Research On The Nonlinear Properties Of The Propagation Of Strong Femtosecond Annular Gaussian Beam In Air

With the development of laser application technology,various non-conventional beams,such as Bessel beams,flat-top beams,vortex beams,and ring beams,etc.,have been appearing due to have special physical properties and advantages.The interaction between femtosecond laser pulses and non-linear media not only depends on the time distribution of intensity,but also on the spatial distribution of intensity.These new beams have a unique spatial intensity distribution,which will strongly affect the interaction between strong laser pulses and matter.The result of the action opens up new prospects for the expansion and control of the filament.In this paper,the nonlinear properties of the propagation of strong femtosecond annular Gaussian beam in air by are numerically investigated.The main work includes the following four parts:The effects of the delayed Kerr nonlinearity on the annular Gaussian filaments nearby the characteristic time of the molecular rotational respond are investigated.The results show that the delayed Kerr nonlinearity leads to the advancement of the filament onset distance.Moreover,in the presence of the delayed Kerr nonlinearity,the length of the filament is obviously extended,and the peak plasma density appears the great oscillations that makes the filament become unstable and nonuniform.These results are mainly induced by the redistribution of the fluence and the modulation of the speed of the total energy loss in the presence of the delayed Kerr nonlinearity.Moreover,the delayed Kerr nonlinearity enhances the self-focusing of the trailing edge and leads further to the extension of the optical filament.The effect of the initial pulse energy on the filaments generated by annular Gaussian beam in the atmosphere was analyzed.Studies have shown that when the initial pulse energy is increased,the length of the plasma channel generated by the annular Gaussian beam in the atmosphere is prolonged.When the pulse energy is increased to a certain value,although the plasma channel length continues to increase,the stability of plasma channel has declined.This isbecause as the pulse energy increases,the energy fluence increases at a faster rate due to the enhancement of the Kerr effect,so that the filament is advanced.But when the pulse energy increases to a certain value,the pulse energy continues to increase.The high intensity energy fluence is no longer advanced,but has a significant lateral expansion,and the high pulse energy also causes complex self-focusing phenomenon,which are not conducive to stabilizing the long distance propagation of the filaments.We have investigated on the supercontinuum generation by a femtosecond annular Gaussian beam in air.Compared with the spectra broadening of the Gaussian filament under the same initial condition,the smooth supercontinuum spectra of the annular Gaussian filament is enough wide to cover the whole visible frequency range in the first focusing cycle.The spectra broadening is analyzed from the frequency shift induced by the ionization and the self-phase modulation.For the blue side of the enhancement of the spectra broadening,the ionization-induced and intensity-induced frequency shifts play the dominant role in the onset distance of the filament and the first maximum value of the spectra broadening,respectively.Then,we have also discussed the influences of the initial pulse energy and the spatial chirp for wide and smooth supercontinuum spectra to cover the whole visible frequency range.We have investigated the formation of long filament generated by the free propagation of femtosecond annular Gaussian beam in air.Studies have shown that,under the same initial conditions,the magnitude of the peak intensity and plasma density of annular Gaussian beam under the free propagation are the same as those in external focusing,respectively.And by comparing the spatial fluence distribution in the two cases,it is found that during external focusing,the fluence before the filament is mainly shrinks linearly on the axis through external focusing.This is completely different from the non-linear shrinkage when free propagation.