Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics

TL;DR

This paper evaluates the accuracy of geometrical and physical optics methods versus boundary integral equations for analyzing small dielectric lens antennas, focusing on 2-D models of hemielliptic lenses made of various materials.

Contribution

It provides a comparative analysis of GO, PO, and boundary integral equations for small dielectric lenses, highlighting the effectiveness of boundary integral methods as benchmarks.

Findings

Boundary integral equations offer guaranteed convergence and controllable accuracy.

GO and PO methods are assessed for their precision in modeling small dielectric lenses.

The study covers various materials and incidence angles, providing comprehensive insights.

Abstract

We assess the accuracy and relevance of the numerical algorithms based on the principles of Geometrical Optics (GO) and Physical Optics (PO) in the analysis of reduced-size homogeneous dielectric lenses prone to behave as open resonators. As a benchmark solution, we use the Muller boundary integral equations discretized with trigonometric Galerkin scheme that has guaranteed and fast convergence as well as controllable accuracy. The lens cross-section is chosen typical for practical applications, namely an extended hemiellipse whose eccentricity satisfies the GO focusing condition. The analysis concerns homogeneous lenses made of rexolite, fused quartz, and silicon with the size varying between 3 and 20 wavelengths in free space. We consider the 2-D case with both E- and H-polarized plane waves under normal and oblique incidence, and compare characteristics of the near fields.