发散光束小尺度自聚焦特性的研究

研究了发散光束的小尺度自聚焦效应。从非线性傍轴波动方程出发,利用坐标变换,推导出发散光束小尺度扰动的传输方程,进而得到小尺度扰动增长的临界频率、最大增长频率和相应B积分值的变化规律。研究了发散光束初始曲率半径对小尺度自聚焦效应的影响。结果表明,对于一定的传输距离,随着发散光束初始曲率半径的减小,小尺度扰动的最大增长频率减小,相应的最大增益减小,即B积分值也减小。对于一定的初始曲率半径,随着传输距离的增大,B积分值增长变缓,并最终停止。利用局部能量守恒定律研究了发散光束的成丝距离,发现小的初始曲率半径可以延长成丝距离。

Small-Scale Self-Focusing of Divergent Beams

The small-scale self-focusing of divergent beams is studied.Based on the nonlinear paraxial wave equation,the propagation equation of small-scale perturbation of divergent beams has been deduced with a coordinate transformation.The evolvement law of the growth critical frequency of small-scale perturbation,maximum growth frequency and relative B integral is obtained.The influence of the initial radius of divergent beams on small-scale self-focusing is discussed.It is found that for a given propagation distance,the fastest growing frequency,the maximum perturbation growth,and thus the B integral decrease with the decrease of the initial radius of divergent beams.For a given initial radius,as the propagation distance increases,the growth of the B-integral becomes slow and stops at last.Also,the expression for the distance at which the filaments are formed is obtained by local energy conservation,and it is shown that a small initial radius extends the filamentation distance.