Kramers-Kronig Relations and high order nonlinear susceptibilities

As previous theoretical results recently revealed, a Kramers-Kronig transform of multiphoton absorption rates allows for a precise prediction on the dispersion of the nonlinear refractive index n2 in the near IR. It was shown that this method allows to reproduce recent experimental results on the importance of the higher-order Kerr effect. Extending these results, the current manuscript provides the dispersion of n2 for all noble gases in excellent agreement with reference data. It is furthermore established that the saturation and inversion of the nonlinear refractive index is highly dispersive with wavelength, which indicates the existence of different filamentation regimes. While shorter laser wavelengths favor the well-established plasma clamping regime, the influence of the higher-order Kerr effect dominates in the long wavelength regime.