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

We discuss the interpretation of the perfectly matched layer (PML) absorbing boundary condition (ABC) as an analytic continuation of the coordinate space to a complex variables spatial domain (complex space). The generalization of the PML to curvilinear coordinates and to general linear media using this rationale is reviewed and summarized. The analytic continuation is shown to be equivalent to a change on the metric of the space. By using such geometric viewpoint on the PML, we then discuss the various PML formulations in connection with fundamental symmetries of Maxwell's equations.