Plane-Wave analysis and comparison of split-field, biaxial, and uniaxial PML methods as ABCs for pseudospectral electromagnetic wave simulations in curvilinear coordinates

In this paper, we discuss and compare split-field, biaxial, and uniaxial perfectly matched layer (PML) methods for absorbing outgoing vector waves in cylindrical and spherical coordinates. We first extend Berenger's split-field formulation into spherical and cylindrical coordinates in such a way that it maintains all the desirable properties it exhibits in rectangular coordinates. Then we discuss the biaxial and the uniaxial medium PML methods in Cartesian coordinates and extend them to spherical and cylindrical coordinates. Properties of plane-wave solutions of the PML methods are analyzed. In particular, the decay and boundness properties of the solutions are considered in order to provide further insight into the different formulations presented herein. Moreover, we propose a set of symmetric hyperbolic equations for both the biaxial and the uniaxial PML methods in the time-domain, which is fine-tuned in numerical experiments and very suitable for time-domain problems. All three types of spherical and cylindrical PML methods are applied in simulations of plane wave scattering as well as radiating dipole problems. We use a multidomain pseudospectral (Chebyshev) numerical scheme, and the effectiveness of the PML methods is demonstrated through the accurate numerical results obtained. The order of outer-boundary reflection is as low as 0.1% of the exact solution.