We apply a numerical basis-state method to determine the electric susceptibility of atomic hydrogen via calculations of the terms of the perturbative power series expansion up to eleventh order as well as from ab initio calculations of the field-induced polarization. The results of the perturbative calculations indicate that the applicability of the power series expansion is limited to intensities of a uniform electric field below 2 × 10 13 W/cm 2 at a wavelength of 800 nm. While the predictions for the electric susceptibility from the perturbative power series tend to strongly increase beyond this intensity regime, those from ab initio calculations have a negative slope as a function of intensity. We therefore interpret that the latter feature is due to the nonperturbative interaction between the atom and the external field and an explanation via higher-order nonlinear terms is not applicable.
We present results of ah initio numerical calculations for low-order-harmonic generation as well as calculations of the higher-order terms in the respective perturbative power-series expansions of the susceptibilities for thirdand fifth-order-harmonic generation. We find that the transition from perturbative to nonperturbative interaction in these low-order nonlinear processes occurs at about 10B W /cm2. Our findings confirm previous results that any deviation from the predictions of lowest-order perturbation theory indicates that the perturbative series expansion is not applicable and, if required, needs to be replaced by a nonperturbative treatment of the interaction between the atom and the field. In particular, the results also show that the observation of low-order-harmonic yields cannot be considered as a test of higher-order Kerr effects.
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