Coherent extreme-ultraviolet radiation extending to wavelengths below
the carbon K edge at 4.37 nanometers (nm) has been generated at a repe
tition rate of 1 kilohertz by focusing 5-femtosecond near-infrared (78
0 nm) laser pulses into a helium gas jet. The incident light field per
forms just a few oscillations, which results in the emission of an x-r
ay supercontinuum rather than discrete harmonics. Owing to the extreme
ly short rise time of the driving pulses, neutral atoms can be exposed
to high fields before they are depleted by ionization. As a result, t
he observed x-ray radiation extends well into the water window and is
delivered in a well-collimated beam (divergence less than 1 milliradia
n). The high repetition rate and spatial coherence result in a brightn
ess of about 5 x 10(8) photons per square millimeter per square millir
adian per second in a 1-percent bandwidth at 4.37 nm, the carbon edge
of the water window. The compact laboratory system holds promise as a
source for biological holography and nonlinear optics in the x-ray reg
ime.