Study On The Propagation Characteristics Of Ultra-short Pulse Laser In Homogeneous Medium With Multi-photon Absorption

At present, there are several physical methods to measure molecular multi-photonabsorption coefficient in homogeneous medium, the theoretical basis for much of the traditionalnonlinear absorption equation. However, being lack of the partial differential for time in thetraditional nonlinear absorption equation, these methods have no rationality in studying theinteraction between ultra-short laser pulses and the homogeneous medium. Based on Maxwell’sequations, the complex of refractive index and the third-order electric susceptibility, weobtained the nonlinear partial differential equation with the partial differential for time. Thenwe devoted to studying those issues relevant to the interaction of ultra-short intense laser pulseswith the homogeneous medium by way of theoretical and numerical analysis, such asmulti-photon absorption and filament. Some academic achievements are obtained as following.1. When we omit the linear absorption (that isnI m0) and retain the third-order nonlinearityonly, then, we have theoretically deduced and obtained the nonlinear partial differentialequation of propagation characteristics of laser pulse in homogeneous medium.The equationcontain the term of time derivative.2. In a certain approximation, we have solved the nonlinear partial differential equation withthe partial differential for time and obtained an analytic solution what is expressed as atranscendental function. We have done numerical simulations to the analytic solutions andobtained some completions.When there is no linear and nonlinear absorption, the nonlinear refractive index of mediumand the real par of third-order electric polarization rate are proportional to the light intensity of laser pulse. The results show that, owing to different intensity of different parts of the pulse, thenonlinear refractive indexes are different respectively. This causes different velocity for differentparts of the pulse during the transmission process of a laser pulse in homogeneous medium. Thepeak has the minimum propagation velocity while the edge of the pulse travels faster. With thespread of pulsed laser process, the laser pulse changes gradually from a bright wafer spot to amore and more long,"silk-liked" bright spot. The propagation characteristic is very similar to"filament phenomenon". We put forward another explanation for filament phenomenon, andgave a method to calculate the length of filament. That is, the length of filament is relative to thereal part of third-order electric polarization rate, the peak intensity of laser pulse and thetransmitting time in the medium. If the rationality of the relation can be confirmedexperimentally, we should realize measuring the real part of third-order electric polarization ratejust through measuring the length of filament.When two-photon absorption exist in the media, we considered qualitatively that, because ofdifferent absorption, which is larger at peak and smaller at the bottom of laser pulse, the lightintensity reduced due to the absorption and the wave velocity decreased due to the light intensityare offset indirectly. The final result is that the propagation velocity of the laser pulse in variousparts is substantially remaining unchanged. In the practical experiment, filament becomes shorterowing to absorption, and the numerical results agree well with the results of qualitative analysis.As peak power of laser pulse in two-photon absorption declines, the width of pulsebroadened. We can get the curve of broadening rate. According to the relationship between thepulse broadening rate and two-photon absorption coefficient, we are proposing a new method ofgetting by measuring the pulse width indirectly.3. Omitting the linear absorption (that isnI m0) and retaining the fifth-order nonlinearityonly, we have theoretically deduced and obtained the nonlinear differential equation of laserpulse in condition just considering three-photon absorption. The same is that we have got anonlinear absorption equation about fifth-order nonlinear effects.We can get the analytic solution that the pulse-width of pump laser is broadened alongwith pulse propagation in medium because of the three-photon absorption of material molecules.The broadening effect of the pulse-width depends on the propagation distance and three-photon absorption coefficient of the molecular. Besides, pulse broadening rate is different for differentmodels of laser pulse. We came to the conclusion that the pulse broadening rate is in directproportion to nonlinear absorption coefficient.According to the broaden effect of pulse-width resulted from the three-photon absorption ofmedia, we suggest a new approach to measure three-photon absorption coefficient. That is tosay, the molecular three-photon absorption coefficient and the absorption cross section ofmaterials may be obtained by measuring the widen rate of pulse-width of ultra-short laserpulses traveling through homogeneous medium.