A Radial Transformation-Optics Mapping for Flat Ultra-Wide-Angle Dual-Polarized Stacked GRIN MTM Luneburg Lens Antenna

A transformation-optics mapping that radially compresses a sphere into a cylindrical slab with an arbitrary ratio of D/t is proposed to design a flat and thin dual-polarized Luneburg lens antenna (LLA) for ultrawide-angle operation at microwave bands. Also, the feasibility of the simple approximations to the transformed material properties is demonstrated in the design procedure of the presented LLA. Compared with the benchmark, the proposed mapping can achieve a moderate index distribution, wider scanning range, lighter weight, as well as an easy implementation. For example, a slab consisting of 18-layered Gaussian-distributed gradient index metamaterials is utilized to realize an X-band dual-polarized LLA with an aperture of 94.3×94.3 mm
²
, a thickness of 14.9 mm, and a focal length of 44 mm. Three nonresonant unit cells of patch, circular, and square holes are used for the upper, middle, and lower index regions, respectively. Moreover, a prototype of half of the designed LLA combined with a PEC sheet is implemented for a conformal application. The experiments reveal that our design can achieve a ~20% bandwidth for both |S
₁₁
| <; -10 dB and |S
₂₁
| <; -17$ dB, a scanning angle of ±54° with a scanning loss of 0.7/2.2 dB, a peak gain of ~13/13.2 dBi, and a cross-polarization level of less than -15/-16 dB for the transverse electric and transverse magnetic polarizations at 10 GHz, respectively. Hence, the proposed mapping is a good method to design a light wide-scan dual-polarized LLA for far-field imaging applications and 5G wireless communications.