Enhanced Harmonic Generation from Expanding Clusters

We report controlled enhancement of optical third harmonic generation (THG) from hydrodynamically expanding clusters of $\sim 6\times {10}^5$ noble-gas atoms several hundred femtoseconds following ionization and heating by ultrashort pump pulses. This resonant enhancement is more pronounced for orthogonal than for parallel pump-probe polarizations, a consequence of faster cluster expansion along the pump polarization. Simulations show that the nonlinear susceptibility ${\chi }^{(3)}$ of the individual clusters and the coherence length of the clustered plasma medium are optimized nearly simultaneously as the clusters expand, and both contribute to the observed THG enhancement. This dual enhancement mechanism may be scalable to relativistic probe intensity and to generation of high-order harmonics in the soft-x-ray regime.

Figure 1

THG (filled circles) by and absorption (open squares) of a weak probe ($2\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$) following pump excitation at ${10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ with parallel pump and probe polarization. Identical absorption is observed with orthogonal polarizations. Solid curve is calculated from uniform density model; dashed curve guides the eye. Each data point represents a 300 shot average.

Figure 2

(a) Time-dependent, probe THG from clustered Ar jet for pump intensity ${10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, for various probe intensities with parallel pump-probe polarizations. Lower panels: $I_{\mathrm{probe}}$-dependence of (b) early THG peak and (c) delayed THG peak, compared to $I_{\mathrm{probe}}^3$.

Figure 3

Anisotropy of THG from expanding clusters, with pump and probe both at ${10}^{15}\mathrm{W}/{\mathrm{cm}}^2$ with parallel (filled squares) or perpendicular (filled circles) polarizations. Each THG data point represents a 100 shot average. Gray shading highlights the region of transient anisotropy.

Figure 4

Results of calculations for gas jet with ${10}^{18}{\mathrm{cm}}^{-3}$ atomic density (85% monomers $+15\%$ clusters) following excitation by ${10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, 400 nm, 100 fs pump: (a) time-dependent phase-mismatch function $|J_{3\omega }(L){|}^2$ (dashed curve) and $|{\chi }^{(3)}|$ (solid curve); (b) time-dependent THG by 800 nm probe pulses of indicated intensities.