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

TL;DR

This paper develops exact formulas for time-domain non-reflecting boundary conditions in Maxwell's equations, introduces a new efficient model for electromagnetic invisibility cloaks, and proposes a spectral-element method for accurate, cost-effective simulations.

Contribution

It provides the first analytic formulas for temporal convolution kernels in NRBC, a novel time-domain model for cloaking with simplified convolutions, and an efficient spectral-element method for spherical cloaks.

Findings

Exact formulas enable accurate, efficient NRBC computation.

New cloaking model with a single unknown field simplifies simulations.

Spectral-element method achieves high accuracy with reduced computational cost.

Abstract

In this paper, we present analytic formulas of the temporal convolution kernel functions involved in the time-domain non-reflecting boundary condition (NRBC) for the electromagnetic scattering problems. Such exact formulas themselves lead to accurate and efficient algorithms for computing the NRBC for domain reduction of the time-domain Maxwell's system in $\mathbb R^3$. A second purpose of this paper is to derive a new time-domain model for the electromagnetic invisibility cloak. Different from the existing models, it contains only one unknown field and the seemingly complicated convolutions can be computed as efficiently as the temporal convolutions in the NRBC. The governing equation in the cloaking layer is valid for general geometry, e.g., a spherical or polygonal layer. Here, we aim at simulating the spherical invisibility cloak. We take the advantage of radially stratified dispersive media and special geometry, and develop an efficient vector spherical harmonic (VSH)-spectral-element method for its accurate simulation. Compared with limited results on FDTD simulation, the proposed method is optimal in both accuracy and computational cost. Indeed, the saving in computational time is significant.