High-order harmonic generation in the presence of a chirped THz pulse is investigated numerically with a complete 3D non-adiabatic model. The assisting THz pulse illuminates the HHG gas cell laterally inducing quasi-phase-matching. We demonstrate that it is possible to compensate the phase mismatch during propagation and extend the macroscopic cutoff of a propagated strong IR pulse to the single-dipole cutoff. We obtain two orders of magnitude increase in the harmonic efficiency of cutoff harmonics ($approx$170 eV) using a THz pulse of constant wavelength, and a further factor of 3 enhancement when a chirped THz pulse is used.
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