Analytical and Numerical High-Frequency Methods for the Analysis and Design of GRIN Lens Antennas

This doctoral research explores the analysis and design methodologies for Graded-Index (GRIN) lens antennas, employing Geometrical Optics (GO) principles and advanced numerical techniques. The first part of the thesis focuses on efficient analysis methods, introducing a novel GO-based algorithm that unifies field and wavefront-curvature transport within a single Ordinary Differential Equation (ODE), enabling highly parallelized computations. Additionally, the Lax-Friedrichs Sweeping Method (LFSM) is proposed as a fast numerical solver that overcomes the limitations of traditional ray tracing by solving the Eikonal and transport equations on a computational grid, offering enhanced speed, robustness, and accuracy. The second part of the thesis presents innovative GRIN lens design approaches. The Phase Tracing Method (PTM) is introduced as a novel framework for synthesizing refractive index distributions directly from predefined ray trajectories. This method eliminates iterative optimization while ensuring isotropic and fabrication-friendly refractive index profiles. Applications of PTM include the design of telescopic lenses and a Bessel beam launcher operating at Ka-band frequencies, achieving non-diffractive beam propagation through the combination of a telescopic lens with a Mariè transducer. Furthermore, an optimization framework based on LFSM is developed to design high-performance GRIN lenses for single-focal and multifocal configurations. This method enables precise control over the refractive index distribution, allowing for beam-steering capabilities and broadband operation. Experimental validation is performed through a 3D-printed prototype, demonstrating good agreement with theoretical and simulated results. This research advances GRIN lens antenna technology by introducing computationally efficient analysis techniques and novel design methodologies. The proposed approaches bridge the gap between theoretical modeling and practical implementation, providing accurate and effective tools for the analysis and design of GRIN lens antennas.