Analytical Derivation of a Conformal Perfectly Matched Absorber for Electromagnetic Waves

We present an analytical derï ation of a 3-D conformal ( ) perfectly matched layer PML for mesh termination in general orthogonal cur̈ ilinear coordinates. The derï ation is based on the analytic continuation to complex space of the normal coordinate to the mesh termination. The resultant fields in the complex space do not obey Maxwell’s equations. Howe ̈er, it is demonstrated that, through simple field transformations, a new set of fields can be introduced so that they obey Maxwell’s equations for an anisotropic medium with properly chosen constitutï e parameters depending on the local radii of cur̈ ature. The formulation presented here reco ̈ers, as particular cases, the pre ̈iously proposed Cartesian, cylindrical, and spherical PMLs. A pre ̈iously ( ) employed anisotropic quasiPML for conformal terminations is shown to be the large radius of cur̈ ature approximation of the anisotropic conformal PML derï ed herein. Q 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 17: 231]236, 1998.