ON ONE APPROACH TO THE PROBLEM OF POLARIZED ELECTROMAGNETIC WAVES DIFFRACTION ON A DIELECTRIC LAYER FILLED WITH A NONLINEAR MEDIUM 

Valovik Dmitriy Viktorovich, Candidate of physical and mathematical sciences, professor, sub-department of mathematics and supercomputer modeling, Penza State University (40 Krasnaya street, Penza, Russia), dvalovik@mail.ru
Demchenko Anna Evgen'evna, Student, Penza State University (40 Krasnaya street, Penza, Russia), dem-94@mail.ru

517.927, 517.968, 519.6

10.21685/2072-3040-2016-4-3

Background. An analytical approach to the problem of diffraction of monochromatic polarized electromagnetic TE waves on a dielectric layer filled with a nonlinear medium is suggested. The nonlinear medium’s permittivity depends on the electric field’s squared module. Such kind of problems attracts attention due to the importance of nonlinear effects in microelectronics and photonics.
Materials and methods. The main theoretical tool to study the problem is the integral dispersion equation method.
Results. The approach used allows one to derive equations binding the amplitude of the incident field with the reflection and transmission coefficients for the Kerr medium. The article shows a comparison between the nonlinear problem and the corresponding linear problem.
Conclusions. Explicit formulas for the sough-for coefficients can be found only in the cases of cubic (Kerr nonlinearity) and quintic nonlinearities. However, explicit solutions to the nonlinear differential equations are complicated for both cases. This makes it practically useless to use the explicit solutions for determination of the sought-for coefficients. The use of explicit solutions is impossible due to higher nonlinearities. However, the approach, suggested by the authors, works well for cubic, quintic as well as for much more complicated cases.

problem of diffraction, dielectric layer, Kerr nonlinearity, Maxwell's equation

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