X-Ray Second Harmonic Generation

We report clear experimental evidence for second harmonic generation at hard x-ray wavelengths. Using a 1.7 Å pumping beam generated by a free electron laser, we observe second harmonic generation in diamond. The generated second harmonic is of order 10 times the background radiation, scales quadratically with pump pulse energy, and is generated over a narrow phase-matching condition. Of importance for future experiments, our results indicate that it is possible to observe nonlinear x-ray processes in crystals at pump intensities exceeding 1016 W/cm2