Exact Near-Fields of the Dielectric Lenses for sub-mm Wave Receivers

Focusing properties of a truncated elliptic dielectric cylinder with a piece-wise "super-elliptic" cross section taken as a 2-D model of a dielectric lens are studied for the plane wave illumination. The Muller integral-equation (IE) technique is used for the analysis of the scattering problem. This full-wave mathematically rigorous method guarantees uniqueness of the numerical solution for an arbitrary set of design and material parameters. To treat the singularities in the Green\´s functions and their derivatives in the discretization scheme we use analytical inversion of the canonical circular-cylinder counterpart of the problem. This procedure enables us to build a very efficient tool for CAD and optimization of the dielectric lenses. Numerical results for the near fields are presented and lens-focusing properties are studied for the E-polarization case.