Diffraction of TE polarized electromagnetic waves by a nonlinear layer: saturated and Kerr nonlinearities

Abstract

The diffraction of a TE wave by a dielectric layer filled with a nonlinear medium is considered. The layer is located between two half-spaces with constant permittivities. Two types of nonlinearities (nonlinearity with saturation and Kerr nonlinearity) are considered and compared. In this paper, we show the difference between solvability results of the problem in these cases. Namely the diffraction problem with saturated nonlinearity has a unique solution under some additional conditions. At the same time, the diffraction problem in the case of Kerr nonlinearity has an infinite number of solutions. The analytical and numerical solution techniques are developed. Numerical results are presented.

COMMUNICATED BY:

• Michael Klibanov

KEYWORDS:

• TE polarized electromagnetic waves
• Kerr nonlinearity
• nonlinearity with saturation
• Maxwell's equations

AMS SUBJECT CLASSIFICATIONS:

• 78A45
• 78A60
• 65L10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Ministry of Education and Science of the Russian Federation [grant number 1.894.2017/4.6].