| Summary: | Novel three-dimensional discrete lens antennas characterized by a number of focal points ranging from one to five and defined explicitly via analytical equations are presented in the paper. A procedure to derive rotationally symmetric afocal lenses starting from multifocal lenses that are not rotationally symmetric is proposed as well. In addition, an innovative method to identify the focal surface minimizing the optical aberrations is derived. The lenses are compared in terms of optical aberrations and accommodation constraints. The most suitable lens architectures depend mainly on the required angular field of view and magnification factor. It is shown that a reduction by a factor close to 3 in the optical aberrations can be obtained when selecting the most appropriate lens architecture and keeping comparable accommodation constraints. The results, derived exploiting a geometrical optics (GO) formulation, provide useful indications for the preliminary design of constrained lens antennas before adopting full wave rigorous techniques. Three-dimensional discrete lens antennas can offer significant advantages as compared to conventional analog beamforming networks (as those based on Butler matrixes) in terms of frequency bandwidth, number of beams and number of radiating elements.
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