Modeling saturable absorption for ultra short X-ray pulses

Saturable absorption was recently observed in transmission measurements above the L_II,III edge of pure Al thin films using ultra short X-ray pulses at a free-electron-laser (FEL) facility. The high fluence reachable by FEL pulses, the shortness of the pulse duration, and the typical lifetime of the excited state are all important factors enabling observation of the phenomenon. We devised a simplified theoretical approach describing the saturation phenomenon using a three-channel model containing ground, excited and relaxed states. This phenomenological model explicitly includes the interaction between the solid and photon field in a semi-classical way, and the resulting non-linear coupled equation is solved numerically. We successfully applied this model to recent experimental results obtained using FEL radiation.