Simulating 3D periodic structures at oblique incidences with discontinuous Galerkin time-domain methods: theoretical and practical considerations

Abstract

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).2010 Mathematics Subject Classification. 35Q61, 65M60, 65M12.

Efficient electromagnetic analysis of multi‐layer and multi‐scale periodic/quasi‐periodic structures

“…In Ref. [22], the above method is introduced into the nanophotonics periodic structures, and the field transformation technology for the propagation of time‐varying electromagnetic waves is emphatically analysed, and the stability analysis is made. Considering the high precision of the PML boundaries in absorbing waves of higher‐order Floquet modes, the Floquet periodic boundary conditions are implemented by the transformed field variable technique, and the DGTD formulations of the PML medium are deduced in detail by auxiliary differential equations and transformed Maxwell equations [16].…”