Pulse-shape control of two-color interference in high-order-harmonic generation

We report on calculations of harmonic generation by neon in a mixed (800-nm + time-delayed 400-nm) laser pulse scheme. In contrast with previous studies we employ a short (few-cycle) 400-nm pulse, finding that this affords control of the interference between electron trajectories contributing to the cutoff harmonics. The inclusion of the 400-nm pulse enhances the yield and cutoff energy, both of which exhibit a strong dependence on the time delay between the two pulses. Using a combination of time-dependent $R$-matrix theory and a classical trajectory model, we assess the mechanisms leading to these effects.

Figure 1

Harmonic spectra produced by neon irradiated by (a) a six-cycle, 800-nm pulse and time-delayed six-cycle, 400-nm pulse; (b) a six-cycle, 800-nm pulse and a time-delayed 12-cycle, 400-nm pulse; and (c) a six-cycle, 800-nm pulse with two cycles at peak intensity and a time-delayed 12-cycle, 400-nm pulse. Insets show pictorially the two laser fields used.

Figure 2

A zoomed view of the spectral caustics for each of the laser pulse scenarios described in the caption of Fig. 1. The swallowtail caustics are marked with black lines in each.

Figure 3

The harmonic photon energy (blue dots) produced by electrons “born” at a given time during the laser pulse (red line) as calculated by a classical trajectory model, for a time delay of (a) 0.3 fs ($2\omega$ peak arriving just after the $\omega$ peak) and (b) 1.0 fs ($2\omega$ peak arriving just before the $\omega$ peak). Panel (a) generates one trajectory with the highest (cutoff) energy, while panel (b) generates two which interfere. The individual $2\omega$ and $\omega$ fields are shown in panels (c) and (d) where the positions of the optimal electron emission times are marked by black dots. The green shaded regions correspond to the overlap of two peaks or two troughs, while the unshaded (white) regions correspond to the overlap of a peak and trough. Thus trajectories launched in the green regions do so with higher probability, as the tunnel-ionization probability is increased.

Figure 4

Intensity of the spectral caustic (central panel) and cutoff energy (right panel) from neon irradiated by short (six-cycle) 800- and 400-nm pulses with varying time delay. The cutoffs of both the first (lower energy: blue dashed line) and second (higher energy: red solid line) plateaus are shown. The 800-nm pulse profile is shown for reference in the left panel. The time delays which give most intense caustic enhancement and the lowest or highest first or second cutoff are marked with the horizontal lines.

Figure 5

Integrated harmonic yield of the first (b) and second (a) plateaus arising in the harmonic spectra of neon exposed to two short laser pulses as described in Fig. 1. The variation of the yield, as marked by the horizontal lines, is periodic with half the period of the 400-nm pulse.