High-Field Quantum Calculation Reveals Time-Dependent Negative Kerr Contribution

The exact quantum time-dependent optical response of hydrogen under strong-field near-infrared excitation is investigated and compared to the perturbative model widely used for describing the effective atomic polarization induced by intense laser fields. By solving the full 3D time-dependent Schrödinger equation, we exhibit a supplementary, quasi-instantaneous defocusing contribution missing in the weak-field model of polarization. We show that this effect is far from being negligible, in particular when closures of ionization channels occur and stems from the interaction of electrons with their parent ions. It provides an interpretation of the higher-order Kerr effect recently observed in various gases.

Figure 1

Nonlinear polarization envelope as a function of time for a 30 (a), 32.5 (b), 38 (c), and 42 (d) $\mathrm{TW}/{\mathrm{cm}}^2$ 48-cycle pulse.

Figure 2

Nonlinear polarizability as a function of peak intensity for 24- (a), 48- (b), 60- (c) and 96-cycle (d) pulses calculated with the TDSE (red solid line) and KD (blue dashed line) models.

Figure 3

(a) Probability of the electron to be in the continuum during a 48-cycle $10\mathrm{TW}/{\mathrm{cm}}^2$ pulse calculated in the length and velocity gauges, compared with the output of the PPT formula. (b) Correction factor $K$ of the PPT ionization probability. Nonlinear polarizability as a function of intensity calculated in (c) the length and (d) velocity gauge. $\Delta {\alpha }_{\mathrm{BB}}$, $\Delta {\alpha }_{\mathrm{BC}}$, and $\Delta {\alpha }_{\mathrm{CC}}$ refer to the partial nonlinear polarizabilities related to bound-bound, bound-continuum, and continuum-continuum transitions, respectively.

Figure 4

Spectral dependence of the nonlinear polarizability for (a) 24 and (b) 48 cycles.