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 There are five parameters, i.e. the initial amplitudes of a pump beam and a signal beam, the ratio of the initial beam width of the pump to that of the signal, the initial separation between the two beams′ centers, and the wavelength ratio of the pump to the signal, which influence the induced focusing of the signal optical beam due to the cross phase modulation of the pump beam in self defocusing nonlinear media. The effect of the ratio of the initial beam width on the focusing of the signal beam is... There are five parameters, i.e. the initial amplitudes of a pump beam and a signal beam, the ratio of the initial beam width of the pump to that of the signal, the initial separation between the two beams′ centers, and the wavelength ratio of the pump to the signal, which influence the induced focusing of the signal optical beam due to the cross phase modulation of the pump beam in self defocusing nonlinear media. The effect of the ratio of the initial beam width on the focusing of the signal beam is discussed under other different parameters. The numerical results show that there exists a pair of optimum values for the ratio of the initial beam width and the initial separation, which can result in the strongest focusing of the signal, and another pair of optimum values for the ratio and the separation, under which the optimum focusing can be obtained for the given length of the medium specimen. The detailed discussion about the effects of all five parameters on the induced focusing of the optical beam in self defocusing nonlinear media can be used to design experiments leading to the best effect of the focusing.  影响自散焦介质中诱导光束聚焦过程的方程参量和初始条件共有 5个 ,即两光束波长比 (方程参量 )、抽运光和信号光的初始振幅、两光束初始束宽比和两光束中心初始间距。通过数值计算讨论了初始束宽比在不同初始光束间距和波长比情况下对信号光聚焦过程的影响 ,得到了信号光聚焦效果的最佳初始参量条件。从而实现了对影响自散焦介质中诱导光束聚焦过程 5个参量的完整详细研究。  A discussion is given about the focusing of optical beams due to the cross phase modulation in three dimensional self defocusing nonlinear media. The effect on the focusing of the probe beams for the three initial parameters is discussed: the amplitude of the pump beam, the separation between the pump and the probe beam centers and the wavelength ratio of the pump and the probe beams. The coupled amplitude equations are optimized based on the fact that the probe beam is much less intense than the pump beam,... A discussion is given about the focusing of optical beams due to the cross phase modulation in three dimensional self defocusing nonlinear media. The effect on the focusing of the probe beams for the three initial parameters is discussed: the amplitude of the pump beam, the separation between the pump and the probe beam centers and the wavelength ratio of the pump and the probe beams. The coupled amplitude equations are optimized based on the fact that the probe beam is much less intense than the pump beam, and cut the time of operating the programs much too. Our numerical results show that, the greater the amplitude of the pump beam and the wavelength ratio of the pump to signal beam are the better the probe focuses; the initial separation between the pump and the probe beams has an optimum values. The results can be used to design experiments in order to obtain the best effect of the focusing.  对三维自散焦介质中由交叉相位调制效应诱导的光束聚焦过程进行了系统研究 ,讨论了抽运光振幅、抽运光信号光初始偏移和抽运光信号光波长比三个参量对信号光聚焦过程的影响。根据自散焦介质中强抽运光诱导弱信号光聚焦满足抽运光与探测光模型 ,对传输方程进行了优化 ,大大减少了数值模拟运算时间。数值方法采用分布傅里叶方法。数值模拟结果表明 :抽运光越强、抽运光信号光波长比越大 ,信号光聚焦程度越大 ;抽运光信号光初始偏移存在一个最佳值 ,使得光束聚焦达到最佳效果。通过参量最佳值的选择 ,可提高光束聚焦的效率。  The effect of elliptic Gauss beam on the focusing of the signal beam under the other different parameters is discussed. There are six parameters, i.e. the wavelength ratio of the pump beam to the signal, the initial amplitudes of a pump beam and a signal beam, the initial separation between the beams' centers, and the ratio of the initial beam width of the X and Y of the pump to that of the signal, which influence the induced focusing of the signal optical beam. The numerical simulations are in good agreement... The effect of elliptic Gauss beam on the focusing of the signal beam under the other different parameters is discussed. There are six parameters, i.e. the wavelength ratio of the pump beam to the signal, the initial amplitudes of a pump beam and a signal beam, the initial separation between the beams' centers, and the ratio of the initial beam width of the X and Y of the pump to that of the signal, which influence the induced focusing of the signal optical beam. The numerical simulations are in good agreement with the experimental results obtained by Hickmann in 1992.  研究了在自散焦介质中诱导光束聚焦过程中椭圆高斯光束对光束聚焦的影响。通过数值计算讨论了在不同初始抽运光束振幅、初始光束间距和波长比情况下椭圆高斯光束对信号光束聚焦的影响。影响光束聚焦过程的方程参量和初始条件共有6个,即两光束波长比(方程参量)、抽运光束和信号光束的初始振幅、两光束初始中心间距和两光束X、Y初始束宽比。采用此理论模型验证了Hickmann在1992 年得出的实验结果,数值计算结果表明理论结果能够和实验结果定量地吻合。  
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