Numerical Aspects of the Application of Ray-Tracing to Geodesic Lenses

This paper presents a model developed to numerically determine the radiation pattern presented by a given geodesic lens. A simplified model describing the trajectory of a TEM-mode wave through the lens was required as a time-efficient alternative to commercial software. Geometrical optics have been used to approximate the ray trajectory from the source to the aperture of the lens. The power conservation in ray tubes is then used to evaluate the amplitude of the electric field in the aperture, knowing the distribution at the source. The Kirchhoff diffraction formula is finally numerically approximated to evaluate the far-field. Three examples have been simulated with our algorithm and compared with full-wave simulations. We demonstrate that our assumptions provide a good agreement with full-wave simulation while reducing significantly the computation time, thus providing an efficient method for design optimization. Most notably, this more general formulation may be extended to non-rotationally symmetric lenses.