Figure 3: Harmonic spectra from three-colour optimized waveforms.

The two secondary colours are the second and third harmonics of the fundamental wave, which is 1,600 nm. (a) The waveforms of the top three optimized pulses (laser parameters for Index=1, 2 and 3 are given in Supplementary Table 1). All three waveforms have comparable electric fields near the ionization times (close to −0.4 optical cycles in the figure). The inset shows the electric fields at ionization times for long- and short-trajectory electrons calculated using classical theory (for Index=1 in Supplementary Table 1). (b) Single-atom harmonic spectra (smoothed by using the Bezier curve) for the three top optimized pulses showing nearly identical yields. All of them are two orders stronger than the single colour one. The peak intensity for the single-colour laser is 3.0 I₀ (I₀=10¹⁴ W cm⁻²). The total peak intensity for the optimized wave is about 3.5 I₀. The harmonic spectra were generated for a three-cycle pulse (16 fs) for the fundamental wave. The same pulse durations are used for the two other waves. (c) Time-frequency analysis of the harmonic emission, showing one emission per optical cycle of the fundamental wave. The second emission within each cycle is much weaker. This is expected since the waveform shown in a indicates that the peak field in the second half optical cycle is 20–30% weaker compared with the peak field in the first half optical cycle. (d) Macroscopic HHG spectra at two gas pressures of 10 and 100 Torr, respectively. The harmonics beyond 210 eV are continuous that is good for generating isolated attosecond pulses.