Luneburg lens antenna radiation fields are calculated with Green's functions of spherical and cylindrical layered structures. Electric field components of spherical and cylindrical Luneburg lenses excited by linear and circular polarized incident field are analysed. Dipole, slot and aperture antennas are described by electric and magnetic extraneous currents. Radiation patterns of cylindrical and spherical Luneburg lens are analysed. Co-polarized and cross-polarized field radiation patterns are shown. The proposed method significantly reduces the computing time for multi-layered lenses in comparison with the most commonly used in antenna design. The first step antenna structure optimization may be performed for a shorter time. The results may be used as the first approximation for Ansys HFSS and other software.
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