Yu. G. Pasternak1, V. A. Pendyurin2, E. A. Rogozin3, R. E. Rogozin4, S. M. Fedorov5
1, 4, 5 Voronezh State Technical University (Voronezh, Russia)
1, 3 MESC AF “N.E. Zhukovsky and Y.A. Gagarin Air Forсe Academy” (Voronezh, Russia)
1, 2 JSC RPE “Automated Communication Systems” (Voronezh, Russia)
3 Voronezh Institute of the Ministry of Internal Affairs (Voronezh, Russia)

In space communications, radar, radio navigation, radio direction finding and other radio systems for various purposes, multibeam antennas (MBA) are widely used. The use of lens MBA allows you to create axisymmetric antenna systems without shading. Luneberg lenses stand out against many designs of lens MBA. They are spherically or cylindrically symmetric lenses with a gradient-changing refractive index, which allows you to generate a large number of radiation patterns without distortion in a wide sector of angles.

The article analyzes the modern open literary and scientific-technical sources on the problem of developing and technical implementation of the Luneberg lens. The main types of lenses are described and presented in the article: spherical, cylindrical and modified. In real conditions, the exact implementation of a continuous gradient-changing law of refraction in a Luneberg lens is very complicated, therefore, when creating a lens, the continuous law of refraction is discretized. The article describes modern (existing) methods of discretization of the continuous law of change of the refractive index - with equal steps in the radial coordinate or in the refractive index, optimized. The use of a large number of layers allows more accurate approximation to the continuous law, while in some cases this complicates the technical implementation of the lens. Based on the analysis, it has been found that the use of more than 6–8 layers is impractical, since with a further increase in them, there is no improvement in directional characteristics, however, in some cases, the complexity of manufacturing the lens increases.

The modern (existing) methods of manufacturing various designs of Luneberg lenses are based on: foamed and composite materials, including those that allow the use of lenses at high temperatures or in antenna systems with high power; homogeneous dielectrics. Lenses made of homogeneous dielectrics or composite materials have high mass and losses, therefore, in the microwave range, artificial media and metamaterials are widely used, which make it possible to manufacture lenses with less mass and losses. The article discusses modern methods of manufacturing Luneberg lenses based on artificial media and metamaterials, and also shows the large-sized and light spherical Luneberg lenses of MatSing for mobile operators. The use of transformational optics, a new direction in the science of light, the appearance of which was made possible thanks to the development of metamaterials, has been also considered. Transformation optics is a new method for creating optical devices. Its use allows you to create Luneberg lenses of various profiles.

The article describes the advantages and disadvantages of each of the manufacturing methods. Based on the results of the analysis, conclusions have been drawn about promising areas of research in the design and technical implementation of Luneberg lenses, including those implemented using transformational optics.

Pasternak Yu.G., Pendyurin V.A., Rogozin E.A., Rogozin R.E., Fedorov S.M. Analysis of modern methods and means of technical implementation of Luneberg lens. Antennas. 2022. № 2. P. 53–62. DOI: https://doi.org/10.18127/j03209601-202202-07 (in Russian)

