依据非局域非线性介质中双光束传输时遵循的非局域非线性薛定谔耦合方程,在强非局域情形下,通过把响应函数作泰勒展开近似取到二阶,运用变分法求出了正交偏振、中心重合的双厄米高斯光束在强非局域介质中传输时各参量演化规律和一个临界功率,并运用分步傅里叶算法数值模拟出了束宽和相位的演化规律。当两光束以临界功率入射时,得到了正交偏振、中心重合的双厄米高斯空间光孤子及其大相移演化规律。当两光束以总临界功率入射,但两束光的入射功率不等时,光束可以形成呼吸子,但随着阶数的增加呼吸子将越来越不稳定。对于各阶呼吸子,功率大的束宽都作周期性压缩振荡变化,功率小的束宽都作周期性展宽振荡变化,且两呼吸子中功率大的相移随传输距离增加更快。在厄米高斯光束阶数小于5时,变分解得到的结果与数值解吻合较好。

Based on nonlocal nonlinear Schrodinger equations of double beams, the evolutional rules of parameters and critical powers of transmission of orthogonal polarization center-coincidence double Hermite-Gaussian beams are calculated with variational approximation method in strongly nonlocal medium by expanding the response function in Taylor’s series to the second order. The evolutional rules of the beam width and phase shift are numerically simulated with split-step Fourier algorithm. The orthogonal polarization center-coincidence double Hermite-Gaussian spatial optical solitons and their large phase shifts evolutional rules are obtained when the two beams are incident with critical powers. The beams can form breathers, but the breathers become unstable with the increasing of the order when the two beams are incident with the total critical power but two incident powers are different. For breathers of each order, the beam width with high power periodically compacted oscillates;the beam width with low power periodically extended oscillates. Moreover, the phase shift of higher power breather increases faster with the increasing of transmission distance.When the order of Hermite-Gaussian is under the fifth order, the variational approximate solution agrees well with the numerical solution.