Reflection characteristics of a PML with a shallow corrugation

The constitutive characteristics of anisotropic materials can be exploited to construct absorbers that provide reflectionless interfaces for waves at arbitrary angles of incidence. In this paper, we investigate how a weak corrugation affects the reflectivity of the anisotropic perfectly matched absorber developed by Sacks et al. (1995) for a flat interface. To do so, we develop a Rayleigh method to calculate the fields diffracted at the periodically corrugated boundary of an anisotropic absorber with constant constitutive tensors, which correspond to a planar (Cartesian) perfectly matched layer. We present numerical results in the nondiffractive regime (where only a specularly reflected wave can propagate) for sinusoidal corrugations with different groove height-to-period ratios. Our results show that the reflectivity of the anisotropic absorber near normal incidence remains very low (less than 0.4% for a 10% modulation), whereas it changes dramatically near grazing incidences.