Analytical properties of the anisotropic PML constitutive tensors in curvilinear coordinates

Abstract

The identification of the perfect matched layer (PML) absorbing boundary condition (ABC) as an analytic continuation (complex stretching approach) of Maxwell's equations (MEs) provided the basis for its extension to cylindrical, spherical, and 3D general orthogonal curvilinear coordinates (conformal mesh terminations). It was then shown that, to achieve a true PML in a curvilinear coordinate system, the metric of the space must also be properly modified since it is, in general, a function of the coordinates. The modification on the metric however, can be translated through simple field transformations to constitutive parameters of the artificial media, thereby allowing anisotropic curvilinear PML formulations. The mapping of the metric introduces additional richness in the formulation and a question naturally arises if these new artificial PML media retain the causality conditions observed by the original MEs. This leads to the study of the analytic properties of the PML tensor constitutive parameters on the complex /spl omega/ plane. We study these analytic properties for various coordinate systems. We point out conditions under which causality is violated and the consequences of on the dynamical stability on the PML-FDTD simulations. Throughout this work, the e/sup =-l/spl omega/t/ convention is used.