Figure 2: Harmonic generation by a sinusoidal and an optimized two-colour fields.

The fundamental pulse is a three-cycle (duration is 16 fs), 1,600 nm pulse. The secondary pulse is its third harmonic. For the single-colour wave, the peak intensity is taken at 3.0 I₀ (I₀=10¹⁴ W cm⁻²). The laser parameters of the two colours for the optimized wave are given in the text. The total pulse energy for the synthesized wave is 10% higher than the single-colour pulse. (a) Single-atom harmonic yields for the two waves, showing that the optimized wave is about two orders stronger than the single-colour one. (b) The yields of high harmonics after macroscopic propagation. In the simulation, the lasers with beam waist of 40 μm are focused 2.5 mm before a 1-mm long gas jet. The gas pressure is 10 Torr. Blue curves in a and b show the smoothed spectra. (c) Time-frequency analysis of the bursts of harmonics generated by the optimized wave at the single-atom level, showing short-trajectory electrons dominate over long-trajectory electrons. The weak signals (features inside each ‘burst’) at lower kinetic energies are contributions from multiple returns. (d) Time-frequency analysis of the bursts of harmonics after propagation in the gas medium for the optimized wave. All the harmonics from long-trajectory electrons and from multiple returns disappear. This figure illustrates that enhancing short-trajectory electrons from each single-atom response is essential for optimizing the yields of macroscopic harmonics. (e) Single-atom harmonics generated using a single-colour sinusoidal wave, showing strong signals from long-trajectory electrons and from multiple returns (features inside each ‘burst’). (f) Propagated harmonics generated using single-colour sinusoidal waves. This figure shows that most of the harmonics from long-trajectory electrons and multiple returns do not survive phase-matching. Only harmonics from short-trajectory electrons are phase-matched. (o.c. stands for optical cycle of a 1600-nm laser.)