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).

Classification: 35Q61, 65M60, 65M12

Keywords: computational electromagnetics, time-domain Maxwell equations, discontinuous Galerkin method, periodic structures, oblique incidence sources, nanophotonics

@article{SMAI-JCM_2019__5__131_0, author = {Jonathan Viquerat and Nikolai Schmitt and Claire Scheid}, 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}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {5}, year = {2019}, doi = {10.5802/smai-jcm.45}, language = {en}, url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.45/} }

Jonathan Viquerat; Nikolai Schmitt; Claire Scheid. 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. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.45/

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