Porras M A, Alda J, Bernabeu E
Appl Opt. 1993 Oct 20;32(30):5885-92. doi: 10.1364/AO.32.005885.
The evolution of non-Gaussian and nonspherical high-power laser beams in cubic nonlinear media is described by means of their mean or gross parameters: width, mean curvature radius, and quality factor. The influence of the beam over its own propagation is contained in a new mean parameter that measures the ability of a beam to build its own waveguide. Beam quality and threshold power for self-focusing are connected. The ABCD and invariance laws for modified complex beam parameter and quality factor allow one to transform in one step the mean beam parameters through a sequence of nonlinear propagations, lenses, mirrors, and nonlinear quadratic graded index.
利用非高斯和非球面高功率激光束的平均或总体参数（宽度、平均曲率半径和品质因数）来描述其在立方非线性介质中的演化。光束对自身传播的影响包含在一个新的平均参数中，该参数衡量光束构建自身波导的能力。光束质量与自聚焦的阈值功率相关联。修正复光束参数和品质因数的ABCD定律及不变性定律，使人们能够通过一系列非线性传播、透镜、反射镜和非线性二次渐变折射率，一步转换平均光束参数。
