| We know that when light interacts with the medium,there will be a variety of optical phenomena.When ultra-short laser pulse does,a strong nonlinear optical effect will appear.Currently,one of the hottest research topics in the optoelectronics field is the multi-photon absorption of medium molecule and its applications.In multi-photon absorption,we focus on the research that the phenomenon of two-photon absorption of transition between lowand high-energy-level when the molecule(or atom)of the medium absorbs the energy of two photons on one time in the impact of high power light.We know that pulse width of ultrafast laser is comparable to the period of light oscillation.Within the scope of a single ultra short pulse,the amplitude changes obviously over time.One of the reflection of the medium polarization is that the higher order dispersion of every orders’ susceptibility of the medium and the nonlinear partial differential equations of the time-varying light intensity.Traditional nonlinear partial differential equations do not contain the partial differential items of the time-varying light intensity.Based on the Maxwell Equations,aiming at the dispersion effects of third-order susceptibility and combining the transient characteristics of ultrafast laser pulses,we theoretically deduced and gave the satisfied nonlinear partial differential equations of light intensity when transverse-uniformed pulsed laser traveling through non-magnetic,non-conductive and no free charge homogeneous medium.On the basis of the one-dimensional oscillator model of quantum reactance,this paper explains the physical meaning of the differential equation,and also some nonlinear phenomena when ultra short pulse laser transferring through the homogeneous medium,such as filament,the group velocity caused by third-order electric susceptibility and how the third-order nonlinear dispersion influences the nonlinear refractive index and so on.The following main results are obtained in this paper:1.Based on the conditions above,this paper deduces the nonlinear partial differential equations.By neglecting the linear absorption,this equation shows the quadratic term of light intensity’s first-order time derivative on one hand and on the other hand,it finds that the group velocity of the pulse laser is not only related to the third-order susceptibility,but also the first-and second-order frequency derivative of third-order susceptibility.2.Taking Gaussian pulse as an example,the results of the partial differential equations are simulated,the corresponding results are also analyzed,the conclusions are as follow:1)Neglecting the linear and nonlinear absorption,during propagation process of the pulse transfers in the medium,if the light intensity of different locations are different,the propagation velocity of corresponding locations will be different.So the shape of the pulse will be changed with the propagation of light.The maximum position of light intensity of the laser pulse is corresponding to the minimum speed;on the contrary,the smallest bottom of the light intensity is corresponding to the maximum pulse propagation speed.2)Without considering the linear absorption,the speed of laser propagation in a medium is related to the refractive index of the medium and third-order susceptibility.And we found that the impact the third-order susceptibility on the group velocity is more apparent.At the same conditions of time,the initial value and boundary,the group velocity is a clear distinction of different propagation distance in the medium.3)We all know that the wavelength corresponds to the peak of the two-photon absorption is exactly twice as the transition wavelengths that determined by energy level difference,that is equal to half of the transition frequency of the energy level difference.So we simulate the growth rate of nonlinear refractive index near the transition frequency on the conditions of two-photon,based on the model of quantum reactance under one dimension harmonic oscillator.The results show that the influence of third-order nonlinear dispersion on nonlinear refractive index is 3 to 28 times greater than the influence of the third-order susceptibility.These results show that the influence of the dispersion of third-order nonlinearity on transmission characteristics of ultrafast laser is very important. |
