Indices governing optical self-focusing and self-induced changes in the state of polarization in ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, ${\mathrm{H}}_2$, and Ar gases

We employ recently published data on the dc Kerr effect and electric-field-induced second-harmonic generation in ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, ${\mathrm{H}}_2$, and Ar gases to calculate the nonlinear-optical indices governing self-focusing, self-induced changes in the state of polarization, and third-harmonic generation, over a wide range of wavelengths in these gases. We construct a new, one-parameter, dispersion formula that not only fits all existing data on the above gases, but also fits recent quantum calculations of each tensor component of the third-order optical susceptibility of helium, over a wide range of frequency arguments. We compare the difference between the predictions of this formula and the predictions of a previously used formula based only on linear refractive-index dispersion. The difference is negligible at 1053 nm but becomes significant at blue or shorter wavelengths (<350 nm), where it indicates the uncertainty in our dispersion calculations. We find the coefficient for self-induced polarization changes in one atmosphere of air to be $c_{1221}$(-ω,ω,ω,-ω) =(24±2)×${10}^{\mathrm{-}19}$ esu, at 1053 nm and 20 °C. This is consistent with one of two reported measurements of this coefficient.