This work addresses the limitations of conventional high-frequency methods in the modeling of lens antennas. While these structures are commonly analyzed using efficient Geometrical Optics (GO) / Physical Optics (PO) techniques, such approaches present significant limitations when the shadow region -defined as the surface area illuminated at incidence angles above the critical angle- is strongly illuminated, or when multilayer stratifications are incorporated. Furthermore, the full-wave validation is computationally intensive for medium-sized lenses, and impractical for electrically-large designs, leaving designers overly reliant on traditional methods and lacking detailed electromagnetic insight.

Firstly, to address the computational challenges with full-wave simulation of large lens designs, an approach based on PPW-embedding (Parallel-Plate Waveguide embedding) of the principal lens sections is followed. This reduction in problem size enables feasible full-wave simulations while also yielding valuable qualitative insights into the lens performance.

Secondly, to overcome the GO-PO limitations in predicting fields beyond the critical angle of incidence, this work follows a rigorous surface field modeling approach based on the Stratified-media Spectral Green’s Function, applied to locally flat surface approximations and evaluated using Inverse Fourier Transform in Steepest Descent Path (SDP) integration. The proposed method shows strong agreement with full-wave simulations and offers deeper insight into surface fields under critical-angle illumination, revealing their impact on radiation performance and enabling more effective lens designs.

Finally, the spectral approach is extended to the analysis of matching layers on the surfaces of high-permittivity lenses, demonstrating greater reliability than GO-PO techniques while maintaining computational efficiency superior to full-wave simulations. This study offers spectral-domain insight into surface lens phenomena and evaluates the performance enhancements provided by anti-reflection coatings.