{"title":"分离克尔非线性介质和指数分级指数介质的非线性界面","authors":"S. E. Savotchenko","doi":"10.1007/s11082-024-07815-4","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":720,"journal":{"name":"Optical and Quantum Electronics","volume":"56 12","pages":""},"PeriodicalIF":3.3000,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Nonlinear interface separating the Kerr nonlinear and the exponential graded-index media\",\"authors\":\"S. E. Savotchenko\",\"doi\":\"10.1007/s11082-024-07815-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":720,\"journal\":{\"name\":\"Optical and Quantum Electronics\",\"volume\":\"56 12\",\"pages\":\"\"},\"PeriodicalIF\":3.3000,\"publicationDate\":\"2024-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Optical and Quantum Electronics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11082-024-07815-4\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optical and Quantum Electronics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s11082-024-07815-4","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Nonlinear interface separating the Kerr nonlinear and the exponential graded-index media
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.
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.
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