Characterization of cluster/monomer ratio in pulsed supersonic gas jets

Cluster mass fraction is an elusive quantity to measure, calculate or estimate accurately for pulsed supersonic gas jets typical of intense laser experiments. The optimization of this parameter is critical for transient phase-matched harmonic generation in an ionized cluster jet at high laser intensity. We present an in-depth study of a rapid, noninvasive, single-shot optical method of determining cluster mass fraction f_c(r,t) at specified positions r within, and at time t after opening the valve of, a high-pressure pulsed supersonic gas jet. A ∼ 2 mJ fs pump pulse ionizes the monomers, causing an immediate drop in the jet’s refractive index n_jet proportional to monomer density, while simultaneously initiating hydrodynamic expansion of the clusters. The latter leads to a second drop in n_jet that is proportional to cluster density and is delayed by ∼ 1 ps. A temporally stretched probe pulse measures the 2-step index evolution in a single shot by frequency domain holography, enabling recovery of f_c. We present the theory behind recovery of f_c in detail. We also present extensive measurements of spatio-temporal profiles f_c(r, t) of cluster mass fraction in a high-pressure supersonic argon jet for various values of backing pressure P, and reservoir temperature T.