1. Shishlov A.V., Levitan B.A., Topchiev S.A., Anpilogov V.R., Denisenko V.V. Mnogoluchevye antenny dlya sistem radiolokatsii i svyazi. Zhurnal radioelektroniki. 2018. № 7. S. 1–30. (in Russian)
2. Kyun R. Mikrovolnovye antenny. L.: Sudostroenie. 1967. (in Russian)
3. Drabkin A.L., Zuzenko V.L., Kislov A.G. Antenno-fidernye ustrojstva. M: Sov. radio. 1974. (in Russian)
4. Zelkin E.G., Petrova R.A. Linzovye antenny. M.: Sov. radio. 1974. (in Russian)
5. Korotkov A.N., Shabunin S.N. Vliyanie sposoba diskretizatsii tsilindricheskoj linzy Lyuneberga na ee kharakteristiki izlucheniya. Informatsionnye tekhnologii, telekommunikatsii i sistemy upravleniya. 2015. S. 20–26. (in Russian)
6. Panchenko B.A., Denisov D.V., Mokhova V.V., Panov H.B. Vliyanie urovnya stratifikatsii linzy Lyuneberga na ee antennye kharakteristiki. Izvestiya vysshikh uchebnykh zavedenij Rossii. Ser. «Radioelektronika». 2014. № 1. S. 3–6. (in Russian)
7. Fuchs B., Le Coq L., Lafond O., Rondineau S., Himdi M. Design optimization of multishell Luneburg lenses. IEEE Transactions on Antennas and Propagation. 2007. V. 55. № 2. P. 283–289.
8. Peeler G.D.M., Coleman H. Microwave stepped-index Luneberg lenses. IRE Transactions on Antennas and Propagation. 1958. V. 6. № 2. P. 202–207.
9. Bor J., Lafond O., Merlet H., Le Bars P., Himdi M. Foam based Luneburg lens antenna at 60 GHz. Progress in Electromagnetics Research Letters. 2014. V. 44. P. 1–7.
10. Gunderson L.C., Kauffman K.F. A high temperature Luneburg lens. Proceedings of the IEEE. 1968. V. 56. № 5. P. 883–884.
11. Patent № 2263124 RF. Dielektricheskaya polimernaya pena i linza dlya radiovoln s ee ispol'zovaniem. M. Aki, Kh. Monde, A. Tabuti, J. Tati, S. Kavakami, M. Kuroda, T. Kisimoto, K. Kimura. Opubl. 27.10.2005. Byul. № 30. (in Russian)
12. Peeler G.D.M., Archer D.F. A two-dimensional microwave Luneberg lens. Transactions of the IRE Professional Group on Antennas and Propagation. 1953. V. 1. № 1. P. 12–23.
13. Kuzikov A.A., Orekhov R.S., Salomatov Yu.P., Sugak M.I. Issledovanie pechatnoj tsilindricheskoj linzy Lyuneberga. Elektronika i mikroelektronika SVCh. 2018. № 1. S. 426–430. (in Russian)
14. Patent № 2657926 RF. Antennoe ustrojstvo na osnove linzy Lyuneberga. D.S. Aliev, A.V. Ivanov, Yu.G. Pasternak. Opubl. 18.06.2018. Byul. № 17. (in Russian)
15. Patent № 2485646 RF. Ustrojstvo dlya fokusirovki tipa «linza Lyuneberga». R.O. Ryazantsev, Yu.P. Salomatov. Opubl. 20.06.2013. Byul. № 17. (in Russian)
16. Kock W.E. Metallic delay lenses. The Bell System Technical Journal. 1948. V. 27. № 1. P. 58–82.
17. Vendik I.B., Vendik O.G. Metamaterialy i ikh primenenie v tekhnike sverkhvysokikh chastot (obzor). Zhurnal tekhnicheskoj fiziki. 2013. T. 83. № 1. S. 3–28. (in Russian)
18. Patent № 5677796 US. Luneberg lens and method of constructing same. K.A. Zimmerman, D.L. Runyon. 1997.
19. Sato K., Ujiie H. A plate Luneberg lens with the permittivity distribution controlled by hole density. Electronics and Communications in Japan. Part 1. 2002. V. 85. № 9. P. 163–166.
20. Antipov S.A., Ashikhmin A.V., Negrobov V.V., Fyodorov S.M. Eksperimental'noe issledovanie sverkhshirokopolosnoj antenny, postroennoj na osnove modifikatsii ploskoj linzy Lyuneberga. Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta. 2012. T. 8. № 3. S. 113–118. (in Russian)
21. Rondineau S., Himdi M., Sorieux J. A sliced spherical Luneburg lens. IEEE Antennas and Wireless Propagation Letters. 2003. V. 2. P. 163–166.
