This paper presents the theoretical performance (input impedance, 10 dB return-loss bandwidth, radiation patterns and surface efficiencies) of reduced size substrate lenses fed by aperture-coupled microstrip patch antennas. The diameter of the extended hemispherical homogeneous dielectric ( lens ) lenses varies between one and five wavelengths in free-space, in order to obtain radiating structures whose directivity is comprised between 10 and 25 dB. A lot of configurations of lenses are investigated using the finite-difference time-domain methods technique and compared in the 47-50 GHz band as a function of their diameter, extension length and dielectric constant. In particular, the analysis of internal reflections-in time and frequency domains-shows that the latter have potentially a strong influence on the input impedance of small lens antennas, even for low values of lens (2 2), whereas the usual limit (beyond which anti-reflection coatings are required) is lens = 4. We also demonstrate that the diffraction limit of reduced size lenses is reached for extension lengths varying between 50% and 175% of the extension of synthesized ellipses, depending on the lens material and diameter. Finally, we show that superdirective structures with surface efficiencies reaching 250% can be obtained with small lens diameters, justifying the interest in reduced size lens antennas.Index Terms-Electrically small antennas, electromagnetic reflection, finite-difference time-domain (FDTD) methods, lens antennas, millimeter-wave antennas.

Abstract-Two new compact lens antenna configurations are presented and compared for data link communications with LEO satellites at 26 GHz. These lenses match a secant type radiation pattern template in the elevation plane while having a mechanically scanned sector beam in azimuth to enhance gain as much as possible. No rotary joints or multiple feeds are required and emphasis is put also on the compactness of the proposed solutions ( 6 0 ). Two alternative lens configurations are evaluated numerically and experimentally: one is based on modified axial-symmetric dome lens geometry, and the other one consists of a full 3-D double-shell lens antenna. In contrast to current nearly omnidirectional antennas, the directivity of our lens prototypes is above 15.4 dBi. Up to 4.2 dB loss obtained in the prototypes can be significantly reduced by using lower loss dielectrics and matching layers, without affecting the conclusions. The numerical and experimental results are in good agreement with the radiation specifications given the compact size of the antennas.