A property-dependent Perfectly Matched Layer with a single additional layer for Maxwell’s equations in finite difference frequency domains

Abstract

A Perfectly Matched Layer (PML) has become a widespread technique for preventing reflections from computational boundaries for electromagnetic wave propagation problems in frequency domains. Especially, a PML for the Helmholtz equation is well developed and applied to the finite difference method. In the currently used methods of PMLs, additional 4 to 6 layers surrounding a computational domain are required to be added in a PML region in order to terminate infinite domain calculations. Such a requirement not only demands a relatively large computer memory, but also increases execution time and complexity in implementations.The objectives of this paper are to show how to derive and implement a highly efficient PML on the termination of a computational grid in electromagnetic scattering simulations by one property-dependent PML (PPML) with just a single additional layer, based on the stretched-coordinate PML (SC-PML) and unsplit-field PML formulations. Its effectiveness is validated by examples with varying background media and applied frequencies in computational domains. These validate our proposed PPML to be a universal and accurate tool for solving frequency-domain Maxwell’s equations discretized by finite differences accurately in both lossless and lossy media under a wide range of applied frequencies. On one hand, PPML effectively reduces requirements of CPU time and computer memory by an additional single layer in the PPML region. On the other hand, the proposed technique simply calculates the property-dependent parameters of the PPML to obtain high computational accuracy over the PMLs which are used currently. In addition, with this novel implementation, the PPML can be easily specified in one or more coordinate systems in the same manner as the standard Finite-Difference-Frequency-Domain (FDFD) equations without any increase in their derivation work.