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

In this work, we focus on the development of the use of Periodic Boundary Conditions (PBC) with sources at oblique incidence in a Discontinuous Galerkin Time Domain (DGTD) framework. Whereas in the context of the Finite Difference Time Domain (FDTD) methods, an abundant literature can be found, for DGTD, the amount of contributions reporting on such methods is remarkably low. In this paper, we supplement the existing references using the field transform technique with an analysis of the continuous system using the method of characteristics and provide an energy estimate. Furthermore, we also study the discrete stability of the resulting DGTD scheme. Additional details about sources, observables (reflectance, transmittance and diffraction efficiency), and the use of Complex Frequency-Shifted Perfectly-Matched Layers (CFS-PMLs) in this framework are also given. After numerical validations, two realistic test-cases are considered in the context of nanophotonics with the Diogenes DGTD solver (http://diogenes.inria.fr).