On the synthesis of anisotropic Luneburg lenses

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Abstract

Two methods for synthesizing Luneburg lenses based on an inhomogeneous anisotropic dielectric are proposed: using an iterative procedure and a gradient medium model, as well as using a recurrent procedure and a layered medium model. As an example of the application of the proposed methods, a synthesis of two variants of a cylindrical Luneburg lens based on a ring dielectric structure was carried out. It is shown that the method based on the iterative procedure is unstable at small values of the radius. Using numerical modeling by the finite element method, an analysis of two versions of lens antennas based on cylindrical Luneburg lens synthesized using a layered dielectric model and a recurrent procedure is carried out.

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About the authors

V. A. Kaloshin

Kotelnikov Institute of radioengineering and Electronics RAS

Author for correspondence.
Email: vak@cplire.ru
Russian Federation, st. Mokhovaya, 11, building 7, Moscow

Bui Van Chung

Moscow Institute of Physics and Technology (National Research University)

Email: vak@cplire.ru
Russian Federation, Institutsky per., 9, Dolgoprudny, Moscow region, 141700

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Supplementary files

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2. Fig. 1. Geometry of the beam in the lens.

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3. Fig. 2. Luneburg cylindrical lens.

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4. Fig. 3. Dependence of the nr component of the refractive index tensor on the radius; the numbers on the curves are the iteration number.

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5. Fig. 4. The modulus of the difference between the exact value of the refractive index in an isotropic lens and the approximate value obtained from the ray equation (1) and from the eikonal equation (2).

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6. Fig. 5. Dependence on the radius of the component nr of the refractive index tensor of an ansotropic lens with a shell (1, 2) and without a shell (3, 4), obtained from the eikonal equation (1, 3) and from the ray equation (2, 4).

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7. Fig. 6. Dependences of the lens synthesis error (∆L) on the ray parameter: a – from the eikonal equation, b – from the ray equation; lens without a shell (1–3), lens with a shell (4–6); number of layers: 50 (1, 4), 100 (2, 5), 150 (3, 6).

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8. Fig. 7. Lens antenna with a shell (a) and without a shell (b).

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9. Fig. 8. Directional patterns at a frequency of 15 GHz of an antenna based on an anisotropic Luneburg lens with a shell (1, 2) and without a shell (3, 4): E-plane (1, 3), H-plane (2, 4).

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10. Fig. 9. Dependences on the frequency of the gain and the magnitude of the efficiency of the antenna based on an anisotropic Luneburg lens with a shell (1, 2) and without a shell (3, 4): gain (1, 3), efficiency (2, 4).

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