Reaction Theorem and Ray Tracing Applied to PPW Lenses for Reflection Coefficient and Mutual Coupling Calculation

As wireless communications systems are heading towards their sixth generation (6G), the operating band of radiating systems is expected to shift to higher frequencies to accommodate the increasing transmission rates per link, in the order of several Gbps up to a few Tbps. In this regime, antennas can be coupled with microwave dielectric lenses to increase their directivity exploiting the same working principles of optical lenses in order to focus the radiated beam. An important concern in the adoption of lens antennas is to reduce the mismatch losses and other undesirable effects caused by internal reflections, which must be assessed during the design stage. However, the computer simulation of dielectric lens antennas can be very time consuming with conventional software based on the Finite Element Method (FEM), because of the typical large electric size of lenses.

In this thesis, an efficient approximate method based on Geometrical Optics (GO) ray tracing is implemented for the calculation of the reflection coefficient of a single feed and mutual coupling of multiple feeds in two-dimensional dielectric lens antennas, for arbitrary shapes and number of reflections. The rays are traced inside the lens and the Fresnel coefficients are applied for each reflection. From geometrical considerations, the fields are approximated on surfaces in proximity of the feeds and the mutual and self-impedances are calculated with the Generalized Reaction Theorem (GRT). The method is validated for lenses inside a parallel plate waveguide (PPW), used to reduce the problem to 2-D. The Python codes estimate the couplings in terms of S-parameters, which are compared to full-wave simulations in various lenses, showing the improvement in the required computational time.