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Motivated by the ongoing controversy on the origin of the nonlinear indexsaturation and subsequent intensity clamping in femtosecond filaments, we studythe atomic nonlinear polarization induced by a high-intensity and ultrashortlaser pulse in hydrogen by numerically solving the time dependent Schr\"odingerequation. Special emphasis is given to the efficient modeling of the nonlinearpolarization at central laser frequency corresponding to 800 nm wavelength.Here, the recently proposed model of the Higher-Order Kerr Effect (HOKE) andtwo versions of the Standard model for femtosecond filamentation, includingeither a multi-photon or tunnel ionization rate, are compared. We find thataround the clamping intensity the instantaneous HOKE model does not reproducethe temporal structure of the nonlinear response obtained from the quantummechanical results. In contrast, the non-instantaneous charge contributionsincluded in the Standard models ensure a reasonable quantitative agreement.Therefore, the physical origin for the observed saturation of the overallelectron response is confirmed to mainly result from contributions of free ornearly free electrons.

On the Saturation of the Nonlinear Refractive Index in Atomic Gases