Phase matching of high-order harmonics in a semi-infinite gas cell

Phase matching of high-order harmonic generation is investigated experimentally for various parameters in a semi-infinite gas-cell (SIGC) geometry. The optimized harmonic yield is identified using two different noble gases (Xe and He) and its parameter dependence is studied in a systematic way. Beside the straightforward setup of the SIGC, this geometry promises a high photon flux due to a large interaction region. Moreover, since the experimental parameters within this cell are known accurately, direct comparison to simulations is performed. Spectral splitting and blueshift of high-order harmonics are observed.

Figure 1

(Color online) Experimental setup. The fundamental laser pulse is focused into the semi-infinite gas cell (see inlet) with a self-drilled pinhole exit. This abrupt transition to vacuum assures absorptionless propagation of the harmonic beam into the spectrometer.

Figure 2

(Color online) Variation in the focus position in 70 mbar helium for a lens with focal length of $f=450\text{mm}$. (a) Sketch of the focus position relative to the gas cell with indication of the interaction region. At position $z_f=0\text{mm}$, the focus is centered at the cell exit. Negative positions indicate that the focus is contained within the gas cell. The arrows indicate the positions of the three cases at subfigure (b). (b) Experimental harmonic peak intensities versus focus position on a logarithmic color (gray) scale. The red solid line shows the position of the maximum peak intensity of a harmonic (same for other presented maps in this paper). [(c)–(e)] Comparison between experiment $(\times )$ and simulation $(+)$ for different harmonic orders (as labeled).

Figure 3

(Color online) Variation in the focus position for different focal lengths: experimental harmonic peak intensities versus focus position on a logarithmic color (gray) scale for a focal length of (a) $f=920\text{mm}$ in 30 mbar helium and (b) $f=280\text{mm}$ in 70 mbar helium. See Fig. 2 for a focal length $f=450\text{mm}$. (c) Phase-matching range (see text) of harmonic H59 versus focus position for 30 mbar and 70 mbar helium, respectively.

Figure 4

(Color online) Experimental $(\times )$ and simulated $(+)$ harmonic peak intensities versus [(a)–(c)] helium and [(d)–(f)] xenon gas pressure for different harmonic orders (labeled). The lens with 450 mm focal length is kept at a fixed position $\left(z_f\approx 0\right)$. The solid line shows a fit for low pressure to a $p^2$ law.

Figure 5

(Color online) Variation in the focus position in 5 mbar xenon. Experimental harmonic peak intensities versus focus position for a lens with focus length $f=450\text{mm}$ on a logarithmic color (gray) scale. Note that the spectra are interpolated between harmonic orders and focus positions for better visualization.

Figure 6

Experimental results on variation in the focus position $z_f$ in 5 mbar xenon using a 450-mm-focal-length lens. Blueshift and spectral splitting and broadening of the harmonics are visible.

Figure 7

Blueshift and spectral splitting and broadening of harmonics in xenon: dependence on pressure and pulse energy. Spectrum of harmonic (a) H11, and (b) H17 are shown at a fixed focus position $\left(z_f\approx 0\text{mm}\right)$ for different pressure (450 mm lens). (c) Spectrum of harmonic H15 at a fixed position and pressure ($-5\mathrm{mm}$; $5\mathrm{mbar}$) with varying pulse energy (280 mm lens).