Rigorous Coupled Wave Analysis of Bipolar
Cylindrical Systems: Scattering from Inhomogeneous Dielectric Material,
Eccentric, Composite Circular Cylinders
Rigorous Coupled Wave Analysis (RCWA) in bipolar coordinates for the first time is used to study electromagnetic (EM) scattering from eccentric, circular, multi-cylinder systems for which spatially, non uniform material (dielectric permittivity) occupies the regions between the interfaces of the cylinders. The bipolar RCWA algorithm presented herein consists of three basic steps which are; (1) solving Maxwell's equations in bipolar coordinates using a state variable (SV) formulation; (2) solving Maxwell's equations in the spatially uniform regions exterior to the inhomogeneous scattering object in terms of circular, cylindrical Bessel-Hankel functions; and (3) enforcement of EM boundary matching equations which leads to a final matrix equation solution of the system. In the paper extensive use of the residue theorem of complex variable theory was made in order to find fast and exact evaluations of the EM boundary interaction integrals that arose between the bipolar, SV solutions and the Hankel- Bessel solutions.
In this paper very extensive reliance on the work of A. A. Kishk, R. P. Parrikar and A. Z. Elsherbeni  who studied EM scattering from uniform material multi-eccentric circular cylinders (called herein the KPE algorithm) was made in order to validate the numerical results of the bipolar RCWA algorithm. In this paper, two important system transfer matrices, called the Bessel transfer matrix (based on the KPE algorithm) and called the bipolar SV transfer matrix, were developed in order to validate the numerical accuracy of the RCWA algorithm. The Bessel and SV transfer matrices were very useful for validation purposes because, from the way they were both formulated, they could be meaningfully compared to one another, matrix element to matrix element.
In the paper extensive numerical results are presented for EM scattering from spatially uniform and non uniform multi-eccentric, composite cylinder systems, including calculation of three dimensional plots of the electric and magnetic fields and including calculation of the back and bistatic scattering widths associated with the scattering systems. Also included are three tables of data documenting peak and RMS errors that occur between the KPE and RCWA algorithms when the number of modes are changed, the number of layers in the RCWA algorithm are varied and when the angle of incidence is varied.