高阶效应对耦合非线性薛定谔方程N-孤子解传输特性的影响  

Influence of Higher-order Effects on N-soliton Solution of the Coupled Nonlinear Schr?dinger Equation

作　　者：宋丽军[1] 房文静 SONG Li-jun;FANG Wen-jing(College of Physics&Electronics Engineering,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学物理电子工程学院,山西太原030006

出　　处：《量子光学学报》2022年第1期18-27,共10页Journal of Quantum Optics

摘　　要：基于广义耦合非线性薛定谔方程及其N-孤子解,采用分步傅里叶方法,数值研究了自陡峭效应和自频移效应对N-孤子解传输特性的影响。结果表明:自陡峭效应和自频移效应均会使1-孤子解在传输过程中发生偏移;对于2-孤子解和3-孤子解的束缚态孤子形式,自陡峭效应和自频移效应会引起孤子的偏转和能量的重新分配;对于类呼吸结构的2-孤子解和3-孤子解,自陡峭效应和自频移效应则会破坏类呼吸结构,使各孤子发生分离,最终形成振幅不等、传输速度不同的孤子。The propagation of optical pulses in lossless single-mode fibers can be described by the nonlinear Schr?dinger(NLS)equation. When the birefringence effect exists and two or more wave packets with different carrier frequencies appear in the system at the same time, the interaction between them is described by the coupled nonlinear Schr?dinger(CNLS) equation. CNLS equation is one of the basic models to describe nonlinear phenomena. In nonlinear optics, in order to realize the wavelength division multiplexing, multiple light field must transmit at the same time. Therefore, CNLS is often used to describe the nonlinear phenomenon of optical soliton in WDM system, birefringence fiber, multimode optical fiber, optical fiber array and Bose-Einstein condensates. In particular, the simultaneous transmission of two ultrashort pulses in the fiber can be described by the CNLS equation with higher order terms. Based on the generalized coupled nonlinear Schr?dinger equation, and its N-soliton solution,the effects of self-steepening effect and self-frequency shift effect on the propagation characteristics of N-soliton solution are numerically investigated by using the split-step Fourier method. The results show that both the self-steepening effect and the selffrequency shift effect cause the 1-soliton solution to shift during transmission. For the bound soliton form of 2-soliton solution and 3-soliton solution, self-steepening effect and self-frequency shift effect cause soliton shift and energy redistribution. For 2-soliton solution and 3-soliton solution with breathing-like structure, self-steepness effect and self-frequency shift effect destroy the breathing structure, making the solution split into several solitons with different amplitudes and transmission speeds.

关 键 词：耦合非线性薛定谔方程 自陡峭效应 自频移效应 

分 类 号：O437[机械工程—光学工程]