We propose a new technique for phase matching high harmonic generation that can be used for generating bright, tabletop, tunable, and coherent x-ray sources at keV photon energies. A weak quasi-cw counterpropagating field induces a sinusoidal modulation in the phase of the emitted harmonics that can be used for correcting the large plasma-induced phase mismatch. We develop an analytical model that describes this grating-assisted x-ray phase matching and predicts that very modest intensities ($<{10}^{10}\mathrm{W}/{\mathrm{cm}}^2$) of quasi-cw counterpropagating fields are required for implementation.

• Received 19 April 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.053902