Fluorescence Measurement Of Critical Self-Focusing Power Of Femtosecond Vortex Beams

Since the phenomenon of filaments formed by ultrafast laser pulses in air was discovered in1995,the related researches have aroused great interest due to its wide applications in weather control,remote sensing,air laser and terahertz.Filamentation involves a number of nonlinear optical processes,including self-focusing,multi-photon ionization,self-phase modulation and self-steepening.When the incident laser energy exceeds a certain value in the optical medium,the self-focusing effect can overcome the diffraction of the beam and cause collapse.This value,known as self-focusing critical power,is a key physical parameter in the study of filamentation and can be widely used in various applications of filamentation.However,the self-focusing critical power of femtosecond vortex beams has not been studied quantitatively.The relationship between the self-focusing critical power of vortex beams and the topological load has been given both theoretically and experimentally.However,the relationship given in previous theoretical studies is only based on continuous pulses,and whether it is applicable to femtosecond laser pulses has not been confirmed.The relationship given experimentally is identified by electrical measurements,the result of which may be influenced by the experience of the researcher.Therefore,it is necessary to quantitatively measure the self-focusing critical power of femtosecond vortex beams experimentally.In this thesis,the development and application of femtosecond laser filamentation are reviewed,and the focus-shifting method is studied whether it is feasible to measure the self-focusing critical power of femtosecond Gaussian beam.Then the mesauring method based on photomultiplier（PMT）is proposed,to obtain the critical power of self-focusing femtosecond Gaussian beam and femtosecond vortex beam,and the relationship between femtosecond vortex beam and topological charges.Finally,the main work of this thesis is summarized and the future work are prospected.The main contents of this article are as follow:First,the critical power of the self-focusing femtosecond Gaussian beam under certain experimental conditions is 1.99 GW.In order to verify whether the focus-shifting method is suitable for measuring the self-focusing critical power of femtosecond vortex beams,we carried out further measurements,and the results showed that the peak position of femtosecond vortex beams no longer showed a monotone tendency.In order to explore the possible reasons,we used the 4f system to image the cross section of femtosecond vortex beams,and the results showed that there were non-single hot spots.Therefore,the possible reason is that there is competition between non-single hot spots,which causes the non-monotone change of peak position.Therefore,the focus-shifting method is a little difficult to measure the self-focusing critical power of femtosecond vortex beams.Second,due to the limitation of focus-shifting method,we measured the fluorescence intensity of 337 nm in the air ionization region using photomultiplier tubes,and obtained the critical power of self-focusing femtosecond Gaussian beams and femtosecond vortex beams with different topological charges.Under our experimental conditions,the critical power of self-focusing femtosecond Gaussian beams is 1.39 GW.For femtosecond vortex beams with topological charge of 1,2 and 3,the critical power measured is 3.55 GW,6.32 GW and 7.89 GW,respectively,when a focusing lens f=500mm(NA=1×10^-2)is used.When a focusing lens with f=750 mm(NA=6×10^-3)is used,the measured critical powers are 5.17 GW,10.20 GW and 16.45GW,respectively.The relationship between the self-focusing critical power and the topological charges of the vortex beam is obtained.By linear fitting of the experimental data,the intercepts are forced to be 0 and 1 respectively,and two relations,P_cr^（m）≈2mP_cr^（0） and P_cr^（m）≈（1.6m+1）P_cr^（0）,are obtained.We propose a new method to measure the self-focusing critical power,the fluorescence measurement method based on PMT.Compared with the focus shift method,PMT method is more sensitiver and simpler.It can not only obtain the self-focusing critical power of vortex beams,but also can be used to measure the self-focusing critical power of Airy,Bessel,vector beams and other structural beams.