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A method for implementing the general Floquet boundary condition in the finite-difference time-domain algorithm (FDTD) is presented. The Floquet type of phase shift boundary condition is incorporated into the time-domain analysis by illuminating the structure with a combination of sine and cosine excitations to generate a phasor representation of the solution at each time step. With this approach, the characteristics of periodic structures comprised of arbitrarily shaped inhomogeneous geometries can be computed for an arbitrary angle of incidence. Theoretical results are compared for various planar frequency selective surfaces (FSS) and for one with a three-dimensional element, e.g., a thick, double, concentric square loop.>
Harms et al. (Sat,) studied this question.