  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.
