%0 Journal Article %T Domain Decomposition Spectral Method Applied to Modal Method: Direct and Inverse Spectral Transforms %+ Institut Pascal (IP) %+ University of California (UC) %+ Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome] (UNIROMA) %+ Laboratoire Charles Coulomb (L2C) %A Edee, Kofi %A Granet, G. %A Paladian, Francoise %A Bonnet, Pierre %A Al Achkar, Ghida %A Damaj, Lana %A Plumey, Jean-Pierre %A Larciprete, Maria Cristina %A Guizal, Brahim %< avec comité de lecture %Z L2C:22-141 %@ 1424-8220 %J Sensors %I MDPI %V 22 %N 8131 %P 8131 %8 2022-10-24 %D 2022 %R 10.3390/s22218131 %K Modal Methods %K Domain décomposition method %K Metasurfaces %Z Physics [physics]/Mathematical Physics [math-ph]Journal articles %X 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. %G English %Z Collaboration au sein du KAVLI Institute of Theoretical Physics durant l'été 2022. Financement obtenu en partie par l'Université de Montpellier. %2 https://hal.science/hal-03826961/document %2 https://hal.science/hal-03826961/file/Edee%20et%20al..pdf %L hal-03826961 %U https://hal.science/hal-03826961 %~ PRES_CLERMONT %~ CNRS %~ UNIV-BPCLERMONT %~ L2C %~ INSTITUT_PASCAL %~ ACL-SF %~ TDS-MACS %~ UNIV-MONTPELLIER %~ CLERMONT-AUVERGNE-INP %~ UM-2015-2021 %~ UM-EPE %~ TEST3-HALCNRS