Many novel mm-wave and THz antennas have planar feeds integrated with medium-size quasioptical hemielliptic lenses extended with flat bottoms. We show that design of such lenses made with ray-tracing theories is not satisfactory. This is because strong internal reflections are present. Moreover, the accurate analysis shows the advanced characteristics of a lens antenna tuned to a resonance, namely, stability of the resonance field with respect to the angle of arrival of incident wave and several times greater values of the peak intensity as well as better radiation pattern and lower side-lobe level. A narrow-band receiver exploiting this effect may potentially have an improved sensitivity and scanning performance. We perform analysis of a two-dimensional lens model by using the Muller boundary integral equation (BIE) technique. This full-wave mathematically rigorous method is combined with trigonometric Galerkin discretization, to result in efficient numerical solution for an arbitrary set of design and material parameters. Numerical results are generated for a silicon lens typical for THz applications and for a quartz lens typical for mm radar applications. The far field analysis for the quartz lens-coupled antenna shows good agreement with the measured data borrowed from.
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