研究了高功率激光放大器中光束的成丝问题.利用弗兰兹-诺德威克(Frantz-Nodvik)模型将准稳态波动方程推广到介质有饱和增益的情形,进而得到高功率激光放大器中小尺度调制的传输方程.在小信号增益和饱和增益情形下,分别得到了小尺度调制方程的精确解析解和数值解.结果表明,对于相同的输入光强,增益使小尺度调制增益谱的范围加宽,最快增长频率增高,最大增长率提高;同时,在放大介质中,小尺度调制的最快增长频率和最大增长率还随传输距离变化.增益饱和效应使小尺度调制的增长速度以及B积分的增长低于无饱和放大情形.

The problem of filamentation of optical beam in high power laser is studied by taking into account the effect of saturating gain. A set of propagation equations for small scale modulation is derived. An exact analytic solution to the derived equation is obtained in the case of small signal gain. In the case of saturating gain, the obtained equation is solved numerically. It is found that for a given input power, the cutoff spatial frequency, the fastest growing frequency and the maximum growth rate increase in an amplifying medium, and varied with propagation distance. The saturating effect of gain lowers the growth rate of the B integral and the small scale modulation propagating in the amplifying medium.