Application and Optimization of PML ABC for the 3-D Wave Equation in the Time Domain

A three-dimensional algorithm with the perfectly matched layer (PML) absorbing boundary condition (ABC) for the scalar wave equation in the time domain is presented for general inhomogeneous lossy or loss-free problems. The proposed PML ABC is applicable to practical finite difference schemes treating the time-domain wave equation, such as the time-domain wave-potential (TDWP) technique and the time-domain scalar wave equation approaches to the analysis of optical structures. The time-domain wave equation for lossy media is expressed in terms of stretched coordinate variables. The algorithm is tested for homogeneous and inhomogeneous media. We demonstrate applications to open (radiation) problems and to port terminations in high-frequency circuit problems. New PML conductivity profiles are developed for use with the second order wave equation, which offer lower reflections in a wider frequency band in comparison with the commonly used (in finite-difference time-domain (FDTD) algorithms) profiles. The effect of the termination walls on the overall PML performance is studied and the best choices are singled out.