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

我们已经检查了来自FERMI自由电子激光器的软X射线脉冲通过厚度不同的碳膜的传输情况，量化了碳K边缘上方和下方的脉冲的非线性影响。在典型的软X射线自由电子激光强度下，脉冲在K边缘之上和之下分别为308和260 eV的光子能量处表现出线性吸收。而双光子吸收在K边缘以下略显着，约为284.2 eV。在284.18 eV（〜6 x 10 ^-48 cm ⁴ s）处测得的双光子吸收截面比基于类氢原子的简单理论所预期的共振效应高7个数量级。