22. Changsheng D., Ziqing C., Yong L., Haidong W., Chao J., Shiwen Y. Permittivity of composites used for Luneburg lens antennas by drilling holes based on 3-D printing technique. Journal of Terahertz Science and Electronic Information Technology. 2017. V. 15. № 4. P. 646–651.
23. Liang M., Ng W.R., Chang K., Gbele K., Gehm M.E., Xin H. A 3-D Luneburg lens antenna fabricated by polymer jetting rapid prototyping. IEEE Transactions on Antennas and Propagation. 2014. V. 62. № 4. P. 1799–1807.
24. Kubach A., Shoykhetbrod A., Herschel R. 3D printed Luneburg lens for flexible beam steering at millimeter wave frequencies. 2017 47th European Microwave Conference (EuMC). 2017. P. 787–790.
25. Larimore Z., Jensen S., Good v, Lu A., Suarez J., Mirotznik M. Additive manufacturing of Luneburg lens antennas using space-filling curves and fused filament fabrication. IEEE Transactions on Antennas and Propagation. 2018. V. 66. № 6. P. 2818–2827.
26. Xin H., Liang M. 3D printed microwave and THz devices using polymer jetting techniques. Proceedings of the IEEE. 2017. V. 105. № 4. P. 737–755.
27. Avdyushin A.S., Volkov K.O., Razinkin K.A., Fyodorov S.M. Issledovanie ploskoj linzy Lyuneberga s radial'nymi dielektricheskimi lepestkami. Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta. 2014. T. 10. № 5-1. S. 23–25. (in Russian)
28. Sayanskiy A., Glybovski S., Akimov V.P., Filonov D., Belov P., Meshkovskiy I. Broadband 3-D Luneburg lenses based on metamaterials of radially diverging dielectric rods. IEEE Antennas and Wireless Propagation Letters. 2017. V. 16. P. 1520–1523.
29. Pfeiffer C., Grbic A. A printed, broadband Luneburg lens antenna. IEEE Transactions on Antennas and Propagation. 2010. V. 58. № 9. P. 3055–3059.
30. Cheng Q., Ma H.F., Cui T.J. Broadband planar Luneburg lens based on complementary metamaterials. Applied Physics Letters. 2009. V. 95. № 18.
31. Dhouibi A., Burokur S.N., Lustrac A. Metamaterial-based 2D multi-beam broadband Luneburg lens antenna. 2014 XXXIth URSI General Assembly and Scientific Symposium (URSI GASS). 2014.
32. Deepthi K.V.B.L., Sankar K.J. An investigation of the substrate-integrated Luneburg lens antenna with gradient index and metamaterial structures. International Journal of Applied Engineering Research. 2016. V. 11. № 8. P. 5762–5766.
33. Cheng G., Wu Y., Yin J.X., Zhao N., Qiang T., Lv X. Planar Luneburg lens based on the high impedance surface for effective Ku-band wave focusing. IEEE Access. 2018. V. 6. P. 16942–16947.
34. Chen H., Cheng Q., Huang A., Dai J., Lu H. Modified Luneburg lens based on metamaterials. International Journal of Antennas and Propagation. 2015. V. 2015. P. 1–6.
35. MatSing. Lens technology enabled [Elektronnyj resurs]. URL: https://matsing.com.
36. Patent № 8518537 US. Artificial dielectric material and method of manufacturing the same. S. Matitsine. 2013.
37. Werner D.H. Broadband metamaterials in electromagnetics technology and applications. Jenny Stanford Publishing. 2017.
38. Foster R., Nagarkoti D., Gao J., Vial B., Nicholls F., Spooner C., Haq S., Hao Y. Beam-steering performance of flat Luneburg lens at 60 GHz for future wireless communications. International Journal of Antennas and Propagation. 2017. V. 6. P. 1–8.
39. Kundtz N., Smith D.R. Extreme-angle broadband metamaterial lens. Nature Materials. 2010. V. 9. P. 129–132.
40. Su Y., Chen Z.N. A flat dual-polarized transformation-optics beamscanning Luneburg lens antenna using PCB-stacked gradient index metamaterials. IEEE Transactions on Antennas and Propagation. 2018. V. 66. № 10. P. 5088–5097.
41. Li Y., Zhu Q. Luneburg lens with extended flat focal surface for electronic scan applications. Optics Express. 2016. V. 24. № 7. P. 7201–7211.