Implications of stimulated resonant X-ray scattering for spectroscopy,imaging, and diffraction in the regime from soft to hard X-rays

The ultrahigh peak brilliance available at X-ray free-electron lasers opens the possibility to transfer nonlinear spectroscopic techniques from the optical and infrared into the X-ray regime. Here, we present a conceptual treatment of nonlinear X-ray processes with an emphasis on stimulated resonant X-ray scattering as well as a quantitative estimate for the scaling of stimulated X-ray scattering cross sections. These considerations provide the order of magnitude for the required X-ray intensities to experimentally observe stimulated resonant X-ray scattering for photon energies ranging from the extreme ultraviolet to the soft and hard X-ray regimes. At the same time, the regime where stimulated processes can safely be ignored is identified. With this basis, we discuss prospects and implications for spectroscopy, scattering, and imaging experiments at X-ray free-electron lasers.