M.M. Kushneryov1, S.P. Skobelev2

1,2 PJSC Radiofizika (Moscow, Russia)

1,2 Moscow Institute of Physics and Technology (National Research University) (Dolgoprudny, Russia)

1 1 kushneryov.mm@phystech.edu; 2 s.p.skobelev@mail.ru

In the present work we have considered a generalized Mikaelian lens using material with negative refractive index in its design. A new formula was derived for calculation of the refractive index profile providing focusing of the rays in a point located at a specified distance from the lens surface. The derivation is based on the assumption of linear dependence of the square of the refractive index on the interval located between the point where a ray enters the lens and the point where it exits the lens.

The problem of scattering of an E-polarized plane wave by the generalized Mikaelian lens was solved numerically. The solution was based on the method of integral equations for electric and magnetic field strengths in the lens. The algebraization of the integral equation was carried out with use of the approach proposed by J. Richmond.

Using the formula derived for the negative refractive index profile, there were obtained new results concerning the field distribution over the lens axis and characterizing the features of wave focusing at different combinations of the lens parameters. Comparison of them was carried out with similar results obtained for the lenses of the same dimensions and focal lengths but with positive refractive index, which revealed some negative effect of the edges in the lens with negative refraction.

Kushneryov M.M., Skobelev S.P. Comparative features of wave focusing by generalized Mikaelian lens with positive and negative refractive indexes. Radiotekhnika. 2022. V. 86. № 4. P. 50−58. DOI: https://doi.org/10.18127/j00338486-202204-07 (In Russian)

1. Mikaelyan A.L. Ispolzovanie sloistoy sredy dlya fokusirovki voln // Doklady AN SSSR. 1951. T. 81. № 4. S. 569-571.
2. Kelleher K.S., Goatley C. Dielectric lens for microwaves // Electronics. № 8. 1955. P. 142-145.
3. Feld Ya.N., Benenson L.S. Antenno-fidernye ustroystva. M.: Izd-vo VVIA imeni professora N.E. Zhukovskogo. 1959.
4. Zelkin E.G., Petrova R.A. Linzovye antenny. M.: Sovetskoe radio. 1974.
5. Theory and Fhenomena of Metamaterials. Ed. by F. Capolino. N.Y.: Tailor & Francis Group. 2009.
6. Veselago V.G. Elektrodinamika veschestv s odnovremenno otricatelnymi znacheniyami e i μ // Uspehi fizicheskih nauk. 1968. T. 10. № 4. S. 509-517.
7. Pinchuk A.O., Schatz G.C. Metamaterials with gradient negative index of refraction. J. Opt. Soc. Am. A. 2007. V. 24. № 10.
8. Driscoll T., Basov D.N., Starr A.F., Rye P.M., Nemat-Nasser S., Schurig D., Smith D.R. Free-space microwave focusing by a negative- index gradient lens // Applied Physics Letters. 2006. V. 88. P. 081101.
9. Kushnerev M.M., Skobelev S.P. Dvumernaya zadacha elektromagnitnogo rasseyaniya na linze Mikaelyana, dva metoda resheniya i osobennosti fokusirovki // Fizicheskie osnovy priborostroeniya. 2020. T. 9. № 4(38). S. 38-47.
10. Hizhnyak N.A. Funkciya Grina uravneniy Maksvella dlya neodnorodnyh sred // Zhurnal tehnicheskoy fiziki. 1958. T. 28. №7. S. 1592.
11. Volakis J.L., Sertel K. Integral Equation Methods for Electromagnetics // Raleigh, NC: SciTech Publishing. 2012.
12. Richmond J.H. Scattering by a dielectric cylinder of arbitrary cross section shape // IEEE Trans. Antennas Propagat. 1965. V. AP-13. № 3. P. 334-341.
13. Richmond J.H. TE-wave scattering by a dielectric cylinder of arbitrary cross section shape // IEEE Trans. Antennas Propagat. 1966. V. AP-14. № 4. P. 460-464.