High harmonic generation in the relativistic limit

The generation of extremely bright coherent X-ray pulses in the femtosecond and attosecond regime is currently one of the most exciting frontiers of physics - allowing, for the first time, measurements with unprecedented temporal resolution(1-6). Harmonics from laser - solid target interactions have been identified as a means of achieving fields as high as the Schwinger limit(2,7) (E = 1.3 x 10(16) V m(-1)) and as a highly promising route to high-efficiency attosecond (10(-18) s) pulses(8) owing to their intrinsically phase-locked nature. The key steps to attain these goals are achieving high conversion efficiencies and a slow decay of harmonic efficiency to high orders by driving harmonic production to the relativistic limit(1). Here we present the first experimental demonstration of high harmonic generation in the relativistic limit, obtained on the Vulcan Petawatt laser(9). High conversion efficiencies (eta> 10(-6) per harmonic) and bright emission (> 10(22) photons s(-1) mm(-2) mrad(-2) (0.1% bandwidth)) are observed at wavelengths <4 nm ( the 'water-window' region of particular interest for bio-microscopy).