HIE-FDTD Method With PML for 2-D Periodic Structures at Oblique Incidence

For analyzing the oblique incident plane wave on periodic structures with the fine structure only in one direction, a hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method with the perfectly matched layer (PML) is derived. First, the field transformation technique is adopted to eliminate the time delay, and the PML formulations are derived by using the auxiliary differential equation (ADE) method. Then, by combining the transformed Maxwell’s equations with the PML formulations and adopting the locally one-dimensional (LOD) scheme, the proposed method with two substep implementations is obtained, which only needs to solve one implicit equation. The Courant–Friedrichs–Lewy (CFL) condition of the proposed method is more relaxed and no longer limited by the fine grid cell size.