Yu. G. Pasternak1, V. A. Pendyurin2, R. E. Rogozin3, E. A. Rogozin4, S. M. Fedorov5

1, 3, 5 Voronezh State Technical University (Voronezh, Russia)

1, 4 Air Force Academy named after professor N.E. Zhukovsky and Y.A. Gagarin (Voronezh, Russia)

1, 2 JSC «Automated communication systems» (Voronezh, Russia)

Spherical Luneberg lenses allow you to form a large number of directional patterns without distortion with any values of the azimuthal and elevation coordinates. However, spherical Luneberg lenses do not find wide practical application due to the complexity and high cost of production. Thanks to advances in science, technology, materials science and the emergence of metamaterials, various designs of Luneburg spherical lenses and their production technologies have now been developed. One known method of realizing a spherical lens is to realize a partially air-filled dielectric lens, in particular on the basis of a perforated dielectric. This design can be made in several ways: based on radial holes of variable diameter, varying depending on the radial coordinate; using a set of perforated discs with holes of various sizes to realize the required refraction law. The technical implementation of both designs is possible using three-dimensional printing technologies, however, the implementation of the Luneberg lens from a set of perforated disks is possible using the CNC machine. The main drawback in the manufacture of a spherical lens from a set of perforated discs is anisotropy, which can lead to deterioration of directional properties at different polarizations.

The purpose of the article is investigation of directional properties at two orthogonal polarizations (linear horizontal and vertical) of a spherical Luneberg lens consisting of a set of dielectric perforated discs with holes of different diameters.

Analytical expression has been obtained for calculation of relative effective dielectric constant based on analysis of energy ratios of electric field, as well as continuity conditions at interface of two dielectrics, at that magnetic interaction with substance is not taken into account in operation. In the course of electrodynamic modeling using the Weiland method, directional properties of the antenna system based on the Luneberg lens in the range of 8–18 GHz at two orthogonal polarizations (linear horizontal and vertical) and a different position of the irradiator relative to the center of the lens have been considered. A vibrator with a reflector is used as an irradiator. Analysis of the obtained results shows that despite the anisotropy of the periodic structure used, the studied lens has similar directional properties on two orthogonal polarizations. This confirms the validity of the method used to calculate the relative effective permittivity.

The obtained analytical expressions allow calculating the relative effective dielectric constant taking into account anisotropy. The results of practical modeling will be useful in the development and technical implementation of a spherical Luneberg lens from a set of dielectric perforated disks with holes of different diameters.

Pasternak Yu.G., Pendyurin V.A., Rogozin R.E., Rogozin E.A., Fedorov S.M. Study of the spherical Luneburg lens, consisting of a set of dielectric perforated disks with holes of different diameters. Antennas. 2021. № 6. P. 13–22. DOI: https://doi.org/10.18127/ j03209601-202106-02 (in Russian)

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