Efficient Computation of Electromagnetic Waves in Anisotropic Orthogonal-Plano-Cylindrically Layered Media Using the Improved Numerical Mode Matching (NMM) Method

Abstract

An orthogonal-plano-cylindrically layered (OPCL) medium consists of materials stratified planarly and layered concentrically in the orthogonal directions. The numerical mode matching (NMM) method has previously been shown to be a fast and robust semianalytical solver to investigate the propagation of electromagnetic (EM) waves in such a complex but isotropic or transversely isotropic medium. In this paper, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for unbounded low conductivity media and applicable to lossless media. We manipulate the weak form of Maxwell’s equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem. Finally, we also offer formulas for computing EM fields excited by a magnetic dipole located at any position with an arbitrary orientation. Numerical results have demonstrated the efficiency and accuracy of this method.