Rigorous Coupled Wave Analysis of Bipolar Cylindrical Systems: Scattering from Inhomogeneous Dielectric Material, Eccentric, Composite Circular Cylinders

Abstract

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 [22] 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. Jarem 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. 1 Introduction 2 RCWA Bipolar Coordinate Formulation 3 Numerical Results 4 Summary, Conclusions, and Future Work Appendix A.

Electromagnetic Scattering From Bi-Periodic Fabric Structures

“…This problem has been studied for many years and several different methods have been adopted for this purpose [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Some of these are general methods, such as the finite-difference time-domain (FDTD) method [11], finite-element method (FEM) [12], boundary-element method [13] and rigorous coupled waveguide analysis (RCWA) [14]. However, the unit-cell of such fabric structures might be extended over many optical wavelengths which inevitably leads to numerical models with enormous numbers of unknowns, considering small geometrical features that necessitate ultra-fine meshing.…”

Huygens Principle Based Imaging of Multilayered Objects With Inclusions

“…Scattering by cylindrical objects, for both concentric and eccentric cases, has been previously investigated by other researchers [17][18][19]. Here, we consider a 3-layer stratified cylinder in free space, illuminated by a plane wave having a frequency f , with T M -polarization and normal incidence with respect to the z-axis.…”

Efficient Analysis of Multilayered Dielectric Rods by Equivalent Microwave Network Method

“…Multilayered eccentric dielectric rods are studied by the indirect mode-matching solution in [7][8][9]. Rigorous Coupled Wave Analysis (RCWA) algorithm is applied in [10][11][12] to study EM scattering by multi-eccentric circular or elliptical cylinders. For single layer dielectric rod forest, we have analysed the EM properties in [13,14], and the equivalent microwave network method (EMN) is applied in the analysis process.…”