Electrically-Small Shaped Integrated Lens Antennas: A Study of Feasibility in $Q$-Band

Integrated lens antennas (ILAs) are essentially high-gain (sub)millimeter-wave radiating structures. They often have a moderate (or even poor) aperture efficiency because their design rules are generally based on high-frequency methods of analysis with no advanced optimization procedures. From the proposed classification of ILA types as a function of their aperture efficiency, we demonstrate the feasibility of designing compact arbitrarily-shaped ILAs with high radiation and aperture efficiencies, which has never been addressed to our best knowledge. The design strategy consists of a local iterative optimization of trial lens shapes that are analyzed with a spherical wave expansion (SWE) of the primary fields and the physical optics (PO) method. This approach assumes that the feed currents are not modified by the irregular lens profile and the dielectric contrast at the lens interface; in addition, the influence of internal reflections and possible indirect paths is neglected. The proposed methodology is thus restricted to the optimization of low-permittivity lenses. The SWE/PO algorithms and the gradient-based optimization procedures are validated numerically in $Q$-band by considering two peculiar ILAs. The first example (designed and characterized experimentally in a previous contribution) is used as a relevant test-case in order to validate the method of analysis. The second prototype is a Teflon compact shaped ILA whose diameter and height equal $1.8\times\lambda_{0}$ and $1.5\times\lambda_{0}$ , respectively. This antenna is shown to have a 92% aperture efficiency and a 70% radiation efficiency. Although purely numerical, these data are among the highest values reported in literature. They are confirmed by FDTD simulations.