Quantitative analysis of the 1st and 3rd order dispersion based on the one -dimensional oscillator with quantized impedance damping

The nonlinear refractive index of group velocity of pulse laser is derived based on Maxwell equations, and considering the 2nd order dispersion approximation of the 3rd order susceptibility. Based on the one −dimensional oscillator with quantized impedance damping (Zhu, et al., 2015) [19], the relative changes of linear and nonlinear refractive index of the 1st order dispersion of the 1st and 3rd order susceptibility of hydrogen atomic gas are quantitative simulated respectively, in region that far from linear and two-photon resonance absorption at room temperature. Relative changes at different temperature and different particle density are also simulated. The results show that the influence range of the linear refractive index dispersion on the refractive index of gas at room temperature is 2.11 nm to 3.70 nm. And increasing with particle density. The dispersion influence range of the 3rd order susceptibility on nonlinear refractive index at room temperature is 509.8 nm to 644.8 nm, and the range also increases with particle density. The linear and nonlinear relative changes can be up to 690 times. The results also show that the changes of the dispersion effect are not obvious at temperature range of −40 to 120 ° centigrade. Our results can be considered as a kind of reference for dispersion compensation for the stability of ultra fast pulse transmitting in the air at room temperature.