Difference-Frequency Generation of Optical Radiation from Two-Color X-Ray Pulses

The nonlinear interactions between X-rays and optical radiation were first described about forty years ago by Freund & Levine [1] and by Eisenberger & McCall [2]. These studies addressed several nonlinear processes including parametric-down conversion of X-rays into the optical region, sum and difference-frequency generation of X-rays and optical pulses. However, until very recently there was no experimental evidence for any of those effects due to the absence of sufficiently bright X-ray sources. Recently, the new X-ray free-electron lasers have enabled the observation of X-ray and optical frequency mixing [3]. 
A new development in X-ray free-electron lasers has opened the possibility to generate two X-ray ultrashort pulses at different central wavelengths, with controllable delay between them. Motivated by this development, we studied the generation of short optical pulses from the X-ray pulses via the process of difference-frequency generation. We found that since the X-ray damage threshold is much higher than the optical damage threshold, the efficiency of difference-frequency generation from two X-ray pulses is orders of magnitude higher than the efficiency of frequency mixing between X-rays and optical intense short-pulses. Moreover, we show that the effect can be used for microscopic studies of chemical bonds and as a probe for light-matter interactions on the atomic scale and with temporal resolution on the order of 10 fs with the current performances of X-ray free-electron lasers. 
References and links
1.    I. Freund and B. F. Levine, “Optically modulated X-ray diffraction,” Phys. Rev. Lett. 25(18), 1241-1245 (1970).
2.    P. M. Eisenberger and S. L. McCall. “Mixing of X-ray and optical photons,” Phys. Rev. A 3(3), 1145-1151 (1971).
3.    T. E. Glover, D. M. Fritz, M. Cammarata, T. K. Allison, Sinisa Coh, J. M. Feldkamp, H. Lemke, D. Zhu, Y. Feng, R. N. Coffee, M. Fuchs, S. Ghimire, J. Chen, S. Shwartz, D. A. Reis, S. E. Harris and J. B. Hastings, “X-ray and optical wave mixing,” Nature 488(7413), 603-608  (2012).