A finite difference-time domain approach for frequency selective surfaces at oblique incidence

Frequency selective surfaces (FSS) are often analyzed using frequency domain integral equation formulations and the method of moments (MoM) solutions. Because of the required evaluation of periodic Green's functions, and the frequent desire to repeat the analysis at multiple frequencies, these approaches can become computationally intensive. For normal incidence, the finite difference-time domain (FD-TD) provides an alternate approach, since symmetry of the fields permits the use of a periodic side boundary condition, while modeling only a single period of the infinite structure. For the oblique case, where the periodic boundary becomes non-causal, several FD-TD approaches have been proposed. However, these methods all involve either potentially divergent iterative solutions for the time advanced boundary, or phase shifting approaches which limit the excitation to a single frequency. This paper presents an alternative FD-TD approach to the oblique incidence problem. New field quantities are defined related to the electric and magnetic fields through spatially varying time shifts. The FD-TD discretization is then applied to Maxwell's equations rewritten in terms of these new field quantities. This transformation permits the use of an unshifted periodic boundary, and allows the simulation of FSS scattering at oblique incidence for multiple frequencies.