超常介质中高阶色散和三、五阶非线性对交叉相位调制不稳定性的影响

发布时间：2018-12-07 07:11

【摘要】：交叉相位调制(XPM)不稳定性是指当两束或多束不同波长的光波在介质中传输时,由于光束之间的非线性效应发生相互作用会产生一些调制不稳定现象。XPM所引起的脉冲压缩、光开关和非互易性等效应已经在光通信器件中获得应用。超常介质特别是左手材料在2000年被制备出来,由于它的介电常数和磁导率同时为负,具备一般材料没有的突出性能,吸引了许多国内外研究学者的关注。而且超常介质中的电磁特性都是色散的,这使得常规介质中的一些理论在超常介质中不再适用。因此,在超常介质中研究交叉相位调制的不稳定性是十分必要的。影响调制不稳定性的主要因素是非线性效应和色散。在常规的非线性材料中对调制不稳定性的研究已经很完善,但在超常介质中对于双光束传输中的交叉相位调制还停留在研究低阶群速度色散和低阶非线性项,缺乏对高阶群速度色散和高阶非线性项等方面的深入研究。因此,有必要进一步研究超常介质中高阶色散和高阶非线性对交叉相位调制不稳定性的影响。论文从扩展的耦合非线性薛定谔方程组出发,基于超常介质中无损耗的Drude色散模型,通过研究两束同向传输的光波在具有高阶色散和三、五阶非线性的超常介质中的传输,推导得出在群速度色散和三阶色散都不相等和两者都相等的情况下,由交叉相位调制引起的调制不稳定性(XMI)的增益公式。并进一步通过MATLAB仿真着重分析了高阶色散项对XMI的产生和其增益谱的影响。本文的创新点： (1)在超常介质中研究交叉相位调制中的调制不稳定性,首次同时考虑高阶色散和高阶非线性效应的影响； (2)运用分离变量的方法逐个分析高阶色散系数对调制不稳定性的增益谱的影响。
[Abstract]:Cross phase modulation (XPM) instability means that when two or more beams of light with different wavelengths propagate in a medium, some modulation instability will occur due to the nonlinear interaction between the beams. Optical switching and non-reciprocity effects have been applied in optical communication devices. The supernormal medium, especially the left-handed material, was prepared in 2000. Because its dielectric constant and permeability are negative at the same time, it has the outstanding property which the general material does not have, which has attracted the attention of many researchers at home and abroad. Moreover, the electromagnetic properties in the supernormal medium are dispersive, which makes some theories in the conventional medium no longer applicable in the supernormal medium. Therefore, it is necessary to study the instability of cross phase modulation in supernormal medium. The main factors affecting modulation instability are nonlinear effect and dispersion. The study of modulation instability in conventional nonlinear materials is perfect, but the cross-phase modulation in supernormal medium is still confined to the study of low order group velocity dispersion and low order nonlinearity. Lack of further research on higher order group velocity dispersion and high order nonlinear term. Therefore, it is necessary to further study the effects of higher order dispersion and high order nonlinearity on cross phase modulation instability in supernormal media. Starting from the extended coupled nonlinear Schrodinger equations and based on the lossless Drude dispersion model in supernormal media, this paper studies the propagation of two beams of co-propagating optical waves in supernormal media with high order dispersion and third and fifth order nonlinearity. The gain formula of modulation instability (XMI) caused by cross phase modulation is derived when both group velocity dispersion and third order dispersion are not equal and both are equal. Furthermore, the effect of higher-order dispersion on the generation and gain spectrum of XMI is analyzed by MATLAB simulation. The innovations of this paper are as follows: (1) the modulation instability in cross-phase modulation is studied in supernormal medium, and the effects of high-order dispersion and high-order nonlinear effect are considered for the first time; (2) the influence of higher order dispersion coefficient on the gain spectrum of modulation instability is analyzed one by using the method of separating variables.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TN761

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