势函数分析高斯光束在对数饱和非线性介质中的传播

ANALYZING PROPAGATION OF GAUSSIAN BEAMS IN LOGARITHMIC ALLY SATURABLE NONLINEAR MEDIUM WITH THE POTENTIAL FUNCTION

导出了在对数饱和非线性介质中传播的强激光基模高斯光束宽度随传播距离变化的方程。此方程与势作用下粒子的运动方程形式一致，因此可用势作用下的粒子行为来描述高斯光束的呼吸模式。对势函数采用二阶近似后，求解此方程得到高斯型呼吸模式的光束宽度的近似解析式。分析了呼吸周期和呼吸深度与入射条件的关系，以及形成空间孤子的条件。

The variation equation describing distance dependence of the beam waist of a fundamental Gaussian beam with high intensity propagating in logarithmically saturable nonlinear media has been deduced. The equation is formally consistent with that of a particle moving in potential well, so we can use the behavior of a particle moving in potential well to describe the breath mode of Gaussian beams. Having adopted the quadratic approximation of potential, we can solve the equation and get the approximately analytical solutions of Gaussian typed breath mode. We analyze the incident condition dependence of its breath period and breath depth, and the conditions of Gaussian spatial solitons forming.