3D Weakly Conditionally Stable FDTD Method for Analyzing Periodic Structures

By dividing the 3D transformed Maxwell's equations into two parts and applying the Crank-Nicolson (CN) scheme to each part, four substep implicit procedures are obtained. After adjusting the order of four substeps, a weakly conditionally stable finite-difference time-domain (WCSFDTD) method is derived for solving the 3D problems of oblique incident plane wave on periodic structures. This method is very suitable for analyzing the problems which have fine structures in one or two directions, and the Courant-Friedrich-Levy (CFL) stability condition of it is more relaxed than that of the original held transformation methods. Numerical examples demonstrate that the presented technology is more efficient, especially at the high incident angle.