Effective Electrodynamic Analysis of Small-Size Dielectric Lenses
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Radiophysics and Quantum Electronics, Vol. 62, No. 11, April, 2020 (Russian Original Vol. 62, No. 11, November, 2019)
EFFECTIVE ELECTRODYNAMIC ANALYSIS OF SMALL-SIZE DIELECTRIC LENSES I. V. Donets,1∗ A. M. Lerer,1 Zimeng Li, S. M. Tsvetkovskaya3
2
and UDC 537.874.6
We develop an electrodynamic method for analysis of the near- and far-zone fields of dielectric lenses, which is based on solving a high-frequency integral equation. It is shown that the accuracy of this method is high for the lens size exceeding four wavelengths. Its advantages are fast internal convergence of the solution, short computation times, and small computer resources needed. The near-zone fields of lenses having various profiles and sizes of about ten wavelengths are analyzed.
1.
INTRODUCTION
Lenses represent a well-known and most widely used type of optical devices [1, 2]. Along with the conventional optics, their application area covers optical-communication means [3], radio-frequency lens antennas [4, 5], and medical applications [6, 7]. The recent trend is the use of small-size lenses having apertures comparable with the wavelength in the optical [8], as well as infrared [9] and terahertz [10] bands. As a rule, the aperture of a microwave antenna lens amounts to only a few wavelengths [11]. However, one should know both the focus position and the distribution of the near-zone field in these bands. If the lens surface is spherical, its analysis is performed rigorously by the method of separation of variables [2] in a sufficiently wide range of sizes, namely, from zero to tens of wavelengths. A fairly effective approach has been developed for the Luneburg lens on the basis of the above-mentioned method [12]. The electrodynamic simulation software packages (HFSS [13] and CST [14]) do this task brilliantly at small ratios of the antenna size to the wavelength (D/λ). However, as the ratio D/λ rises, the required computation time and resources increase rapidly. The approximate analysis is performed by using not only the methods of geometric optics [15], but also the more rigorous hybrid methods combining geometric and physical optics [16, 17] or geometric optics and modal analysis [18]. The physical-optics method implemented in the HFSS package allows one to calculate the scattering pattern of lenses for their sizes of about ten wavelengths, but yields inadequate results when calculating the near-zone field and the focal distance. In this paper, we propose using the method of a volume integro-differential equation. 2.
BASIC FORMULATION
In the case of diffraction by a single dielectric body, the volume integro-differential equation is written (1) E(r) = Eext (r) + (grad div + k 2 ) τ (r )E(r )G0 (r, r ) dv ,
as
V ∗
igor [email protected] 1
Southern Federal University, Rostov-on-Don, Russia; 2 Guangzhou Compass Antenna Design Institute Co. Ltd., Guangzhou, China; 3 Don State Technical University, Roston-on-Don, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 62, No. 11, pp. 855–865, November 2019. Origina
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