中文摘要：

采用光线光学方法对非线性自聚焦现象进行仿真，能够从宏观上直观地体现强激光的传输过程，同时避免采用近轴近似、自相似近似等．本文采用在光传输路径上垂直于光轴切片的方法，将光的非线性传输转化为切片上的光对折射率的调制作用和切片间的线性传输．在切片端面上统计光强后对量化误差进行了抑制，而线性传输过程采用了亚当斯法求解光线方程从而解决了龙格库塔法等不能用于非线性光传输仿真的问题．仿真结果显示，强激光自聚焦在轴上有多个焦点，且第一个焦点的位置随光功率的增大而更靠近入射位置；由于追迹的是实际光线，故可以得到近轴区以外区域自聚焦及成丝（环）的情况，这对于强激光系统安全是有重要意义的．利用已有的同样基于光线追迹方法的光学设计、仿真软件，可以把非线性自聚焦介质和线性介质结合起来，仿真光在实际强激光系统中的传输．

英文摘要：

The simulation of nonlinear self-focusing phenomenon using ray-tracing method can macroscopically provide an intuitive picture of the propagation of light in a self-focusing material, without adopting paraxial approximation or self-similar hypothesis. In this paper, propagation of light is sampled by discrete slices along a certain direction. Thus nonlinear propagation is turned into the combination of optical modulation of the refractive index on separate slices and linear propagation between each two adjacent slices. On each slice, after calculating the flux, we use a novel algorithm to suppress the quantized errors. For the linear propagating process, Adams method is adopted to solve the ray equations, which solve the problem that the widely used Runge-Kutta method cannot be used in simulation of light in nonlinear materials. The simulation results reveal that there are several foci along the propagating axis and the location of the first focus becomes closer to the incident plane as the power of light goes up. Furthermore, because the program traces real rays, it is possible to reach the non-paraxial region and reveal the phenomenon of ring-structure flux distributions caused by self-focusing. This is significant for the safety of high-power laser systems. Some commercial optical design and simulation software are also based on ray-tracing methods. Thus the systems including both nonlinear and linear materials are possible to simulate, which can guide people to set up the corresponding experimental systems.