Journal of «Almaz – Antey» Air and Space Defence Corporation

Advanced search

Special beamforming by means of a semi-spherical Lüneburg lens


The paper considers a semi-spherical Lüneburg lens with a conductive shield. In certain conditions a lens of such design may form radiation patterns without the side lobe or cosecant-type patterns. Such radiation patterns can be formed by controlling the following parameters: antenna feed angle, conductive shield diameter, dielectric substrate thickness. The paper focuses on particular cases of obtaining special-type radiation patterns.

For citation:

Denisov D.V., Tangamyan A.A. Special beamforming by means of a semi-spherical Lüneburg lens. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2021;(2):28-34.

1. Structure and parameters of semi-spherical Lüneburg lens

A Lüneburg lens is a spherically symmetric lens with a refraction gradient-index n, which decreases radially from its centre to the surface. The Lüneburg lens can be used as a broadband antenna. Its efficiency greatly depends on the material radioparency parameters in a selected range. Each spot on the surface of ideal lens of this type is a focus for the opposite side emission. Dielectric permeability of the lens material changes from 2 (in the centre) to 1 (on the surface) in line with the law , where a – lens outer radius (in Fig. 1), r – spherical system radial coordinate [1].


Fig. 1. Configuration of studied semi-spherical Lüneburg lens


The objective is dual-focus. The first focus spot, F1, is on the illuminated surface of the lens. Usually the antenna is located in this spot. The second focus spot, F2, is on the shadow side of the objective at an infinite distance. The Lüneburg lens far field radiation pattern is generated in this spot. The lens antenna’s main disadvantages are dimensions and weight which are based on the lens material. The disadvantage can be mitigated by removing the objective’s shadow part and replacing it with a flat shield. In this case, the second focal spot, F2, is at the illuminated lens side, and the primary source rays go twice as far as the lens body. The Lüneburg lens loses its geometric symmetry. The radiation pattern of such type of the Lüneburg lens antenna is object location oriented.

The discussed structure is shown in Fig. 1 and appears to be the semi-spherical Lüneburg lens mounted on a conductive shield with the diameter d [2, 3].

The Lüneburg lens antenna can be a three-dimensional hemisphere. At this, it is possible to obtain the radiation patterns of a special type that extend the antenna’s application scope.

There is a substrate between the shield and the lens body made from a dielectric material with dielectric permeability close to 2. The substrate height h, feed rotation angle θ, and shield diameter d, determine the radiation pattern characteristics, and can be used to transform it, as well as to control the emission level. The antenna’s structure ensures its mounting on the surface of both fixed (building façades) and moving objects (vehicles). Moreover, the discussed structure is of high strength and less exposed to wind effect; an enlarged area of the conducting shield ensures sufficient support to mount the antenna [4]. An electromagnetic solution of the lens antenna is implemented by using the ANSYS HFSS high frequency structural simulator with the Driven Modal inference engine and the finite elements numerical method (Fig. 2).


Fig. 2. Model of the semi-spherical Lüneburg lens antenna in HFSS (a) and open-ended rectangular waveguide (b)


Since the matching problem solution usually provides an approximate result (even with exact formulas), this result can be improved using the electrophysical 3D modelling systems. It is caused by the fact that such systems consider many additional factors, including dielectric material attenuation, fringing effects, etc.

Table 1 provides lens dimensions with the patterns shown in Fig. 2.


Table 1

Semi-spherical Lüneburg lens parameters

Relative radii of the antenna system layers are indicated with the relative radius values a, provided in Table 1.

Air constitutes the seventh layer, and a standard open-end rectangular waveguide, shaping the wave of the H10 type, is used as a feed [5, 6]. The parameters were analysed with the frequency of 10 GHz. It corresponds to the wavelength λ ~30 mm. The lens antenna systems are broadband antennas. Studies were also conducted with other frequencies, and the results showed the dependence typical for electromagnetic interference behaviour (change of the radiation pattern width with the wave length change) when changing the emission frequency for the given antenna system. To prevent clumsy research results presentation and previous results repetition, we provided the results only for one studied frequency.

Figure 3 covers amplitude radiation pattern sections in the H plane emitted at 90 and 0 degrees with no gap between the hemisphere and shield (h = 0), and with the conducting shield as the perfect conducting plane.

At this, the semi-spherical Lüneburg lens preserves its guiding properties and continues to function as the antenna [7]. Graph symbols: Gain – amplification factor (dB), θ – emission angle (degree).

Minor changes of the radiation pattern graph are possible when developing the antenna systems, i.e. axial symmetry loss related to the use of such type of waveguides.

2. Radiation patterns of special type

Antennas with a narrow radiation pattern in one plane and a wide one in the orthogonal plane are often required for radars. To ensure such radiation pattern, two methods are usually practised: mirror profiling and distributed feed system use [7]. The amplitude and phase of separate feed in the antenna structures with the pattern of special shape covering distributed feed are controlled in a way that both phase and amplitude distributions in the aperture are in line with the required radiation pattern. Such system calculation is limited due to insufficient knowledge of the field distribution in the mirror focal area, as well as physical limitations related to feed spatial location and interdependence effect.

Antennas with the radiation patterns of special type are used either to determine direction to the emission source or to study spatial location of many emission sources. In this regard, the task of the antenna shape and directivity characteristics real-time control remains relevant [8].

For example, for the aircraft radars designed for ground targets detection (Fig. 4), it is desirable to have the radiation pattern which, with the narrow horizontal radiation pattern, would ensure the uniform intensity of reflection from similar objects within the radar operation radius.


