由光束在吸收克尔介质中传输的非线性近轴波方程,推导出具有二次相位分布的圆对称高斯光束在线性吸收介质中的耦合传输方程以及光束束腰的演化方程.数值计算的方法证实了光束束腰变化的几种可能,分析了稳态自聚焦的阈值特性.在给定参数的情况下,得到了稳态自聚焦的阈值入射光强和阈值聚焦长度.

Equations describing circular Gaussian beams (CGB) propagating inside the absorptive Keer medium have been derived from nonlinear paraxial equation. Based on these equations, an evolution equation of the beam waist has been obtained. The evolution equation indicates that, depending on the beam and material parameters, the circular Gaussian beams may be convergent or divergent when travelling inside the nonlinear medium. There is a special threshold beam whose waist approaches zero at the point where the self focusing can just compensate for the diffraction. After solving the evolution equation, the threshold intensity and threshold focal length of the threshold beam have also been specified.