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In this paper, we present analytic formulas of the temporal convolutionkernel functions involved in the time-domain non-reflecting boundary condition(NRBC) for the electromagnetic scattering problems. Such exact formulasthemselves lead to accurate and efficient algorithms for computing the NRBC fordomain reduction of the time-domain Maxwell's system in $\mathbb R^3$. A secondpurpose of this paper is to derive a new time-domain model for theelectromagnetic invisibility cloak. Different from the existing models, itcontains only one unknown field and the seemingly complicated convolutions canbe computed as efficiently as the temporal convolutions in the NRBC. Thegoverning equation in the cloaking layer is valid for general geometry, e.g., aspherical or polygonal layer. Here, we aim at simulating the sphericalinvisibility cloak. We take the advantage of radially stratified dispersivemedia and special geometry, and develop an efficient vector spherical harmonic(VSH)-spectral-element method for its accurate simulation. Compared withlimited results on FDTD simulation, the proposed method is optimal in bothaccuracy and computational cost. Indeed, the saving in computational time issignificant.

On time-domain NRBC for Maxwell's equations and its application in accurate simulation of electromagnetic invisibility cloaks