X-ray two-photon absorption competing against single and sequential multiphoton processes

The success(1,2) of X-ray free-electron lasers (XFELs) has extended the frontier of nonlinear optics into the hard X-ray region. Recently, sum-frequency generation(3) has been reported, as well as parametric downconversion(4-6). These are of the lowest (second) order, and higher-order processes remain unexplored. Here, we report the first observation of a third-order process: two-photon absorption of a 5.6 keV XFEL beam by germanium. We find that two-photon absorption competes with single and sequential multiphoton processes(7,8), but we successfully determine the intrinsic cross-section by analysing the pulse-energy dependence. We also discuss the two-photon absorption cross-section by comparing a new mechanism unique to X-rays with the conventional mechanism and show that the latter is consistent with the present result. The experimental determination and understanding of the cross-section would allow two-photon absorption spectroscopy. Our result indicates that X-ray analogues of other third-order nonlinear optical processes(9), such as nonlinear Raman and optical Kerr effects, are available for XFEL applications in spectroscopy, imaging and beam control.