Two-photon absorption of soft X-ray free electron laser radiation by graphite near the carbon K-absorption edge

We have examined the transmission of soft X-ray pulses from the FERMI free electron laser throughcarbon films of varying thickness, quantifying nonlinear effects of pulses above and below the carbonK-edge. At typical of soft X-ray free electron laser intensities, pulses exhibit linear absorption atphoton energies above and below the K-edge, 308 and 260 eV, respectively; whereas two-photonabsorption becomes significant slightly below the K-edge, 284.2 eV. The measured two-photonabsorption cross section at 284.18 eV (6  1048cm4s) is 7 orders of magnitude above what is expectedfrom a simple theory based on hydrogen-like atoms – a result of resonance effects.