Well-conditioned T-matrix method for a polarization-decoupling cylinder with arbitrary cross-section near a dipole source

The 2.5-dimensional (2.5-D) scattering solutions of an infinitely long dielectric cylindrical body illuminated by a 3-D finite source, such as a dipole, involve a linear superposition of line source-type fields. For electric or magnetic dipole source excitation oriented in any direction, the problem reduces to a two-dimensional coupled problem with excitation of the electric or magnetic line sources, whose radial and longitudinal spectral dependences are cylindrical and obliquely planar respectively. On the other hand, the nature of the T matrix method for each spectral component of the excitation source is ill-conditioned for cylindrical scatterers with arbitrary cross-section. Besides, when the excitation source is close to the scatterer, increasing the number of cylindrical harmonics does not improve the accuracy of the solutions. In this paper, an isorefractive scatterer that simplifies the analysis by decoupling the fields into TM/TE components is examined to address three improvement keys of the inherent difficulties in the T matrix method for 2.5-D scattering case: Efficient numerical integration of the infinite continuous $k_z$ spectrum, well-conditioned T-Matrix formulation for each excitation component, and truncation of the plane wave spectral content of the incident field coefficients for the T-Matrix formulation in the proximate source case. Genetic algorithms were used to tune the parameters resulting from the proposed improvements. Our results with optimized parameters, benchmarked against boundary integral formulations and a 3-D solver, highlight the efficacy of our approach in handling 2.5-D scattering problems with different geometries and excitation conditions.