Review of X-ray nonlinear optics

We review the emerging sub-field of nonlinear optics - nonlinear optics of X-rays. After briefly addressing the early theoretical and experimental work on the subject, we review in detail the recent theoretical research on soft-X-ray nonlinear optics. This research has already shown the feasibility of numerous resonant nonlinear optical processes (nonlinear absorption and refraction, third-harmonic generation, four-wave mixing, and stimulated Raman scattering) in plasma and gases irradiated by soft-X-ray lasers. Plasma media with ionic transition frequencies matching existing X-ray laser lines have been found and evaluated for potentially efficient transformations of the radiation of all the most powerful X-ray lasers reported to date. For Xray stimulated Raman scattering, resonant non-ionized media (atomic gases and vapors) have been proposed and evaluated.