光束在非局域非线性介质中传输时遵循非局域非线性薛定谔方程(NNLSE)。对应用变分法得到的傍轴高斯光束在强非局域非线性介质中的束宽演化方程进行了简化,消除了由于强非局域非线性介质响应函数作泰勒级数展开产生的势函数假根的影响;求出了傍轴高斯光束各参量的演化表达式。结果表明,傍轴高斯光束在强非局域非线性介质中传输时束宽的近似演化规律为正弦函数和余弦函数,并存在一个临界功率。当初始功率等于临界功率时,可以得到空间光孤子。对于一般情形,束宽作周期性压缩或展宽变化。当束宽比α≤0.3时,所得结果与非局域非线性薛定谔方程的数值解基本一致。

The propagation of the optical beam in the nonlocal nonlinear media is governed by the nonlocal nonlinear Schrdinger equation (NNLSE). In this paper, the paraxial Gaussian beam width evolution equation, which is obtained by means of variational approach, is simplified, the affection of the potentially functional spurious root, which arises from the Taylor′s series expansion of the strongly nonlocal nonlinear material response function, is eliminated, and the formulae of the paraxial Gaussian optical beam parameters′ evolution in the strongly nonlocal nonlinear media are obtained. The result shows that the beam width varies as sine-function and cosine-function, and there exists a critical power. When the input power equals the critical power, a spatial optical soliton occurs; in general, the narrowing and broadening of the beam width is periodical; when α≤0.3, the result of beam width evolution is almost coincident with the numerical solution of the nonlocal nonlinear Schrdinger equation.