中文摘要：

用分步傅里叶方法计算了高斯光束在克尔介质中的传输过程，采用最小均方根办法对光场进行二项式曲线拟合得到光束质量因子，计算结果表明：当B积分在2rad以内，克尔效应越强则它对因子影响越大；同时，它的这种影响能力也受到光束宽度和光束腰平面到克尔介质的距离的两个因素的影响，即光束越宽，影响越小，距离越大，影响反而较小；最后，基于B积分的可叠加性，提出用具有负非线性折射率系数的非线性介质来补偿正克尔效应、降低光束因子，并指出两端补偿是最优的方式之一．

英文摘要：

The process of the Gaussian beam propagating through the nonlinear medium is calculated by step FFT, and the M^2 factor is get by minimizing the root-mean-square of the quadratic curve, the simulation results show： on the condition that the B integral is no more than 2, the stronger the Kerr effect is, and the bigger the M^2 factor is; and in which the beam width and the length between the waist plane and the nonlinear medium are two important factors on the influence between the Kerr effect and M^2 factor, namely the narrower beam width and the longer length are, the and the bigger the M^2 factors are. The compensation adopting the negative nonlinear refractive index medium to reduce the Kerr effect is studied and the beam quality is improved effectively. The both side compensation is selected as an idea method in the three types of methods.