Third-order nonlinear effects on femtosecond x-ray-absorption near-edge spectra

Abstract

Reduced density matrix equations combined with a cluster molecular-orbital method are formulated to describe resonant core-valence electron excitation by an intense femtosecond x-ray pulse. The electron-hole interaction is treated by the time-dependent unrestricted Hartree-Fock approximation supplemented by a screening correction in the Born approximation. Nonlinear $K$-shell absorption spectra of metallic copper are thereby computed. Numerical results indicate that, in the third-order nonlinear regime, where the fraction of excited electrons increases in proportion to the x-ray intensity, the absorption spectra above the $K$ edge undergo shifts toward high-energy side. The origin of this third-order nonlinearity can be traced to a negative renormalization of the core orbital energy due to strong electron-hole attraction, which offers a sharp contrast to the usual optical nonlinearity due simply to the increment of upper-state populations. For higher intensities, broadening of the absorption edge and saturation of absorption are predicted. These trends are qualitatively consistent with nonlinear spectroscopy experiments using the SACLA x-ray free-electron laser.