Nonlinear processes with X-rays

Summary form only given. We give an overview of research on nonlinear processes with X-rays, most of which have become feasible with the advent of soft X-ray lasers. We begin with the early theoretical and experimental work on X-ray nonlinear optics, which preceded the development of soft-X-ray lasers. This early research addressed mainly parametric conversion of X-rays in solids. After the first (soft) X-ray lasers were reported, the attention in X-ray nonlinear optics moved to the soft X-ray domain, with wavelengths between 300 /spl Aring/ and 40 /spl Aring/. We review recent theoretical research on resonant soft-X-ray nonlinear optics. Finally, we briefly address the new opportunities opened by the availability of intense and polarized coherent X-rays. In particular, we discuss the feasibility of high-order harmonic generation and difference-frequency mixing, which may result in X-ray coherent radiation around 10 /spl Aring/ and some applications of nonlinear polarization effects to plasma diagnostics.