Cluster size dependence of high-order harmonic generation

Abstract

High-order harmonic generation (HHG) in clusters (instead of separate gas atoms) is of high promise due to expanded options for quasi-phase matching and because clusters appeared to offer an increased optical nonlinearity [1]. To verify the latter, we investigate HHG from noble gas clusters in a supersonic gas jet. To identify a possible dependence of HHG on the average cluster size, we change the total atomic number density in the j et over a broad range (from 3 × 1016 cm−3 to 3 × 1018 cm−3) which maximize the variation in cluster size. For disentangling the contribution to HHG from clusters and gas monomers, we perform experiments at two different reservoir temperatures (303 K and 363 K), in order to vary the liquid mass fraction, g, for the same range of cluster sizes (see variation of g in Fig. 1). We note that this is actually the first time in the evaluation of the harmonic yield in such measurements that the dependence of, g, vs. pressure and temperature is taken properly into consideration, and we determine g, reliably and consistently, to lie below 20% in the parameter range in Fig. 1. 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 [2]. 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 [1] concluding that the single-atom response in small clusters (average cluster size < 700 atoms) 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.