Rigorous Coupled Wave Analysis (RCWA) (used for electromagnetic (EM) analysis of planar diffraction gratings) has been applied to solve EM scattering and diffraction problems for spatially inhomogeneous, cylindrical, elliptical systems. The RCWA algorithm and an appropriate method for matching EM boundary conditions in the elliptical system are described herein. Comparisons of the eigenfunctions determined by RCWA (found in spatially homogeneous elliptical regions) and Mathieu functions are presented and shown to agree closely with one another. Numerical results of scattering from a uniform elliptical shell system (excited by an electrical surface current) obtained by using both a Mathieu function expansion method and by using the RCWA algorithm are presented and also shown to agree closely with one another. The RCWA algorithm was used to study EM scattering and diffraction from an elliptical, azimuthally inhomogeneous dielectric permittivity, step profile system. EM field matching and power conservation were shown to hold for this step profile example. A comparison of the EM fields of the step profile elliptical shell example and that of a uniform profile elliptical shell having the same excitation and bulk material parameters (permittivity and permeability) was made and significant differences of the EM fields of the two systems were observed.

We report the formation of thin anisotropic phase gratings in a nematic liquid-crystalline film by use of lateral (fringing) electric fields induced by transparent interdigitated electrodes. These gratings yield high diffraction efficiency (>30%) with a strong dependence on the readout beam incidence angle. In addition, the formation of a defect wall is observed that has a significant effect on the diffraction properties of the phase grating.

Abstract-A Rigorous Coupled Wave Analysis (RCWA) algorithm for electromagnetic (EM) scattering from radially and azimuthally inhomogeneous material elliptical systems based on State Variable (SV) techniques and based on circular-cylindrical Hankel-Bessel expansion modes is developed for the first time. The algorithm in conjunction with the elliptical system RCWA algorithm [1], which was based on SV techniques and Mathieu expansion modes, is used to validate and study numerical convergence of both elliptical RCWA algorithms. The formulation of the SV, Hankel-Bessel elliptical algorithm is presented. Two numerical elliptical examples are studied in detail by both algorithms, a homogeneous one which consists of three different uniform materials located in three elliptical regions and an inhomogeneous one which consists of an azimuthal, dielectric, step profile which is located between two uniform material elliptical regions. In this paper EM field scattering from a step profile which possessed a much larger dielectric step profile difference than was studied in [1] is presented. Validation and numerical convergence data of the Hankel-Bessel and the Mathieu [1] RCWA algorithm is presented for the first time, both in plot figures and in tables, when different numbers of expansion modes were used, when different number of layers were used, and when different numbers of SV harmonics were used. Validation of the RCWA algorithms was further carried out for the homogeneous case, by using Mathieu expansion modes in all regions and was carried out by using Hankel-Bessel expansion modes and Mathieu expansion modes in different regions. Validation of the Hankel-Bessel and Mathieu [1] RCWA algorithms was observed to 154 Jarem a high degree of accuracy. It was found for the numerical example tested, that the number of modes used in the RCWA algorithms needed to exceed a critical minimum value in order to obtain meaningful, accurate results, and after this critical number of modes was exceeded, that convergence occurred rapidly as the number of modes increased. It was also found that as the number of layers used in the algorithm increased that the numerical accuracy of the RCWA solution slowly increased.

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Abstract-The problem of determining the Green's function of an electric line source located in a permeable, anisotropic (μ xx ,μ xy ,μ yx ,μ yy andε zz nonzero interacting parameters) half-space above a Perfect Magnetic Conductor (PMC) ground plane (called the T M z case herein) for the case where image theory cannot be applied to find the Green's function of the PMC ground plane system has been studied. Monzon [2,3] studied the Green's function T E z problem dual to the present one for two cases; (1) when the system was unbounded, anisotropic space whereε xx ,ε xy ,ε yx ,ε yy andμ zz were the nonzero interacting parameters; and (2) when the scattering system was an anisotropic half-space located above a Perfect Electric Conductor (PEC) ground plane and whereε xx ,ε yy andμ zz were the nonzero interacting parameters andε xy =ε yx = 0. Monzon [2] referred to the latter ground plane case as the case where "usual image" theory could be used to find the Green's function of the system. The Green's function for the T M z -PMC case studied herein was derived by introducing and using a novel, linear coordinate transformation, namelyx = (σ P /τ )x + σ Mỹ ,ỹ =ỹ, (Eqs. (6c,d), herein). This transformation, a modification of that used by [2,3], reduced Maxwell's anisotropic equations of the system to a non-homogeneous, Helmholtz wave equation from which the Green's function, G, meeting boundary conditions, could be determined. The coordinate transformation introduced was useful for the present PMC ground plane problem because it left the position of the PMC ground plane and all lines parallel to it, unchanged in position from the original coordinate system, thus facilitating imposition of EM boundary conditions at the PMC ground plane. 40 JaremIn transformed (or primed) coordinates, for the T M z -PMC and T E z -PEC ground plane problems, respectively, the boundary conditions for the Green's functions G T M ≡ E z and G T E ≡ H z were shown to be αor α T E , where α T M and α T E are complex constants (dually related to each other byμ ↔ε), and whereỹ = 0 is the position of the ground plane. An interesting result of the analysis was that the constant α T E (as far as the author knows) coincidently turned out to be the same as the first of two important constants, namely S 1, which were used by Monzon [2, 3] to formulate integral equations (based on Green's second theorem) from which EM scattering from anisotropic objects could be studied.Spatial Fourier transform (k-space) techniques were used to determine the Green's function of the Helmholtz wave equation expressed in transformed coordinates which satisfied the mixed-partial derivative boundary condition of the system. The Green's function G was expressed as a sum of a "free space" Green's function g f (proportional to a Hankel function H (2) 0 and assumed excited by the line source in unbounded space) and a homogeneous Green's function g whose spectral amplitude was chosen such that, when g was added to g f , the sum G = g f + g, satisfied boundary conditions. The kspace, ...