非线性光学中的暗孤子分子  

Dark soliton molecules in nonlinear optics

作　　者：徐丹红 楼森岳[1] Xu Dan-Hong;Lou Sen-Yue(School of Physical Science and Technology,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学物理科学与技术学院

出　　处：《物理学报》2020年第1期134-142,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11975131,11435005)资助的课题~~

摘　　要：孤子分子是当前非线性光学中的重要课题.本文首先研究具有高阶色散和高阶非线性效应非线性光学模型中各种周期波(孤子晶格)的严格解,及各种可能的单孤子解.然后在一个可积的情况下,利用推广的双线性形式,给出多孤子解,并从多孤子解的速度共振条件给出暗孤子分子的严格解析表达式.对于本文给出模型的多暗孤子分子之间,以及孤子分子和通常孤子之间的相互作用都是弹性的.值得指出的是,在不可积的情况下孤子分子也是可以存在的.The study on soliton molecules is one of the important topics in nonlinear science especially in nonlinear optics.The bright soliton molecules have been experimentally observed in optics,however,the dark soliton molecules have not yet been experimentally observed.Theoretically,the soliton molecules have been found for some coupled nonlinear systems.Nevertheless,the soliton molecules have not been obtained for non-coupled single component nonlinear models.In this paper,we first study the exact periodic waves(soliton lattices)and solitary waves for a nonlinear nonintegrable optical model with second and third order dispersions and high order nonlinear effects including self-steeping,Raman scattering and nonlinear dispersion.Two types of dark soliton lattice and three types of soliton lattice are explicitly exhibited for general nonintegrable system.Five types of bright(with and without gray background),dark and gray solitons can be obtained from the limit cases of the modules of the soliton lattices.For an integrable case,using a novel generalized bilinear form of a single component nonlinear system,the multi-soliton solutions are obtained and expressed by a completely new form which are invariant under the full reversal transformations such as the parity,the time reversal,the charge conjugate and the field reversal.To find soliton molecules,a novel mechanism,the velocity resonant,is proposed.Starting from the multi-soliton solutions and using the velocity resonance mechanism,the analytical expression of the dark soliton molecules can be readily obtained.For the model given in this paper,the integrable higher order nonlinear Schrodinger equation,one can proved that the interactions among the dark soliton molecules and the usually solitons are elastic.It is worth pointing out that soliton molecules can also exist in the case of nonintegrable systems.

关 键 词：暗孤子分子 高阶非线性效应 弹性相互作用 可积系统 

分 类 号：O43[机械工程—光学工程]