Perfect Plane-Wave Injection into a Finite FDTD Domain through Teleportation of Fields

Abstract

A new method is proposed for injecting plane waves (although not constrained solely to plane waves) into the computational domain of a finite-difference time domain (FDTD). Fields from a background FDTD space that can support perfect plane waves traveling at an arbitrary angle of incidence are used to calculate the equivalent currents on a rectangular boundary such that the currents so defined satisfy the discrete curl operator of FDTD. When these equivalent currents are copied onto another FDTD domain, the rectangular boundary acts as a perfect teleportation window, inside of which the plane wave exists and outside of which no fields are produced. Thus a scatterer within the window is illuminated with a perfect plane wave and its scattered fields exit transparently through the window. Thus a total field-scattered field FDTD formulation is attained automatically. This method correctly accounts for the nonlinear grid dispersion created by the discretization of the Yee grid. The only error in the plane wave injection is numerical round off of the CPU and is of the order of −300dB for double precision (−150 dB single precision).