Complex space approach to perfectly matched layers: a review and some new developments

We discuss the interpretation of the perfectly matched layer (PML) absorbin g boundary condition (ABC) as an analytic continuation of the coordinate sp ace to a complex variables spatial domain (complex space). The generalizati on of the PML to curvilinear coordinates and to general linear media using this rationale is reviewed and summarized. The analytic continuation is sho wn to be equivalent to a change on the metric of the space. By using such g eometric viewpoint on the PML, we then discuss the various PML formulations in connection with fundamental symmetries of Maxwell's equations. Copyrigh t (C) 2000 John Wiley & Sons, Ltd.