Specifying PML conductivities by considering numerical reflection dependencies

Berenger´s perfectly matched layer (PML) absorbing boundary condition (ABC) has greatly enhanced finite-difference time-domain (FDTD) scattering analysis. In a discretized domain, however, performance is signal-dependent and large-angle performance is poor due to a rapid reduction in layer decay rate. Increasing the conductivity to offset this reduction increases the discretization errors, especially at near-normal incidence angles. However, by carefully specifying the conductivity in each of the PML sublayers, it is possible to balance the small and large angle performance. The signal-dependence of reflections may be described in terms of the number of spatial points per wavelength. This lends itself to an overall strategy for which to search for PML profiles that provide superior performance for waves incident on a PML at angles between 0-75° and signals that have at least 15 spatial points per wavelength sampling. A one-dimensional (1-D) projection method may be employed to allow an exhaustive search to become a viable alternative to optimization. Such a search provides profile parameters that, while not necessarily “optimal,” give excellent wide-angle wide-band reflection performance