3D perfectly matched medium from modified Maxwell's equations with stretched coordinates

Abstract

A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies. The modified equations are also related to the perfectly matched layer that was presented recently for 2D wave propagation. Absorbing-material boundary conditions are of particular interest for finite-difference time-domain (FDTD) computations on a single-instruction multiple-data (SIMD) massively parallel supercomputer. A 3D FDTD algorithm has been developed on a connection machine CM-5 based on the modified Maxwell's equations and simulation results are presented to validate the approach.