We report the experimental observation of an enhancement in the yield of high-order harmonics using an array of gas jets as the source medium. By comparing the experimental outcome for jet arrays of different spacings with the predicted harmonic intensity in the case of slit sources of equivalent lengths, we clearly show how the periodic modulation of the gas density can improve the harmonic yield. This behavior may attributed to a quasi-phase-matching effect which increases the length of coherent harmonic build-up during propagation by partially counteracting the dephasing induced by free electrons.PACS numbers: 32.80. Rm,42.65.Ky,32.80.Fb Keywords: Since its discovery in 1987 [1], the phenomenon of highorder harmonic generation (HHG) has become one of the most interesting topics in the field of highly nonlinear processes. Apart from its fundamental physics interest, HHG is now one of the most promising ways to obtain tunable, short-pulse, narrow-band radiation in the vacuum and extreme ultraviolet (VUV and XUV), and in the soft X-ray regions, where other coherent sources are scarcely available. However, the possibility of using high-order harmonics as a table-top VUV-XUV coherent source for applications is strongly connected to the optimization of the brightness of the source over the broadest spectral range.As in many other nonlinear processes, conversion efficiency in HHG depends on the interplay between the single-atom response [2] and the macroscopic response during propagation in the medium [3]. In particular, a constructive interference of the harmonic field emitted from different locations of the source length can only be obtained over the so-called coherence length L c . For media longer than L c , destructive interference soon depletes the generated field and dramatically limits the conversion efficiency. By an appropriate choice of the interaction parameters it is often possible to make the coherence length longer than the medium, thus reaching the so-called phase-matching conditions. However, when phase-matching is not achievable, one can still artificially beat the coherence length limits by properly modulating the interaction parameters along the field propagation direction. Examples of such quasi-phase-matching (QPM) techniques now abound for low-order nonlinear phenomena in structured crystals, and a few examples have been recently demonstrated in HHG. Many different phenomena contribute to limit the coherence length in HHG. Here, the atomic dispersion and the geometric Guoy phase [4,5], are always accompanied by the dispersion connected to free electrons in the partially ionized medium [6,7], and by the characteristic atomic dipole phase [8,9,10,11,12]. Depending on the gas type and density, and on the level of ionization, the coherence length in HHG is usually so short as to pose a serious limit to significant conversion efficiencies. Differently from QPM in periodically-poled nonlinear crystals [13], where the sign of the nonlinear coefficient is periodically flipped so as to always add c...

We report the first direct measurements of the atomic dipole phase in the process of high-order harmonic generation. Differently from previously reported studies based on frequency chirp measurements, we use extreme ultraviolet interferometry as the most natural and direct way to measure phase shifts. Our approach has the important advantage of allowing us to investigate the effects associated to both the main quantum paths involved in the emission of a particular harmonic, thus offering a particularly clear and simple picture of the underlying electronic dynamics.

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