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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 4, Pages 684–698 (Mi zvmmf10883)  

On the solvability of the problem of electromagnetic wave diffraction by a layer filled with a nonlinear medium

V. Yu. Kurseeva, Yu. G. Smirnov, E. Yu. Smol'kin

Penza State University, Penza, 440026, Russia

Abstract: The problem of diffraction of a polarized electromagnetic wave by a layer filled with a nonlinear medium is considered. The layer is located between two half-spaces with constant permittivities. Two widely used types of nonlinearities: saturation nonlinearity and Kerr nonlinearity are considered. It is proved that the results on the solvability of the problems in these cases are qualitatively different: in the case of saturation nonlinearity, there are conditions under which the diffraction problem has a unique solution and, in the case of Kerr nonlinearity, the diffraction problem always has an infinite set of solutions. Analytical and numerical methods for solving this kind of problems are developed. Numerical results are presented.

Key words: polarized electromagnetic waves, Kerr nonlinearity, saturation nonlinearity, Maxwell's equations.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.894.2017/4.6
This work was supported by the Ministry of Education and Science of the Russian Federation, state task no. 1.894.2017/4.6.


DOI: https://doi.org/10.1134/S0044466919040094


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:4, 644–658

Bibliographic databases:

UDC: 517.958
Received: 23.08.2018
Revised: 14.11.2018
Accepted:14.11.2018

Citation: V. Yu. Kurseeva, Yu. G. Smirnov, E. Yu. Smol'kin, “On the solvability of the problem of electromagnetic wave diffraction by a layer filled with a nonlinear medium”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 684–698; Comput. Math. Math. Phys., 59:4 (2019), 644–658

Citation in format AMSBIB
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\pages 684--698
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