Abstract

The three-layered symmetric structure consisting of a linear layer sandwiched between defocusing nonlinear media was considered. The layers are separated by interfaces with nonlinear properties. The nonlinear symmetrical localized states arising in such a structure were described theoretically. The proposed model is based on the nonlinear Schrödinger equation with negative Kerr-type nonlinear term and nonlinear self-consistent potential describing the interaction of the waves and interfaces. Even and odd solutions of nonlinear Schrödinger equation correspond to the localized states of two types existing in different energy ranges. The stationary state energies as the system parameter functions are calculated in explicit form. The conditions of their existence were analyze depending on the combination of signs of nonlinear interface parameters. The localized states of the special kinds existing only for the case of interfaces, which are characterized by a strong nonlinear response, were found. The dependencies of localization energies on the amplitude of the interface oscillations were studied analytically.

Graphic abstract

中文翻译：

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三层结构中的对称局部状态，该结构由散焦介质之间的线性层组成，该线性层由具有非线性响应的界面分开

摘要

考虑了由夹在散焦非线性介质之间的线性层组成的三层对称结构。层由具有非线性属性的界面分开。从理论上描述了这种结构中出现的非线性对称局部状态。所提出的模型基于带有负Kerr型非线性项和描述波与界面相互作用的非线性自洽势的非线性Schrödinger方程。非线性薛定ding方程的偶数和奇数解对应于存在于不同能量范围内的两种类型的局部状态。作为系统参数函数的稳态能量以显式形式计算。根据非线性界面参数符号的组合，分析了它们的存在条件。发现了仅对于界面情况才存在的特殊种类的局部状态，这些局部状态具有强烈的非线性响应。通过分析研究了局部能量对界面振荡幅度的依赖性。

图形摘要