{'fraction_non_alphanumeric': 0.020169851380042462, 'fraction_numerical': 0.0021231422505307855, 'mean_word_length': 5.203947368421052, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Shaped-profiled and material-engineered inhomogeneous lens antennas: GO curved ray tracing and aperture fields

In this paper, we present an algorithm for tracing rays through an isotropic inhomogeneous medium with the aim to incorporate the algorithm in a lens synthesis technique based on Geometrical Optics and Particle Swarm Optimization (PSO). The algorithm tracks the phase, amplitude, and polarization variation of the electric field along the ray, which in this case becomes a space curve. The rays are found by solving the light-ray equation numerically using the Runga-Kutta to the 4th order (RK4) algorithm. Key governing equations are summarized allowing the implementation of numerical techniques for the complete determination of GO fields. Validation of the ray paths are given by comparing the numerical results with the analytic formulation of the ray paths in an ideal Luneburg Lens Antenna. The results show good agreement.