Gouy Phase Shift for Few-Cycle Laser Pulses

We measured for the first time the influence of the Gouy effect on focused few-cycle laser pulses. The carrier-envelope phase is shown to undergo a smooth variation over a few Rayleigh distances. This result is of critical importance for any application of ultrashort laser pulses, including high-harmonic and attosecond pulse generation, as well as phase-dependent effects.

Figure 1

Schematic of the experimental setup. W: pair of glass wedges to control the CE phase; M: flat mirror; F: focusing spherical mirror ($f=250\mathrm{mm}$); MCP: microchannel plates; S: moveable slits ($\mathrm{width}=250\mu \mathrm{m}$). The angle of incidence on the focusing mirror is minimized to reduce astigmatism.

Figure 2

Varying the glass thickness in the beam path changes the CE phase of the pulses. The left$/$right ratio of the electron yield exhibits clear oscillations with a periodicity consistent with glass dispersion at the wavelength of the laser. The measurement was performed before (dashed line) and after (solid line) the focus. The $\pi$ phase shift is due to the Gouy CE phase shift in passing through the focus.

Figure 3

Left$/$right asymmetry maps (logarithmic scale) for different longitudinal positions as a function of the electron energy and glass thickness introduced. Reddish colors indicate dominant left emission; bluish colors dominant right emission. The maps (a)–(f) correspond, respectively, to the positions: $z=-1.75\mathrm{mm}$, $z=-1.0\mathrm{mm}$, $z=-0.25\mathrm{mm}$, $z=+0.25\mathrm{mm}$, $z=+1.0\mathrm{mm}$, $z=+1.75\mathrm{mm}$ (positive values represent positions after the focus). The phase difference is determined by evaluating the shift of the characteristic structures (indicated by the dashed lines) of the asymmetry pattern. The extension of the electron yield to higher energies in the central part of the focus is due to the higher intensity.

Figure 4

Retrieved CE Gouy phase shift as a function of the propagation distance in the focus. The solid line is the Gouy phase of a cw Gaussian beam, shown for comparison. Note that, in the outer part of the focus, the electron count rate rapidly decreases, making detection of additional experimental points difficult.