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.