Numerical Simulation Of Femtosecond Laser Filamentation And Its Induced Aerodynamic Response

When powerful femotsecond pulse laser transmits in the atmosphere,if the peak power of the incident pulse exceeds the self-focusing critical power,the so-called filamentization phenomenon will be observed,and the transmission distance of the filament can far exceed the Rayleigh length corresponding to its diameter.The process of filamentation is accompanied by very complex nonlinear effects,among which the heat deposition effect induced by laser energy deposition can trigger hydrodynamic response of air.This provides a theoretical basis for the formation of air waveguides.In this paper,the nonlinear Schrodinger equation describing femtosecond filamentation,hydrodynamics equation and thermal diffusion equation are used for theoretical analysis and numerical simulation of temporal characteristics of filament,high-order Kerr effect and acoustic and thermal waveguides formed by hydrodynamic responses to heat deposition.The main achievements and innovations as follows:（1）The nonlinear Schrodinger equation describing the propagation of femtosecond pulse laser in the atmosphere is numerically solved with symmetrical Split-Step Fourier method.The concept of equivalent pulse duration is proposed to solve the problem of pulse temporal splitting during femtosecond laser filamentation,which provides a new method for studying the overall characteristics of pulse in time-domain.The results show that the higher the incident power is,the earlier the starting point is,and the larger the clamping intensity is.The use of focusing lens will aggravate the asymmetry of pulse splitting and increase the clamping intensity of filament.By comparing the variation law of equivalent pulse duration and main pulse duration along the whole propagation path with the distance z,the analysis shows that the pulse temporal splittring is irreversible.Based on the existing model of filamentation,the uncertainty of high order nonlinear coefficients is introduced in equal proportion,and their influence on the characteristics of filamentation is studied.The results show that:the clamped intensity varies by 5-15%with the HOKE coefficients change by 4-20%and the peak plasma density maximally changes by a factor about 7.（2）Using the hydrodynamic equations of mass,momentum and energy and the beam propagation method,the spatial and temporal distribution of air density caused by the hydrodynamic response of air to heat deposition and its evolution with different temperature increments are studied,and a new method for generating bottle beams is proposed.When the temperature elevations increases from 1 00K to 600K,the variation coefficients of the depth and width of the air density hole are CV_depth=0.4912 and CV_width=0.0273,respectively,indicating that the depth is more sensitive to the temperature elevation than the width.In the range of time and temperature elevations calculated in this paper,for the guided beam at 355nm,the optimal bottle beam can be generated by using the acoustic waveguide at dT=600K,t=90ns;for the guided beam at 532nm,the acoustic waveguide at dT=600K,t=50ns can produce the best bottle beam.（3）Using the thermal diffusion equation and the beam propagation method,the spatial and temporal characteristics and fiber parameters of the air thermal waveguide generated by different lobe spacing are studied,and the coupling efficiency of the laser transmission guided by the thermal waveguide is calculated,which provides a theoretical basis for the selection of lobe spacing in the practical application of the thermal waveguide.The calculation shows that the lifetime of the thermal waveguide is up to ms level.The four-filament arrays with large lobe spacing can produce longlife thermal waveguides.In addition,a basis for judging whether the air density structure generated by the filament array is a waveguide is proposed.In the simulation experiment of guided propagation,the coupling efficiency of 81%is calculated,which greatly improves the transmission efficiency of laser.