基于强非局域非线性介质中的Snyder-Mitchell模型,利用分离变量法得到了(1+1)维光束传输的厄米-高斯型解析解。比较厄米-高斯型解析解与非局域非线性薛定谔方程的数值解,证实了,在强非局域条件下,该厄米-高斯型解与数值解完全吻合。对厄米-高斯光束的传输特性进行研究,结果表明,光束束宽会出现周期性的压缩或者展宽现象。并且得到了实现厄米-高斯光束稳定传输的临界功率、厄米-高斯孤子解及传输常量,临界功率与厄米-高斯光束的阶数无关,但传输常量随阶数的增加而增加。高斯呼吸子和高斯孤子就是基模厄米-高斯呼吸子和基模厄米-高斯孤子。

Based on the Snyder-Mitchell model, with the method of separation of variables, exact analytical Hermite-Gaussian (HG) solutions are obtained in strongly nonlocal nonlinear media. The comparison of analytical solutions with numerical simulations of the nonlocal nonlinear Schrdinger equation (NNLSE) shows that the analytical HG solutions are in good agreement with the numerical simulations in the case of strong nonlocality. The evolution of the HG beam in strongly nonlocal nonlinear media is discussed. The results demonstrate that the width of the HG breathers vibrates periodically as they travel. Furthermore, the critical power for the soliton propagation, the solution of HG solitons, and the propagation constant are obtained. The critical power does not change with the mode number, and the propagation constant increases as the mode number increases. Gaussian breathers and Gaussian solitons can be treated as special cases of HG breathers and HG solitons.