Fig. 4. Mounting and use of the aircraft radars: a – cosecant type pattern, b – example of mounting on the aircraft body


To ensure uniform exposure of any ground objects from the minimum elevation angle εmin to the maximum one εmax, it is required to have the pattern that provides the radar field density proportionate to the distance Дн from aircraft to ground.

Considering that the field density decreases in inverse proportion to the distance when radio waves propagate from the radar to an object, the radius vector of the field radiation pattern shall change in inverse proportion to the elevation angle sine ε, or in proportion to this angle cosecant – cosec ε.

The pattern in Fig. 4a has the shape similar to the cosecant one. In this case, the radiation patterns of the ground radar antennas for aerial targets detection shall be similar.

Known ways to create the cosecant shape radiation pattern for the conventional antenna types ensure no emission and receipt of ultra broadband signals. The task to create the antenna systems for such signals is still relevant. Thus, use of the broadband lens antenna is also relevant to ensure the cosecant type pattern [9, 10].

Moreover, the semi-spherical structure can be also mounted on the aircraft body as shown in Fig. 4b.

Figure 5 shows the cosecant type graphs for the semi-spherical lens. The feed element’s rotation angle for the provided graphs is θ = 83°, the shield diameter changes within the range from 4λ to 10λ.

Table 2 shows dimensions and main characteristics of the shield, the shield patterns are given in Fig. 5.


Table 2

Conducting shield geometric parameters

The provided cosecant type graphs for the semi-spherical lens with the varying conducting shield diameter demonstrate that when the shield diameter is 8λ (240 mm), the lens antenna’s radiation pattern is mostly similar to the cosecant graph in terms of its characteristics.

When mounted on the ideally conducting plane, the semi-spherical lens ensures the radiation pattern with the side lobe at the level below –25 dB, which is an insignificant value for the conducted research (Fig. 6).

3. Conclusion

Analysis of the developed antenna device calculation results revealed that the described model of the special shape radiation pattern making allows solving similar tasks with sufficiently high accuracy.

The resulting semi-spherical Lüneburg lens antenna model ensures the special type of radiation pattern (csc – cosecant) to detect aerial and ground objects when used in radars. This model allows emission distribution adapting and ensures more ideal space scanning. The resulting antenna radiation pattern ensures required signal coverage in terms of height when there is no received power dependence on the range of the radar for ground targets.

At this, the semi-spherical lens mounting on the ideally conducting plane ensures the pattern with the side lobe low level (below –25 dB), which eliminates additional radar jamming.

The studied antenna system’s model can be used within the wide frequency range.


1. Luneburg R.K. The Mathematical Theory of Optics. Providence. RI: Brown Univ. Press, 1944.

2. Thornton J. Wide-scanning multilayer hemispherical lens antenna for Ka band. IET Proc. Microw. Antennas Propag. 2006. Vol. 153, No. 6. P. 573–578.

3. Fuchs B., Palud S., Le Coq L., Lafond O., Himdi M., Rondineau S. Scattering of spherically and hemispherically stratified lenses fed by any real source. IEEE Trans. Antennas Propag. 1998. Vol. 56, no. 2. P. 450–460.

4. Panchenko B., Shabunin S., Denisov D. Fast Analysis of Luneburg Lens Radiation by Green’s Function Method. Proc. of European Radar Conf. EuRAD 2015. Paris, France, 2015. P. 568–571.

5. Fuchs B., Le Coq L., Lafond O., Rondineau S. Design Optimization of Multishell Luneburg Lenses. IEEE Trans. Antennas and Propag. 2007. Vol. 55, no. 2. P. 283–289.

6. Панченко Б.А. Рассеяние и поглощение электромагнитных волн неоднородными телами. Монография. М.: Радиотехника, 2013. 264 с.

7. Veselov A., Gavrilova Y. Surface synthesis of the reflector antenna with radiation pattern of special form. Progress In Electromagnetics Research Symposium – Spring, PIERS 2017 St. Petersburg, 22–25 May. P. 2058–2064. DOI: 10.1109/PIERS.2017.8262088

8. Nikolic N., Weily A.R. Dual-Polarized Planar Feed for Low-Profile Hemispherical Luneburg Lens Antennas. IEEE Transactions on Antennas and Propagation. 2012. Vol. 60, np 1. P. 402–407. DOI: 10.1109/tap.2011.2167941

9. Santos R.A., Fré G.L., Mejia F.B., Spadoti D.H. Reconfigurable Hemispherical Dielectric Lens. IEEE Antennas in MM-Waves. 2018. P. 456–459.

10. Fuchs S., Palud L., Le Coq O., Lafond M., Rondineau S. Scattering of Spherically and Hemispherically Stratified Lenses Fed by Any Real Source. IEEE Trans. Antennas and Propag. 2008. Vol. 56, no. 2. P. 450–460.

About the Authors

D. V. Denisov
Ural Technical Institute of Communications and Informatics – branch of the Federal State Institution of Higher Education “Siberian State University of Telecommunications and Information Science” in Ekaterinburg
Russian Federation

Denisov Dmitry Vladimirovich – Cand. Sci. (Engineering), Assoc. Prof., Department of Information Systems and Technologies.
Science research interests: telecommunications, antenna theory and technology. 


A. A. Tangamyan
Ural Technical Institute of Communications and Informatics – branch of the Federal State Institution of Higher Education “Siberian State University of Telecommunications and Information Science” in Ekaterinburg
Russian Federation

Tangamyan Аnatoly Аnatolyevich – Post-graduate student, Faculty Member, Department of Information Systems and Technologies.
Science research interests: diffraction theory, antenna theory and technology 



For citation:

Denisov D.V., Tangamyan A.A. Special beamforming by means of a semi-spherical Lüneburg lens. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2021;(2):28-34.

Views: 372

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

ISSN 2542-0542 (Print)