mmWave Substrate Lens Antenna for Wireless Communications
Wu et. al.  proposed designs for both single and multi-beam mmWave circularly polarized substrate lens antennas in 2001. This white paper demonstrates these designs via FEKO modeling.
Single-Beam Substrate Lens Antenna
Wu's single-beam substrate antenna is essentially a slot coupled microstrip antenna with a large lens constructed on top of the microstrip antenna. Typical microstrip antennas have very wide main lobes and the lens has the effect of sharply focusing the main beam of this microstrip construct. This focusing effect can be demonstrated by comparing the performance of the microstrip patch in isolation to the same construct with the lens in place.
Single-beam microstrip lens antenna dimensions
POSTFEKO representation of microstrip lens antenna current distribution
The measured beam width of the microstrip antenna on its own is a typical 71.6°, while the lens focused construct has a beam width of only 6.5°. The focusing effect of the lens is thus very powerful in this case and also shapes the resulting radiation pattern to have a good side-lobe level (SLL) at -14.6 dB.
Comparison between gain patterns for (blue) lens focused microstrip antenna, (green) antenna without lens and (red) measured data for lens focused antenna 
The FEKO simulation data presented here was created by setting up the antenna and lens as a Method of Moments (MoM) problem, utilizing the Surface Equivalence Principle (SEP) as the method of modelling the dielectrics of the microstrip antenna substrate and the Rexolite lens. The solution of the problem was then solved optimally with the Multilevel Fast Multipole Method (MLFMM). The excellent agreement between the FEKO simulated data and measurements  demonstrate that the FEKO solution is highly accurate for this problem.
|3D radiation pattern||Comparison of (green) microstrip antenna only,
(blue) lens focused antenna, and
(red) measurement data 
|3D and polar chart radiation patterns for single-beam antennas
|||X. Wu, G.V. Eleftheriades, and T.E. van Deventer-Perkins, "Design and Characterization of Single- and Multiple-Beam MM-Wave Circularly Polarized Substrate Lens Antennas for Wireless Communications," IEEE Transactions on Microwave Theory and Technique, vol. 49, no. 3, pp. 431–441, March 2001|