# Millimeter-Wave High-Gain Dual-Polarized Flat Luneburg Lens Antenna with Reflection Cancellation
###### Abstract  
Because of its good beam coverage and beam scanning abilities, the Luneburg lens (LL) is a promising multibeam antenna for the fifth-generation (5G) wireless communications. However, the conventional LL has a spherical formfactor, exhibiting a large volume, large weight, and curvature surface, all of which limit the adoption of an LL in practice. To alleviate the problem, a flat LL is proposed, with transformation optics to convert the conventional spherical structure into a flat one. However, a high permittivity distribution is usually required in a transformed flat LL, causing of server reflections, which further degenerates the performance of the LL in terms of both gain and efficiency. In this article, a millimeter-wave dual-polarized flat Luneburg lens antenna (FLLA) is proposed following the transformation of optics, and implemented using multilayer PCBs, where a reflection cancellation method is introduced to optimize the multilayer structure to improve its gain and efficiency. The designed FLLA is exemplified in the _Ka_-band and fed using a dual-polarized patch antenna. The measured results show that the designed FLLA has an impedance bandwidth (\(1S_{11}\leq-10\) dB) of 27.5-32.6 GHz, a gain of 16.8-18.8 dBi over the operating band, and a beam scanning range up to \(\pm 25^{\circ}/\pm 24^{\circ}\) with a gain loss of 1.72 dB/1.7 dB in either E- or H-plane, respectively. beam scanning; dual polarization; flat Luneburg lens; reflection cancellation +
Footnote †: journal: Applied  
the output power from the power amplifier is lower as well, which also saves power consumption or contributes an energy-effective system. Among the various lenses, the Luneburg lens (LL) exhibits excellent beam converging ability, i.e., identical scanning beams in terms of gain and radiation pattern no matter what the beam direction is [5; 6]. The conventional LL is a dielectric sphere with a radially gradient refraction index distribution ranging from \(\surd\)2-to-1, corresponding to a permittivity variation of 2-to-1 if a nonmagnetic material is considered, as shown in Figure 1a. To realize the desired permittivity variation, an LL is usually designed by using several dispersed concentric spherical shells and an innermost small sphere with stepped discrete permittivity to mimic the gradient distribution [7; 8; 9], as depicted in Figure 1b, which is suitable for engineering manufacturing. However, the spherical LL has a large volume and requires the feeding sources to be mounted on its curvature surface, both of which make it difficult to be equipped in practice. To solve the problem, the flat LL (FLL) concept is proposed for designing LL with either a flat formfactor or a much smaller size as well as weight for applications [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. There are two categories of FLLs designed following different schemes. One type of FLL is a horizontally placed cylinder, and it only supports one-dimensional (1D) beam scanning in the horizontal plane, as shown in Figure 1c. The permittivity is only varied radially as that of conventional LL, also known as a 1D gradient index, but it is unvaried along the axis of cylinder, truncating by the air or parallel conductor plates at its two end surfaces [10; 11; 12; 13; 14]. Though it perfectly keeps the foci on the cylindrical surface, this type of planar LL is hardly to be adopted for dual polarization applications. Hence, this type of FLL cannot be regarded as a good alternative to a conventional LL, because both the two-dimensional (2D) beam scanning and dual polarization properties are sacrificed. Another type of FLL is a vertically placed cylinder, designed following transformation optics, as shown in Figure 1d, which can support 2D beam scanning as the conventional LL does [15; 16; 17; 18; 19; 20]. It has varied permittivity along both its radius and axis, and the required permittivity is much greater than 2, certainly causing an evident reflection.