多频锁模脉冲激光器稳定性分析

Stability Analysis of Multi-frequency Mode-locked Pulse Fiber Laser

光纤激光器中增益物质提供的增益大小,会影响激光器脉冲的稳定性。当增益过低时,调制不稳定性的增长率为正,噪声被放大,模式会不稳定;当激光器增益足够高时,调制不稳定性增长率为负,就能抑制调制不稳定性的产生,实现脉冲的稳定。该文对薛定谔光纤传输方程进行线性化分析,并通过数值模拟,求出调制不稳定性增长率,解析地推导了增长率与脉冲激光器增益之间的关系。对连续的平面波情况,线性增益过小,则增长率为正;增益大于某个门限值则增长率为负,且能够抑制调制不稳定性的产生,得到稳态的平面波。对具有双曲正割脉冲解的情况,也得到同样的结论,表明了线性增益高于某个门限值时,就能抑制调制不稳定性的产生,从而实现了光纤激光器的锁模。

In fiber laser,the gain provided by the gain substance can influence the laser pulse's stability.While the gain is low,the growth rate of the modulation instability is positive,the noise is magnified and the mode is unstable,while the gain surpasses the threshold,the growth rate of the modulation instability is negative,it can suppress the modulation instability and realize the pattern stable.In this paper,we analyze the Schr?dinger fiber transmission equation linearly,derive the growth rate of the modulational instability then get the relationship between the growth rate and the laser's gain.To CW,when the linear gain is low,the growth is positive;when it is above the threshold,the growth is negative,it can suppress the modulational instability production and get stationary CW.We also obtain the same conclusion to the hyperbolic secant pulse solution situation.It indicates that when the linear gain is higher than the threshold,it will suppress the modulational instability production,consequently realize the optical fiber laser mode-locking.