Numerical reflection of evanescent waves from perfectly matched layers

Berenger (see IEEE Ant. and Propag., vol.44, no.1, p.110-17, 1996) found the conditions to be satisfied by a perfectly matched layer (PML) located close to scattering structures so as to make the numerical reflection negligible. This analysis was mainly based on numerical experiments. Since then, other authors have investigated the problem of numerical reflection from a theoretical point of view. De Moerloose and Stuchly (see IEEE Micr., and Guid. Wav. Letters, vol.5, no.10, p.344-6, 1995) considered the reflection of evanescent waves from PMLs bounding waveguides. Starting from De Moerloose et al. proposals, we investigated the propagation of general evanescent waves in a PML, along with the numerical reflection of such waves from PML interfaces. From this theory, the observations of Berenger can be clearly interpreted. The numerical reflection is due to strongly evanescent waves that are totally reflected below a cutoff frequency which is exactly the cutoff empirically found by Berenger.