Spherical modal analysis of a patch array dielectric lens antenna

Steered Patch arrays with a dielectric lens for collimation are well suited for mobile applications due to their small form factor and effective sealing ability. In this paper we present an accurate analytical formulation of a patch array radiating in the presence of a hemispherical Dielectric lens based on spherical modal expansion (SME) and experimentally demonstrate an increase in directive gain due to lens collimation. The analysis treats the lens as a scatterer, and utilizes techniques for radial translation and coordinate rotation of the patch array SME coefficients to align them to the phase center of the Lens. The SME coefficients of the scattered fields are then obtained by application of boundary conditions. A sample computation using this approach shows a good match with experimental results. The analysis is flexible enough to accommodate different types of small radiating apertures with different shapes of dielectric lenses that are inherently broadband.