Hybrid Geometrical Optics and Uniform Asymptotic Physical Optics for Rapid and Accurate Practical GRIN Lens Design

In this paper, an improved numerical ray-tracing method is proposed to solve radiating fields of Gradient-Refractive Index (GRIN) lens antennas with a shadow region. A shadow region results from geometrical optics (GO) rays which undergo total internal reflection (TIR) and cannot propagate to the radiating aperture. This occurs in practical lenses with sidewall index of refraction nmin > 1. The uniform asymptotic physical optics (UAPO) method is implemented and combined with GO using a phase-continuity method to solve the electric fields within the shadow region. Three practical GRIN lens designs with different $F$ / D are simulated and comparison shows the proposed method achieves directivity within 0.5 dB, side lobe level (SLL) within 1.8 dB, and half-power beamwidth within 0.6 ^º of the full-wave solution. This represent an improvement of error tolerance over GO-only methods of 4 dB, 7.7 dB, and 1.3º, respectively.