Cluster size dependence of high-order harmonic generation

We investigate high-order harmonic generation (HHG) from noble gas clusters in a supersonic gas jet. To identify the contribution of harmonic generation from clusters versus that from gas monomers, we measure the high-order harmonic output over a broad range of the total atomic number density in the jet (from 3x10^{16} cm^{-3} to 3x10^{18} cm^{-3}) at two different reservoir temperatures (303 K and 363 K). For the first time in the evaluation of the harmonic yield in such measurements, the variation of the liquid mass fraction, g, versus pressure and temperature is taken into consideration, which we determine, reliably and consistently, to be below 20% within our range of experimental parameters. Based on measurements with a thin jet where significant variations in reabsorption and the phase matching conditions can be neglected, we conclude that atoms in the form of small clusters (average cluster size < 1000 atoms) provide the same higher-order nonlinear response as single-atoms. This implies that HHG in small clusters is based on electrons that return to their parent ions and not to neighbouring ions in the cluster. This conclusion is consistent with the measured harmonic spectra showing no obvious changes of the cut-off wavelength. Our results are in clear contrast to previous work concluding that the single-atom response in small clusters increases with the cluster size, thereby promising a higher output than with monomers. Cluster may still increase the yield of high-order harmonic generation, however, not via the single-atom response but possibly via quasi-phase matching, as the higher mass of clusters allows for a higher density contrast in spatially structuring the nonlinear medium.