Study Of Dispersion Of Medium Based On The One-dimensional Oscillator With Quantized Impedance Damping

Interaction of ultrafast laser and matter,may produce completely different nonlinear phenomena to ordinary light,such as two-photon absorption,filament,dispersion,etc..In this paper,we mainly study the dispersion effect of the medium under the action of ultra fast laser.Based on the one-dimensional oscillator with quantized impedance damping,and took the hydrogen atom as an example,we quantitatively analyzed the influences of the1st order dispersion of the linear refractive index on group velocity,and the 2nd order dispersion of the 3rd order susceptibility on nonlinear refractive index under different conditions.The numerical simulation is carried out to obtain the detailed information of the above influences.Our results may provide a kind of useful reference for the dispersion compensation.Typical main results we have made are as following:1.Based on the one-dimensional oscillator with quantized impedance damping,we theoretically calculated the quantized average collision frequency of electronic transitions between different energy levels at room temperature,and also the corresponding transitions frequencies.2.Based on Maxwell equations and on the one-dimensional oscillator with quantized impedance damping,we theoretically calculated the nonlinear refraction of group velocity of laser pulse.The 2nd order dispersion approximation of the 3rd order susceptibility is considered in our calculation.The results involved the 3rd order susceptibility and its 1st order dispersion.The effects of the dispersion of the linear refractive index of the gaseous hydrogen atom at room temperature on the group velocity and the effect of the dispersion of the 3rd order susceptibility on the nonlinear refractive index are quantified.In order to give expression to the two kinds of influences above,we defined the relative changes of the linear and the nonlinear situations and gave the influence range as:The dispersion of the linear refractive index has a greater impact on group velocity in the range of2.11nm-3.70nm;the range that the dispersion of the 3rd order susceptibility affect on the nonlinear refractive index is 644.8nm at 509.8nm.The linear and nonlinear relative changes can be up to 690 times.3.the linear and nonlinear relative changes with the change of particle number density and temperature are discussed.1)the influence of particle number densityThe range of the effect of dispersion of linear refractive on the group velocity is increased with the particle number density(the range can increased to 22.3nm when particle number density is 10²⁷).Similarly,the range of the nonlinear situation is also increased with the increase of the particle number density.The results show that the larger the particle number density,the greater the influence of the dispersion on the refractive index is.2)the influence of temperatureIn the temperature range of 233.15K to 393.15K?-40?-120??,we discussed the influences of dispersion of linear refractive index on group velocity and the dispersion of the 3rd order susceptibility on nonlinear refractive index,at the situation far from absorption.The results showed that in the temperature range,these two kinds of effects were all not significantly changed.This indicated that temperature has little effect on the dispersion.Based on the above results,we can draw the following conclusion:In order to maintain the stability of the ultra-fast pulse laser in the air at room temperature,the dispersion compensation must be considered.