An Improved DGTD-GSTC Method Equipped With Normal Surface Polarizabilities for Oblique Incidence

A novel transient solver based on the discontinuous Galerkin time-domain (DGTD) method incorporating generalized sheet transition conditions (GSTCs) for metasurfaces is proposed, which uses equivalent surface polarizabilities (SPs) instead of the actual structure of meta-atoms to achieve high efficiency. Compared with the previous work of the DGTD-GSTC method from the authors, this article takes the normal component of SP into account for the first time. These normal components play an important role in the accurate simulation of metasurfaces under oblique incidence at the expense of extra numerical simulation difficulty. To equip the normal SP in the DGTD method, we rigorously derive the new numerical flux with normal SP and propose the corresponding time integration scheme based on the explicit Runge-Kutta method. Numerical examples including the ideal model, the periodic array, and the curved metasurface are given. The results are compared with analytical results or commercial simulation software. The comparisons show that the proposed method can accurately obtain the macroscopic response of the metasurfaces. Finally, based on the example, the effects of the new numerical flux with SP on stability and choice of basis functions are discussed.