Multiphoton ionization of hydrogen by an intense 248-nm linearly polarized field

We study multiphoton ionization of hydrogen by a linearly polarized 248-nm field (the photons have an energy of 5.0 eV) up to an intensity of ${10}^{15}$ W/${\mathrm{cm}}^2$. We compare two very different computational methods for the calculation of the total ionization rate: on the one hand, the full numerical solution of the time-dependent Schrödinger equation; on the other hand, results obtained within the Floquet formalism, which assumes a quasiperiodic time dependence. We obtain very good agreement between the two sets of calculations throughout the whole intensity range. The calculated rates also agree well with third-order perturbation theory up to ${10}^{13}$ W/${\mathrm{cm}}^2$, but are orders of magnitude lower at ${10}^{15}$ W/${\mathrm{cm}}^2$. The shortfall at high intensities is attributed to the change from a nonresonant third-order process to a resonant fourth-order process caused by ac Stark-induced shifts in the energy-level structure of hydrogen. In fact, the ionization rate between 2 and 6×${10}^{14}$ W/${\mathrm{cm}}^2$ is almost constant, giving rise to a plateau feature in the rate versus intensity curve.