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In this work, we focus on the development of the use of Periodic Boundary Conditions (PBC) with sources at oblique incidence in a nanophotonics context. In particular, we concentrate on the field transform technique used for time dependent electromagnetic wave propagation problems. We especially supplement the existing references with an analysis of the continuous model equations. Furthermore, we propose to use a Discontinuous Galerkin Time Domain (DGTD) discrete framework and study stability issues. In order to consider realistic test cases, we also provide additional details about sources, observables (reflectance, transmittance and diffraction efficiency), and the use of Complex Frequency-Shifted Perfectly-Matched Layers (CFS-PMLs). Finally, after academic numerical validations, two engineering relevant test cases are considered in the precise physical context of nanophotonics with the Diogenes DGTD solver (http://diogenes.inria.fr).
Keywords: computational electromagnetics, time-domain Maxwell equations, discontinuous Galerkin method, periodic structures, oblique incidence sources, nanophotonics
Viquerat, Jonathan 1 ; Schmitt, Nikolai 1 ; Scheid, Claire 1
Viquerat, Jonathan; Schmitt, Nikolai; Scheid, Claire. Simulating 3D periodic structures at oblique incidences with discontinuous Galerkin time-domain methods: theoretical and practical considerations. The SMAI Journal of computational mathematics, Volume 5 (2019), pp. 131-159. doi: 10.5802/smai-jcm.45
@article{SMAI-JCM_2019__5__131_0,
author = {Viquerat, Jonathan and Schmitt, Nikolai and Scheid, Claire},
title = {Simulating {3D} periodic structures at oblique incidences with discontinuous {Galerkin} time-domain methods: theoretical and practical considerations},
journal = {The SMAI Journal of computational mathematics},
pages = {131--159},
year = {2019},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {5},
doi = {10.5802/smai-jcm.45},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.45/}
}
TY - JOUR AU - Viquerat, Jonathan AU - Schmitt, Nikolai AU - Scheid, Claire TI - Simulating 3D periodic structures at oblique incidences with discontinuous Galerkin time-domain methods: theoretical and practical considerations JO - The SMAI Journal of computational mathematics PY - 2019 SP - 131 EP - 159 VL - 5 PB - Société de Mathématiques Appliquées et Industrielles UR - http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.45/ DO - 10.5802/smai-jcm.45 LA - en ID - SMAI-JCM_2019__5__131_0 ER -
%0 Journal Article %A Viquerat, Jonathan %A Schmitt, Nikolai %A Scheid, Claire %T Simulating 3D periodic structures at oblique incidences with discontinuous Galerkin time-domain methods: theoretical and practical considerations %J The SMAI Journal of computational mathematics %D 2019 %P 131-159 %V 5 %I Société de Mathématiques Appliquées et Industrielles %U http://geodesic.mathdoc.fr/articles/10.5802/smai-jcm.45/ %R 10.5802/smai-jcm.45 %G en %F SMAI-JCM_2019__5__131_0
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