Molecular quantum wake-induced pulse shaping and extension of femtosecond air filaments

Two-pulse excitation of a molecular quantum wake in air during filamentary propagation is shown to controllably shape an intense femtosecond probe pulse and to significantly extend the filament compared to single-pulse excitation. The effect is sensitive to pump-probe delay on a ∼10-fs time scale.

Figure 1

(a) Experimental setup showing the interferometer for measuring electron-density profiles and SPIDER for measuring the envelope and phase of the probe pulse. (b) Electron density at the center of the filament core vs distance (in cm) relative to the laser vacuum focus. Probe delays are all in advance of the air revival zero crossing at 8.341 ps. (c) Same as (b), except probe delays are closer to and beyond the zero crossing.

Figure 2

Left side: envelope $I$($t$) and phase Φ($t$) plots of the probe pulse exiting the two-pulse filament. The shortest pulse, with 21-fs FWHM, occurs in the range of $-$11 fs < $t_{\mathrm{R}}$ < 2 fs. For all probe delays, ∂${}^2$Φ/∂$t^2$ < 0 throughout the pulse envelope, indicating a dominant redshift to blueshift. Right side: Wigner plots corresponding to the plots on the left. The Wigner plot for the prefilamenting probe alone is shown highlighted in the upper left panel.

Figure 3

Density-matrix simulation of the self-consistent refractive index change experienced by a variably delayed 2 $\times$ 10${}^{13}$ W/cm${}^2$ 100-fs probe pulse perpendicularly polarized with respect to a similar pump pulse. The probe delays $t_{\mathrm{R}}$ are relative to the zero crossing of the pump-induced air rotational revival near 8.3 ps, shown as the dashed curve.

Figure 4

(a) Pump-induced index variation at first air revival as seen by the probe. The colored dots denote probe delays $t_{\mathrm{R}}$ relative to the revival zero crossing. From left to right, $t_{\mathrm{R}}$ $=$ $-$91, $-$78, $-$65, $-$52, $-$39, $-$26, $-$13, 0, 13, and 26 fs. Solid black curve: pump-alone and probe-alone curves are the same and sit under the first hump of the red-dashed curve. (b) Two-pulse axial electron-density profiles. Dashed curves are for $t_{\mathrm{R}}$ > 0. The ∼10-fs probe delay sensitivity of Fig. 1 is well reproduced. Solid black curve: pump-alone and probe-alone curves are the same and sit under the first hump of the red-dashed curve. (c) Probe pulse envelopes for delays before (grey) and after (red) the revival zero crossing. The shortest compressed pulse is 35 fs FWHM. The black curve is the initial probe envelope, and the brown curve is for $t_{\mathrm{R}}$ ∼ 0. Peak signals are normalized to unity.