Research On Self-focusing Of Finite Energy Airy Beam

In recent years,the finite energy Airy beams(FEAB)have attracted wide interest in the field of Optical particle manipulation,plasma channel,light bullets and electron acceleration due to its unique properties of transverse self-accelerating,diffraction-free and self-healing during propagation.Most of these applications need high power FEAB,however self-focus,especially small-scale self-focus is the main break-up factor in the high power laser system,which may led to the decrease of the quality of the beam and the destruction of the laser medium.At present,the research about small-scale self-focusing on finite energy Airy beams is very few,based on the summary analysis of Airy beam and its generation,we make a systemic research on the self-focusing of the FEAB combined with the basic concepts of self-focusing and the theoretical models and numerical methods,especially the theory of small scale self focusing,the main work is as follows:Firstly,we systematically studied the small-scale self-focusing transmission characteristics of the main lobe of the FEAB in the process of Kerr nonlinear media.The results show that the main peak of the limited energy Airy beam not only exists the whole beam self-focusing,but also exists the small-scale self-focusing.Affected by noise,the small-scale self-focusing is more likely to occur than the whole beam self-focusing and more easy to cause the beam generating filaments in the case of noise.In addition,with the increase of truncated coefficient a,the growth rate of space strength of the main peak of the FEAB increases slowly.The gain spectrum curve of the main peak of the FEAB is similar to Gaussian beam fitted by its main peak,and with the increase of a truncated coefficient,the two curves becomes more close.Secondly,we studied the self-focusing characteristics of the secondary lobe of the FEAB during propagation in the Kerr nonlinear media.We found that the noise growth rule of secondary lobe of the FEAB is inconsistent with the main lobe.It is found that the secondary peak of the FEAB can occur the whole beam self focusing and the small-scale self-focusing,and the whole beam self-focusing and small-scale self-focusing of the secondary peak of the finite energy Airy beam is not easy to happen related to the main peak.Besides,the gain spectrum curve of the secondary peak of the FEAB would decrease with increasing of truncated coefficient;the gain spectrum curve of the secondary peak of the finite energy Airy beam is similar to the gain spectrum of the gaussian beam fitted by its secondary peak,and smaller than it.