Analytical Derivation of a Conformal

We present an analytical derivation of a 3D conformal perfectly matched layer (PML's) for mesh termination in general orthogonal curvilinear coordinates. The derivation is based on the analytic continuation to complex space of the normal coordinate to the mesh termination. The resultant elds in the complex space do not obey the Maxwell's equations. However, it is demonstrated that through simple eld transformations, a new set of elds can be introduced so that they obey Maxwell's equations for an anisotropic medium with a properly chosen constitutive parameters depending on the local radii of curvature. The formulation presented here recovers, as particular cases, the previously proposed Cartesian, cylindrical, and spherical PML's. A previously employed anisotropic (quasi-) PML for conformal terminations is shown to be the large radius of curvature approximation of the anisotropic conformal PML derived herein.