A time-marching scheme for analyzing transient scattering from nonplanar doubly periodic structures

The paper presents a novel marching-on-in-time (MOT) based scheme for solving a time domain integral equation (TDIE) pertinent to the analysis of plane wave scattering from (potentially nonlinearly loaded) nonplanar doubly periodic structures. Historically, the analysis of transient scattering from doubly periodic structures has been carried out predominately using FDTD methods. Unfortunately, when the periodic structure is excited by obliquely incident fields, noncausal terms enter the FDTD update equations (unless specific measures are taken). Our recently developed a Floquet wave-based TDIE solver (Chen, N.-W. et al., IEEE APS Int. Symp., 2003) expands fields generated by quiescent and bandlimited periodic currents into time domain Floquet waves. We now present an improvement of that scheme aimed at rendering the solver applicable to nonplanar structures. Specifically, it introduces a scheme for evolving TDFW mode amplitudes along one-dimensional domains that permits their efficient evaluation not only on the source plane, but also removed from it. The proposed scheme evolves individual TDFWs using a spectral scheme supplemented with Huygen based boundary conditions. The resulting scheme applies without difficulty to nonplanar doubly periodic structures comprising PEC elements and sculptured dielectric substrates.