Localization of Excitations near a Thin Defect Layer with Nonlinear Properties, Separating Linear and Nonlinear Crystals
- Authors: Savotchenko S.E.1
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Affiliations:
- Sukhov Belgorod State Technological University
- Issue: Vol 64, No 9 (2019)
- Pages: 1231-1236
- Section: Theoretical and Mathematical Physics
- URL: https://journals.rcsi.science/1063-7842/article/view/204030
- DOI: https://doi.org/10.1134/S1063784219090159
- ID: 204030
Cite item
Abstract
It is shown that localized and quasi-local states exist near a thin defect layer with nonlinear properties, separating a linear medium from a Kerr-type nonlinear medium. Localized states are characterized by a monotonically decreasing field amplitude on both sides of the interface between the media. Quasi-local states are described by the field in the form of a standing wave in the linear medium and a monotonically decreasing field in the nonlinear medium. Contacts with nonlinear self-focusing and defocusing media are analyzed. The mathematical formulation of the proposed model is a system of linear and nonlinear Schrödinger equations with a potential simulating the thin defect layer, which is nonlinear relative to the field. Dispersion relations determining the energy of local and quasi-local states are obtained. The expressions for energy in explicit analytic form are indicated in the limiting cases and the conditions of their existence.
About the authors
S. E. Savotchenko
Sukhov Belgorod State Technological University
Author for correspondence.
Email: savotchenkose@mail.ru
Russian Federation, Belgorod, 308012