microsoft Office LTSC Professional Plus 2021 URL: www.microsoft.com ; COMSOL <t>Multiphysics</t> 6.3, URL: www.comsol.com ).
    Finite Element Model (Fem) Using Comsol Multiphysics® Software, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/multiphysics+modelling+software/pmc12134283-69-24-24?v=COMSOL+Inc
    Average 90 stars, based on 1 article reviews
    finite element model (fem) using comsol multiphysics® software - by Bioz Stars, 2026-08
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    1) Product Images from "Angular interrogation analysis of metal-dielectric grating metasurfaces for efficient tuning of surface plasmons"

    Article Title: Angular interrogation analysis of metal-dielectric grating metasurfaces for efficient tuning of surface plasmons

    Journal: Scientific Reports

    doi: 10.1038/s41598-025-04353-1

    Angular interrogation analysis of grating coupled surface plasmons. ( a ) Schematic illustration of the proposed geometry for grating coupled surface plasmons (GC-SPR) in angle interrogation mode. ( a ) Cross-sectional view of the sinusoidal metal-dielectric grating, with the inset highlighting the key geometric parameters: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t$$\end{document} (film thickness), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:d$$\end{document} (grating depth), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varLambda\:$$\end{document} (grating period), and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\theta\:}_{i}$$\end{document} (angle of incidence). ( b ) Illustration of the unit cell containing the sinusoidal grating geometry used in the finite element method (FEM) computations, along with the associated material domains: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{n}_{d}$$\end{document} (dielectric material) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{n}_{a}$$\end{document} (incident medium). ( c ) Magnetic field intensity distribution at the SPR condition for a sinusoidal grating metasurface \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:(\varLambda\:=320\:nm)$$\end{document} . (Microsoft PowerPoint, Microsoft Office LTSC Professional Plus 2021 URL: www.microsoft.com ; COMSOL Multiphysics 6.3, URL: www.comsol.com ).
    Figure Legend Snippet: Angular interrogation analysis of grating coupled surface plasmons. ( a ) Schematic illustration of the proposed geometry for grating coupled surface plasmons (GC-SPR) in angle interrogation mode. ( a ) Cross-sectional view of the sinusoidal metal-dielectric grating, with the inset highlighting the key geometric parameters: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t$$\end{document} (film thickness), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:d$$\end{document} (grating depth), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varLambda\:$$\end{document} (grating period), and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\theta\:}_{i}$$\end{document} (angle of incidence). ( b ) Illustration of the unit cell containing the sinusoidal grating geometry used in the finite element method (FEM) computations, along with the associated material domains: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{n}_{d}$$\end{document} (dielectric material) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{n}_{a}$$\end{document} (incident medium). ( c ) Magnetic field intensity distribution at the SPR condition for a sinusoidal grating metasurface \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:(\varLambda\:=320\:nm)$$\end{document} . (Microsoft PowerPoint, Microsoft Office LTSC Professional Plus 2021 URL: www.microsoft.com ; COMSOL Multiphysics 6.3, URL: www.comsol.com ).

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    Angular interrogation analysis of grating coupled surface plasmons. ( a ) Schematic illustration of the proposed geometry for grating coupled surface plasmons (GC-SPR) in angle interrogation mode. ( a ) Cross-sectional view of the sinusoidal metal-dielectric grating, with the inset highlighting the key geometric parameters: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t$$\end{document} (film thickness), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:d$$\end{document} (grating depth), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varLambda\:$$\end{document} (grating period), and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\theta\:}_{i}$$\end{document} (angle of incidence). ( b ) Illustration of the unit cell containing the sinusoidal grating geometry used in the finite element method (FEM) computations, along with the associated material domains: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{n}_{d}$$\end{document} (dielectric material) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{n}_{a}$$\end{document} (incident medium). ( c ) Magnetic field intensity distribution at the SPR condition for a sinusoidal grating metasurface \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:(\varLambda\:=320\:nm)$$\end{document} . (Microsoft PowerPoint, Microsoft Office LTSC Professional Plus 2021 URL: www.microsoft.com ; COMSOL Multiphysics 6.3, URL: www.comsol.com ).

    Journal: Scientific Reports

    Article Title: Angular interrogation analysis of metal-dielectric grating metasurfaces for efficient tuning of surface plasmons

    doi: 10.1038/s41598-025-04353-1

    Figure Lengend Snippet: Angular interrogation analysis of grating coupled surface plasmons. ( a ) Schematic illustration of the proposed geometry for grating coupled surface plasmons (GC-SPR) in angle interrogation mode. ( a ) Cross-sectional view of the sinusoidal metal-dielectric grating, with the inset highlighting the key geometric parameters: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t$$\end{document} (film thickness), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:d$$\end{document} (grating depth), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varLambda\:$$\end{document} (grating period), and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\theta\:}_{i}$$\end{document} (angle of incidence). ( b ) Illustration of the unit cell containing the sinusoidal grating geometry used in the finite element method (FEM) computations, along with the associated material domains: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{n}_{d}$$\end{document} (dielectric material) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{n}_{a}$$\end{document} (incident medium). ( c ) Magnetic field intensity distribution at the SPR condition for a sinusoidal grating metasurface \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:(\varLambda\:=320\:nm)$$\end{document} . (Microsoft PowerPoint, Microsoft Office LTSC Professional Plus 2021 URL: www.microsoft.com ; COMSOL Multiphysics 6.3, URL: www.comsol.com ).

    Article Snippet: To numerically evaluate the angular response of the SPs as a function of grating geometrical parameters, we employed a Finite Element Model (FEM) using COMSOL Multiphysics ® software .

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