Nonlinear interface separating the Kerr nonlinear and the exponential graded-index media

IF 3.3 3区工程技术 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC Optical and Quantum Electronics Pub Date : 2024-11-20 DOI:10.1007/s11082-024-07815-4

S. E. Savotchenko

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Abstract

The influence of the nonlinear response of the interface on the localized state formation near at the boundary between medium with Kerr nonlinearity an exponential graded-index medium is analyzed. The linear and nonlinear responses of the interface are taken into account. The cases of self-focusing and defocusing nonlinearities of the Kerr medium are considered. Exact analytical solutions describing the asymmetrical spatial profiles of localized states and analytical solutions to dispersion equation in different cases are found. The intensity at the interface reduces in the case a defocusing nonlinear response of the interface and it enlarges in the case a self-focusing nonlinear response of the interface with an increase in the localization energy. The spatial distribution of localized states with two asymmetrical maxima can arise with a relatively small value of the characteristic width of an exponential graded-index medium corresponding to the ground state characterized by no more than one maximum in the graded-index medium. The appearance of the second maximum is possible in the case of contact only between a self-focusing medium and the graded-index medium and is due solely to the presence of a nonlinear response of the interface. The localized states with the spatial profiles attenuating with oscillations in the graded-index medium are found with a significant increase in the characteristic width of a graded-index medium.

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分离克尔非线性介质和指数分级指数介质的非线性界面

分析了界面的非线性响应对克尔非线性介质和指数分级指数介质边界附近局部状态形成的影响。界面的线性和非线性响应都考虑在内。考虑了克尔介质的自聚焦和散焦非线性情况。找到了描述局部态非对称空间剖面的精确解析解，以及不同情况下色散方程的解析解。在界面的非线性响应为散焦的情况下，界面上的强度会减小；而在界面的非线性响应为自聚焦的情况下，随着局部化能量的增加，界面上的强度会增大。在指数分级指数介质的特征宽度值相对较小的情况下，会出现具有两个不对称最大值的局部态空间分布，这与分级指数介质中不超过一个最大值的基态相对应。第二个最大值只可能出现在自聚焦介质和渐变指数介质接触的情况下，这完全是由于界面存在非线性响应。随着梯度指数介质特征宽度的显著增加，会发现梯度指数介质中空间轮廓随振荡而衰减的局部状态。

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来源期刊

Optical and Quantum Electronics 工程技术-工程：电子与电气

CiteScore

4.60

自引率

20.00%

发文量

810

审稿时长

3.8 months

期刊介绍： Optical and Quantum Electronics provides an international forum for the publication of original research papers, tutorial reviews and letters in such fields as optical physics, optical engineering and optoelectronics. Special issues are published on topics of current interest. Optical and Quantum Electronics is published monthly. It is concerned with the technology and physics of optical systems, components and devices, i.e., with topics such as: optical fibres; semiconductor lasers and LEDs; light detection and imaging devices; nanophotonics; photonic integration and optoelectronic integrated circuits; silicon photonics; displays; optical communications from devices to systems; materials for photonics (e.g. semiconductors, glasses, graphene); the physics and simulation of optical devices and systems; nanotechnologies in photonics (including engineered nano-structures such as photonic crystals, sub-wavelength photonic structures, metamaterials, and plasmonics); advanced quantum and optoelectronic applications (e.g. quantum computing, memory and communications, quantum sensing and quantum dots); photonic sensors and bio-sensors; Terahertz phenomena; non-linear optics and ultrafast phenomena; green photonics.