对数饱和非线性介质中的自洽多模高斯孤子解

Self-Consistent Multimode Gaussian Soliton Solution in Logarithmically Saturable Nonlinear Medium

通过解对数饱和非线性介质中光场满足的非线性薛定谔方程,得到一组厄米高斯型的自洽多模解。在借鉴了R.G.Glauber的相干态理论的基础上,合理假设这组解在非线性介质中呈泊松分布,进而得到了在对数饱和非线性介质中存在高斯孤子的结论,并获得高斯孤子解、非线性系数与泊松参量三者之间的关系。该关系说明,若在介质中存在高斯孤子解,其非线性系数必须满足条件α≥1。当α=1,在介质中仅存在单模高斯孤子,其光斑尺寸必须满足的条件w=1knn20。在该条件下,以"束腰"注入介质中的高斯光束才可以在保持其光斑尺寸不变的情况下传输,否则光斑尺寸会存在一定的振荡。而振荡方式、振荡范围(表示光斑尺寸展宽或压缩及大小)与输入光束光斑尺寸及其一次导数有直接关系。

Through solving the nonlinear Schrodinger equation that optical field in logarithmically saturable media satisfies, a set of solutions were founded, which were self-consistent multimode Hermite-Gaussian functions. Because these self-consistent solutions are much like the solutions of one-dimensional harmonic oscillator, it is assumed reasonably that the mode occupation obeys Poisson distribution, just like quantum mechanical Glauber＇s coherent states. The assumed Possion distribution self-consistently leads to the conclusion that there is Gaussian soliton in logarithmically saturable nonlinear media, and the relationships among the Gaussian soliton, the nonlinear coefficient and the Possion parameter are obtained. If the soliton solution exists, the nonlinear coefficient must satisfy a condition of α≥1. When α= 1, there is single mode Gaussian soliton only, and the beam size must be restricted as a fixed value ω=1/ k √n0/ n2 . Under the condition, the Gaussian beam injected in medium at waist can transmits in the nonlinear medium keeping its beam size constant, otherwise the beam size will oscillate. The oscillating form and amplitude rely directly on the input beam size and its first-order derivative which indicates the beam waist would be expanded or compressed.