The generalized theory of perfectly matched layers (GT-PML): numerical reflection analysis and optimization

The use of a perfectly matched layer (PML) has been demonstrated as a highly efficient absorbing boundary condition in FDTD (Berenger 1994). Although the PML is supposed to absorb the outgoing wave totally, its discrete implementation gives rise to numerical reflections. Investigation of the numerical reflection properties of Berenger´s PML, based on the 2D FDTD method with split components, and the Chew-Weedon stretched-coordinate formulation can be found in Fang and Wu (1996) and Chew and Jin (1996). An alternative approach to Berenger´s implementation is based on properly designed anisotropic absorbers and doesn´t require splitting of the fields (Sacks et al. 1995). In this paper the generalized theory of a PML of Zhao and Cangellaris (1996) is used to quantify the numerical reflection properties of such anisotropic perfectly matched absorbers (PMAs). An optimum implementation to minimize the numerical reflection is presented also. Numerical results using a parallel plate waveguide demonstrate the validity and accuracy of the formulation.