Quasi-phase matching of high-order harmonic generation at high photon energies using counterpropagating pulses

We extend all-optical quasi-phase matching of high-order harmonic generation into spectral regions where conventional phase matching is not possible. The high laser intensities required to generate harmonics at energy $>130\mathrm{eV}$, coupled with the resulting high level of ionization, preclude conventional phase matching in all nonlinear media. Selective enhancement factors between 40 and 150 in the flux of harmonics at photon energies around $140\mathrm{eV}$ are demonstrated using a train of two counterpropagating pulses.