微扰法求解铅玻璃中的涡旋空间光孤子

Perturbation Method for Solving Vortex Spatial Optical Solitons in Lead Glass

在量子力学的微扰理论框架下,利用微扰法求解得到了1+2维强非局域非线性介质--铅玻璃中二阶微扰修正的“类拉盖尔高斯型”涡旋孤子的近似解析解。从非局域非线性薛定谔方程(NNLSE)出发,以铅玻璃中的真实折射率与Snyder-Mitchell(SM)模型中描述的抛物线型折射率的差值为微扰,以SM模型中的拉盖尔高斯孤子解为基态解,求得了铅玻璃材料中二阶微扰修正的“类拉盖尔高斯型”涡旋孤子的解析解。拓扑荷值分别为1、2、3、4的微扰修正的“类拉盖尔高斯型”光孤子比未加微扰的拉盖尔高斯型光孤子更稳定,非常接近孤子真解的传输行为。

In this study, an approximate analytical solution of the Laguerre-Gauss-like vortex solitons was obtained after conducting a second-order perturbation correction in lead glass, a kind of strongly nonlocal nonlinear (1+2)-dimensional medium. Specifically, the nonlocal nonlinear Schrodinger equation (NNLSE) was perturbed using the difference between the real and parabolic refractive indices in lead glass, where the parabolic index was described using the Snyder-Mitchell (SM) model. The Laguerre-Gaussian soliton solution in the SM model is considered to be the ground state solution. Further, the perturbation-corrected Laguerre-Gauss-like solitons with topological charges of 1,2,3, and 4 are more stable when compared to those without perturbation, and their propagation behaviors are almost similar to that of the true soliton solution.