We demonstrate enhanced generation of coherent light in the "water window" region of the soft x-ray spectrum at 4.4 nanometers, using quasi-phase-matched frequency conversion of ultrafast laser pulses. By periodically modulating the diameter of a gas-filled hollow waveguide, the phase mismatch normally present between the laser light and the generated soft x-ray light can be partially compensated. This makes it possible to use neon gas as the nonlinear medium to coherently convert light up to the water window, illustrating that techniques of nonlinear optics can be applied effectively in the soft x-ray region of the spectrum. These results advance the prospects for compact coherent soft x-ray sources for applications in biomicroscopy and in chemical spectroscopy.
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