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ISSN 2415-3400 (Online)
ISSN 1028-821X (Print)

Scattering of a plane electromagnetic wave by a piecewise homogeneous Luneberg lens

heading: 
MICROWAVE AND TERAHERTZ TECHNOLOGY
Velichko, EA, Nickolaenko, AP
Organization: 

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine
E-mail: sasha@ire.kharkov.ua
https://doi.org/10.15407/rej2019.02.057
Language: russian
Abstract: 

Subject Subject and purpose. The results of studies of the physical effects arising in the scattering of a plane electromagnetic wave on a piecewise homogeneous multilayered lens simulating a Luneberg lens, as well as in scattering on a dielectric cylinder with a graphene coating are presented. The purpose of the paper is to estimate the size of the focal spot and the range of frequencies in which focusing is observed due to plasmon resonance phenomenon.

Methods and methodology. A numerical simulation was performed of the diffraction of a plane TE-wave on a cylindrical piecewise homogeneous Luneberg lens of six layers, as well as on a dielectric cylinder coated by a graphene layer. The exact classical solution of the boundary value problem was used. Specific feature of our approach is application of Bessel functions of the complex argument. For the case of a graphene coating, the resistive boundary conditions were applied with the conductivity of graphene is determined by the Kubo formula.

Results. The spatial distribution of the field amplitude was analyzed for different sizes of the outer radius of the lens measured in the wavelength of the incident radiation. It was shown that if the radius of the lens is smaller than the wavelength, focusing at the rear wall of the cylinder is not possible, but applying a layer of graphene can solve this problem due to arising plasmon resonances.

Conclusion. A piecewise homogeneous lens consisting of six layers provides focusing when its radius exceeds the wavelength by the factor of 3 or more. The method of approximation of the continuous radial dependence of the refractive index plays a significant role in focusing. The best results are obtained in approximation with an «excess», when the center of the focal spot is closest to the rear wall of cylinder. When it is required that the radius of the cylinder is smaller or of the order of the wavelength, instead of the Luneberg lens, a uniform dielectric cylinder coated with a graphene layer might be used and operate at plasmon resonance frequencies of graphene.
Keywords: diffraction by a circular cylinder, piecewise homogeneous Luneberg lens

Manuscript submitted 29.11.2018

PACS: 07.57.−c, 41.20.Jb, 42.25.Fx 
Radiofiz. elektron. 2019, 24(2): 57-67
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