非局域非线性介质中多极表面光孤子的解析解及其稳定性分析

摘要

本文主要对非局域非线性介质中存在的多极表面亮孤予进行了研究.理论研究表明多极表面孤了也可以被看做是具有反对称振幅分布的体孤子的一半,由此我们可以给出多极表面孤子的解析解.其次,用数值计算的方法给出了它的数值解,比较结果表明数值解与解析解基本符合.最后,研究了本模型下的多极表面孤子的稳定性,发现二极表面孤子的不稳定区间比四极体孤子的不稳定区间小,另外,二极以上的表面孤子皆不稳定.%In this paper,the research on the multipole surface soliton in nonlocal nonlinear medium is done.Theoretical study indicates that multipole surface soliton in nonlocal nonlinear medium can also be regarded as a half part of a bulk soliton with an antisymmetric amplitude distribution.Using this fact,we could obtain the analytical solution of multipole surface soliton easily.Secondly,comparing the numerical solution acquired by numerical computation with analytical solution,we find that analytical solution is in good agreement with numerical solution.Finally,a research is done on the stability of multipole surface soliton using our model.The result shows that the width of the instability domain of dipole surface soliton is smaller than that of quadrupole bulk soliton.In addition all higher-order multipole surface solitons are unstable.