运用变分法研究了傍轴高斯光束在三维轴对称强非局域介质中的传输特性,得到了光束各参量的演化方程、一个势函数、一个临界功率和一个由强非局域介质特性与初始束宽决定的特征参量ε。通过对势函数的进一步分析,结果表明,作为强非局域模型,必须满足0≤ε<1/3。在此前提下,当初始功率等于临界功率时,可以得到稳定的空间孤子;对于一般情形,束宽则作周期性压缩或展宽变化,也可能将不断展宽。该结果与数值解基本一致。

The propagation of paraxial Gaussian beam in three-dimensional strongly nonlocal media is disccussed with a variational approach. A set of evolution equations are obtained for the beam. The potential function, critical power and ε determined by both the material property and the initial beam width are obtained. The analysis of the potential function shows that the model for the beam propagation in the strongly nonlocal media is valid only when 0≤ε<1/3. A stable optical spatial soliton is found when the input power equals the critical power. Generally, the beam width takes periodical contraction, diffraction, or always diffracts respectively. The results agree with the numerical solutions.