Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms

We introduce a Domain Decomposition Spectral Method (DDSM) as a solution for Maxwell’s equations in the frequency domain. It will be illustrated in the framework of the Aperiodic Fourier Modal Method (AFMM). This method may be applied to compute the electromagnetic field diffracted by a large-scale...

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Autores principales: Edee, Kofi, Granet, Gérard, Paladian, Francoise, Bonnet, Pierre, Al Achkar, Ghida, Damaj, Lana, Plumey, Jean-Pierre, Larciprete, Maria Cristina, Guizal, Brahim
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9657735/
https://www.ncbi.nlm.nih.gov/pubmed/36365826
http://dx.doi.org/10.3390/s22218131
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author Edee, Kofi
Granet, Gérard
Paladian, Francoise
Bonnet, Pierre
Al Achkar, Ghida
Damaj, Lana
Plumey, Jean-Pierre
Larciprete, Maria Cristina
Guizal, Brahim
author_facet Edee, Kofi
Granet, Gérard
Paladian, Francoise
Bonnet, Pierre
Al Achkar, Ghida
Damaj, Lana
Plumey, Jean-Pierre
Larciprete, Maria Cristina
Guizal, Brahim
author_sort Edee, Kofi
collection PubMed
description We introduce a Domain Decomposition Spectral Method (DDSM) as a solution for Maxwell’s equations in the frequency domain. It will be illustrated in the framework of the Aperiodic Fourier Modal Method (AFMM). This method may be applied to compute the electromagnetic field diffracted by a large-scale surface under any kind of incident excitation. In the proposed approach, a large-size surface is decomposed into square sub-cells, and a projector, linking the set of eigenvectors of the large-scale problem to those of the small-size sub-cells, is defined. This projector allows one to associate univocally the spectrum of any electromagnetic field of a problem stated on the large-size domain with its footprint on the small-scale problem eigenfunctions. This approach is suitable for parallel computing, since the spectrum of the electromagnetic field is computed on each sub-cell independently from the others. In order to demonstrate the method’s ability, to simulate both near and far fields of a full three-dimensional (3D) structure, we apply it to design large area diffractive metalenses with a conventional personal computer.
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spelling pubmed-96577352022-11-15 Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms Edee, Kofi Granet, Gérard Paladian, Francoise Bonnet, Pierre Al Achkar, Ghida Damaj, Lana Plumey, Jean-Pierre Larciprete, Maria Cristina Guizal, Brahim Sensors (Basel) Article We introduce a Domain Decomposition Spectral Method (DDSM) as a solution for Maxwell’s equations in the frequency domain. It will be illustrated in the framework of the Aperiodic Fourier Modal Method (AFMM). This method may be applied to compute the electromagnetic field diffracted by a large-scale surface under any kind of incident excitation. In the proposed approach, a large-size surface is decomposed into square sub-cells, and a projector, linking the set of eigenvectors of the large-scale problem to those of the small-size sub-cells, is defined. This projector allows one to associate univocally the spectrum of any electromagnetic field of a problem stated on the large-size domain with its footprint on the small-scale problem eigenfunctions. This approach is suitable for parallel computing, since the spectrum of the electromagnetic field is computed on each sub-cell independently from the others. In order to demonstrate the method’s ability, to simulate both near and far fields of a full three-dimensional (3D) structure, we apply it to design large area diffractive metalenses with a conventional personal computer. MDPI 2022-10-24 /pmc/articles/PMC9657735/ /pubmed/36365826 http://dx.doi.org/10.3390/s22218131 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Edee, Kofi
Granet, Gérard
Paladian, Francoise
Bonnet, Pierre
Al Achkar, Ghida
Damaj, Lana
Plumey, Jean-Pierre
Larciprete, Maria Cristina
Guizal, Brahim
Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms
title Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms
title_full Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms
title_fullStr Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms
title_full_unstemmed Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms
title_short Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms
title_sort domain decomposition spectral method applied to modal method: direct and inverse spectral transforms
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9657735/
https://www.ncbi.nlm.nih.gov/pubmed/36365826
http://dx.doi.org/10.3390/s22218131
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