Analytical regularization

Abstract: We discuss the advantages of the conversion of electromagnetic field problems to the Fredholm second kind integral equations (analytical regularization) and Fredholm second-kind infinite-matrix equations (analytical preconditioning). Special attention is paid to specific features of the characterization of metals and dielectrics in the optical range and their effect on the problem formulation and on the methods applicable to the mentioned conversion.

Abstract: We study the plane wave scattering and absorption by a flat grating of thin silver nanostrips located in free space, in the visible-light range. The formulation involves generalized boundary conditions imposed on the strip median lines. We use an accurate numerical solution to this problem based on the dual-series equations and the method of analytical regularization. This guarantees fast convergence and controlled accuracy of computations. Reflectance, transmittance, and absorbance as a function of the wavelength and the grating parameters are analyzed. In addition to well-known surface-plasmon resonances, sharp resonances are revealed in the H-polarized scattering near but not equal to the Rayleigh wavelengths of nonzero diffraction orders; in the E-polarized scattering these resonances are not visible. Asymptotic formulas for the frequencies and natural fields of the grating resonances are presented.

Abstract: The role of edge illumination in the performance of compact-size dielectric lens antennas (DLAs) is studied in accurate manner using a highly efficient algorithm based on the combination of the Muller's boundary integral equations and the method of analytical regularization. The analysis accounts for the finite size of the lens and directive nature of the primary feed placed close to the center of the lens base. The problem is solved in a two-dimensional (2-D) formulation for both E - and H -polarizations. It is found that away from internal resonances that spoil the radiation characteristics of DLAs made of dense materials, the edge illumination has primary importance. The proper choice of this parameter helps maximize DLA directivity, and its optimal value depends on the lens material and feed polarization.

Abstract: The aim of this paper is the introduction of a new analytically regularizing procedure, based on Helmholtz decomposition and Galerkin method, successfully employed to analyze the electromagnetic scattering by zero-thickness perfectly electrically conducting circular disk. After expanding the fields in cylindrical harmonics, the problem is formulated as an electric field integral equation in the vector Hankel transform domain. Assuming as unknowns the surface curl-free and divergence-free contributions of the surface current density, a second-kind Fredholm infinite matrix-operator equation is obtained by means of Galerkin method with expansion functions reconstructing the expected physical behavior of the surface current density and with closed-form spectral domain counterparts, which form a complete set of orthogonal eigenfunctions of the most singular part of the integral operator. The coefficients of the scattering matrix are single improper integrals which can be quickly computed by means of analytical asymptotic acceleration technique. Comparisons with the literature have been provided in order to show the accuracy and efficiency of the presented technique.