Theoretical And Numerical Study Of The High Power Laser Pulse Self-focusing And Filamentation

Ultra-short high intensity laser pulses propagation in air have been studied for 20 years since the first experimental observation of laser filamentation in the mid-1990s.Due to its potential values for applications,much increasing attraction has been rapidly paid to the case of filament formation in air both in experiment and theoretical studies.The paper is devoted to investigate the intense femtosecond laser propagation in air as follows.Two parallel methods are developed for the high intensity laser pulse propagation in transparent media.The energy flux of the Gaussian pulse propagation in transparent media is also studied.A new semi-empirical formula for the nonlinear focus is got,which is better than the traditional Marburger's formula.The HOKE model and Kerr-plasma model for the propagation of laser in air are studied.(1)A parallel 2D+1 split-step Fourier method with Crank-Nicholson scheme running on multi-core shared memory architectures are developed basing OpenMP and POSIX thread to study the propagation of ultra-short high intensity laser pulses in air.The parallel method achieves a near linear speed-up with results for the efficiency of more than 95%on a 24-core machine for POSIX.This method is of great potential application in studying the long-distance propagation of the ultra-short high intensity laser pulses.(2)Energy density flux is a characterization tool for analyzing the high power laser pulses propagation in transparent media.We first derive the analytical formula for energy flux by neglecting the GVD effect,and the analytical formula can work when the propagation distance is small.We find that at the beginning of the propagation the energy density flux is proportional to the propagation distance.We second derive the power threshold for the on-axis intensity increasing of Gaussian pulse based on the concept of energy flux.The asymptote of the on-axis intensity is also got.We then demonstrate there exists a transition point in the radius of laser pulse,beyond which the self-focusing cannot overcomes diffraction and the energy will flow outwards,and it indicates that for equi-phase Gaussian pulse,there does not exist a power threshold above which all the energy of the pulse can flow toward the axis.Finally,we obtain a formula for approximately estimating the energy for Gaussian pulse which will be diffused by diffraction in the process of propagation.(3)Nonlinear focus is an important parameter for the filamentation phenomena since it denotes the beginning of the filamentation stage when the initial power is near or larger than the filamentation threshold.We combine the pulse's dispersion length with the Dawes and Marburger's formula and achieve a new formula that can predict the nonlinear focus very well regardless of the dispersion being important or not.We also find that there exists a threshold,for the initial peak power with which the nonlinear focus has a maximum length due to the competition between Kerr self-focusing and dispersion.(4)The annular Gaussian beams having different initial energies propagation in air are numerically studied by two models,the linear model and the nonlinear model.Numerical results show that(i)at the beginning of the propagation the nonlinear Kerr effect slightly suppresses the focusing caused by the spatial chirp,and(ii)the focusing caused by the spatial chirp generates a high intensity core making the beam shape near the axis similar to the Gaussian shape arid this can enhance the Kerr-self-focusing,and(iii)the initial energy of the annular beams can influence the nonlinear foci,filamentation length,and the fluence of the propagation.The nonlinear foci decrease with the initial energy,but the foci are not inversely proportional to the square root of the initial peak power,which is not the same as the Gaussian beam.The filamentation length increases with the initial input energy.(5)The effects of the nonlinear refraction indexes(n2,n4,n6,n8)on the propagation of femtosecond high-intensity laser pulse are studied.We consider three models.The first model includes n2,n4,n6 and n8.The second one only includes n2 and n4.The third model includes n2,n4 and n6.Numerical simulations show that the third model cannot properly describe the propagation of the ultra-short high intensity laser pulse,and the index n2 is the most important focusing mechanism at the beginning of the propagation,and n8 and n6 are the most important indexes in the stable propagation stage,and the pulse's radius in the first model is almost the same as that in the second model,so does the number of filamentations splitted in the temporal direction.This work is useful in understanding the mechanism of the femtosecond laser pulse propagation in air.(6)The life cycle of ultra-short high intensity laser pulses propagation in air is studied.As the controversial of the high-order Kerr indices measured by Loriot et al we focus on two models which are high-order Kerr effect included and not included.Two factors are mainly analyzed,group-velocity-dispersion and the energy evolution of the pulse.It is found that the group-velocity-dispersion can not be simply ignored even though the pulse's duration is as long as several hundreds femtoseconds.The energy loss due to the multi-photon-absorption is very small,and it may hardly change the propagation length of the pulse.Another contribution of this work is to introduce a probability quantity,which may be useful in validating the positive and negative alternating of Kerr and high-order Kerr indices.