Abstract
Motivated by the ongoing controversy over the origin of the nonlinear index saturation and subsequent intensity clamping in femtosecond filaments, we study the atomic nonlinear polarization induced by high-intensity ultrashort laser pulses in hydrogen by numerically solving the time-dependent Schr\"odinger equation. Special emphasis is given to the efficient modeling of the nonlinear polarization at a central laser frequency corresponding to a wavelength of 800 nm. Here, the recently proposed model of the higher-order Kerr effect (HOKE) and two versions of the standard model for femtosecond filamentation, including either a multiphoton or tunnel ionization rate, are compared. We find that around the clamping intensity the instantaneous HOKE model does not reproduce the temporal structure of the nonlinear response obtained from the quantum-mechanical results. In contrast, the noninstantaneous charge contributions included in the standard models ensure a reasonable quantitative agreement. Therefore, the physical origin for the observed saturation of the overall electron response is confirmed to mainly result from contributions of free or nearly-free electrons.
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