研究了有限能量Airy光束在克尔介质中的非线性传输过程及整体自聚焦(特别是小尺度自聚焦)特性.研究发现相对于整体自聚焦，有限能量Airy光束主峰的小尺度自聚焦更容易发生，而且其噪音调制的增长速度随着截断系数的增加而变慢.通过对比研究不同截断系数小尺度自聚焦的增益谱，发现截断系数也极大地影响有限能量Airy光束的增益谱，截断系数越小Airy光束受噪音影响分裂的可能性就越大；对于较大的截断系数，有限能量Airy光束增益谱和由它主瓣拟合的高斯光束的增益谱越来越接近.研究结果对于有限能量Airy光束的潜在应用有一定的指导作用.

The nonlinear propagation of finite energy Airy beam (FEAB) in Kerr media was investigated numerically. The characteristics of whole beam self-focusing (WBSF) and small-scale self-focusing (SSFS) of the FEAB were thoroughly studied during its nonlinear propagation. It was found that the SSFS is more likely to take place than the WBSF, and the growth rate of noise modulation decreases with increasing the truncation factor. By comparing the gain spectra of SSFS for different truncaed factors, it can been seen that the truncation factor has a large impact on the gain spectrum of the FEAB indicating the possibility of the breakup of the FEAB induced by noise is inversely proportional to the truncated factor. In addition, the gain spectrum of FEAB is more similar to that of the Gaussian beam fitted from the main lobe of FEAB in the case of larger truncation factor. These results are very important for the potential application of the FEAB.