Terahertz emission by X-ray difference-frequency generation

Nonlinear interactions between X-rays and matter represent a new frontier in ultrafast science. However, X-ray difference-frequency generation (DFG)—a fundamental second-order nonlinear optical process—has not been experimentally observed until now. Here, we report the first observation of terahertz emission induced by hard X-ray free-electron laser (XFEL) pulses in solids, providing evidence for X-ray DFG. Using 10-fs, 10-keV XFEL pulses incident on ZnTe, we detected terahertz emission arising from wave mixing between different spectral components within the XFEL bandwidth. The emitted terahertz waves originate from second-order nonlinear polarization evolving on a femtosecond timescale. The polarization and angular dependences of the terahertz emission confirm that X-ray DFG is mediated not only by DFG without spatial inversion symmetry but also by DFG with spatial inversion symmetry. Quantitative analysis yields a DFG susceptibility ratio of the former to the latter of 58±4%, and the generation efficiency for 10 keV excitation is approximately 1% of that for near-infrared 1.55 eV excitation in the 100-μm-thick ZnTe crystal, while the intrinsic response normalized by interaction length is comparable. These results establish XFEL-induced terahertz emission as a general platform for probing second-order X-ray nonlinearities and ultrafast polarization dynamics in solids.