Saturation of the all-optical Kerr effect.

Saturation of the intensity dependence of the refractive index is directly computed from ionization rates via a Kramers-Kronig transform. The linear intensity dependence and its dispersion are found to be in excellent agreement with complete quantum mechanical orbital computations. Higher-order terms concur with solutions of the time-dependent Schrödinger equation. Expanding the formalism to all orders up to the ionization potential of the atom, we derive a model for saturation of the Kerr effect. This model widely confirms recently published and controversially discussed experimental data and corroborates the importance of higher-order Kerr terms for filamentation.