Finite-Element Time-Domain Analysis of Electrically and Magnetically Dispersive Periodic Structures

A formulation is presented for the finite-element time-domain (FETD) analysis of periodic structures that contain electrically and/or magnetically dispersive materials. The formulation is based on the previously developed transformed field. variable approach and the Floquet absorbing boundary condition, which are both applicable to arbitrary scan or incident angles. The paper describes an implicit finite-element time-marching equation for the transformed electric field variable coupled with a finite-difference type equation for the evaluation of the transformed magnetic field variable. The technique is applicable to general dispersive materials, although the required convolution calculations can be greatly accelerated when the electric and magnetic susceptibilities can be represented by a pole expansion. Numerical examples are presented to demonstrate the validity and capability of the proposed numerical approach which is effective for the efficient broadband analysis of complex periodic structures such as engineered materials and phased-array antennas.