Lawrence Berkeley National Laboratory

Since the invention of the laser, nonlinear effects such as filamentation1, Rabi cycling2,3 and collective emission4 have been explored in the optical regime, leading to a wide range of scientific and industrial applications5, 6, 7–8. X-ray free-electron lasers (XFELs) have extended many optical techniques to X-rays for their advantages of ångström-scale spatial resolution and elemental specificity9. An example is XFEL-driven inner-shell Kα1 (2p3/2 → 1s1/2) X-ray lasing in elements ranging from neon to copper, which has been used for nonlinear spectroscopy and development of new X-ray laser sources10, 11, 12, 13, 14, 15–16. Here we show that strong lasing effects similar to those in the optical regime can occur at 1.5–2.1 Å wavelengths during high-intensity (>1019 W cm−2) XFEL-driven Kα1 lasing of copper and manganese. Depending on the temporal XFEL pump pulse substructure, the resulting X-ray pulses (about 106−108 photons) can exhibit strong spatial inhomogeneities and spectral splitting, inhomogeneities and broadening. Three-dimensional Maxwell–Bloch calculations17 show that the observed spatial inhomogeneities result from X-ray filamentation and that the broad spectral features are driven by sub-femtosecond Rabi cycling. Our simulations indicate that these X-ray pulses can have pulse lengths of less than 100 attoseconds and coherence properties that provide opportunities for quantum X-ray optics applications.