{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T06:05:23Z","timestamp":1772777123298,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T00:00:00Z","timestamp":1666569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We introduce a Domain Decomposition Spectral Method (DDSM) as a solution for Maxwell\u2019s 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\u2019s 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.<\/jats:p>","DOI":"10.3390\/s22218131","type":"journal-article","created":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T10:09:23Z","timestamp":1666606163000},"page":"8131","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9896-9519","authenticated-orcid":false,"given":"Kofi","family":"Edee","sequence":"first","affiliation":[{"name":"INP, CNRS, Institut Pascal, Universit\u00e9 Clermont Auvergne, F-63000 Clermont-Ferrand, France"},{"name":"Kavli Institute of Theoretical Physics (KITP), University of California, Santa Barbara, CA 93106, USA"}]},{"given":"G\u00e9rard","family":"Granet","sequence":"additional","affiliation":[{"name":"INP, CNRS, Institut Pascal, Universit\u00e9 Clermont Auvergne, F-63000 Clermont-Ferrand, France"}]},{"given":"Francoise","family":"Paladian","sequence":"additional","affiliation":[{"name":"INP, CNRS, Institut Pascal, Universit\u00e9 Clermont Auvergne, F-63000 Clermont-Ferrand, France"}]},{"given":"Pierre","family":"Bonnet","sequence":"additional","affiliation":[{"name":"INP, CNRS, Institut Pascal, Universit\u00e9 Clermont Auvergne, F-63000 Clermont-Ferrand, France"}]},{"given":"Ghida","family":"Al Achkar","sequence":"additional","affiliation":[{"name":"INP, CNRS, Institut Pascal, Universit\u00e9 Clermont Auvergne, F-63000 Clermont-Ferrand, France"}]},{"given":"Lana","family":"Damaj","sequence":"additional","affiliation":[{"name":"INP, CNRS, Institut Pascal, Universit\u00e9 Clermont Auvergne, F-63000 Clermont-Ferrand, France"}]},{"given":"Jean-Pierre","family":"Plumey","sequence":"additional","affiliation":[{"name":"INP, CNRS, Institut Pascal, Universit\u00e9 Clermont Auvergne, F-63000 Clermont-Ferrand, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7876-628X","authenticated-orcid":false,"given":"Maria Cristina","family":"Larciprete","sequence":"additional","affiliation":[{"name":"Kavli Institute of Theoretical Physics (KITP), University of California, Santa Barbara, CA 93106, USA"},{"name":"Dipartimento di Scienze di Base ed Applicate per l\u2019Ingegneria, Sapienza Universita di Roma, Via A. Scarpa 16, I-00161 Roma, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0743-8852","authenticated-orcid":false,"given":"Brahim","family":"Guizal","sequence":"additional","affiliation":[{"name":"Kavli Institute of Theoretical Physics (KITP), University of California, Santa Barbara, CA 93106, USA"},{"name":"Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Universit\u00e9 de Montpellier, F-34095 Montpellier, France"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/16M109781X","article-title":"A class of iterative solvers for the Helmholtz equation: Factorizations, sweeping preconditioners, source transfer, single layer potentials, polarized traces, and optimized Schwarz methods","volume":"61","author":"Gander","year":"2019","journal-title":"SIAM Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"B942","DOI":"10.1137\/15M104582X","article-title":"Nested domain decomposition with polarized traces for the 2d Helmholtz equation","volume":"40","author":"Demanet","year":"2018","journal-title":"SIAM J. 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