Single-photon ionization in intense, fluctuating pulses

High intensities in laser-matter interaction drive nonlinear processes. Whereas at low frequencies thereby multi-photon absorption and above-threshold ionization emerges, in the case of high frequencies single-photon absorption remains prevailing. However, multiple absorption and emission of photons renders this single-photon ionization sensitive to energy and shape of the laser pulse. This becomes relevant for intense, fluctuating pulses as generated in existing and upcoming free-electron laser sources. We study their effect on the ionization of a model atom numerically and formulate suitable parameters to characterize the evolution from the linear response at low intensity to the intricate dynamics at high intensities