Quasi-phase-matching of high-order harmonics using a modulated atomic density

We present a numerical study of high-order harmonic generation in a gas medium with spatial modulation of the density. We show that, by adjusting the modulation period, the contributions of the short and long quantum paths to harmonic emission can be selectively quasi-phase-matched on axis. In particular, quasi-phase-matching of the short path contribution dramatically improves the spatial and spectral properties of the harmonic beam, increasing peak brightness by a factor close to 40 for the 45th harmonic of a Ti:sapphire laser at $17.8\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. Finally, simultaneous or selective quasi-phase-matching of the short and long paths makes it possible to control their relative weight.

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