High-energy mid-infrared sub-cycle pulse synthesis from a parametric amplifier

High-energy phase-stable sub-cycle mid-infrared pulses can provide unique opportunities to explore phase-sensitive strong-field light–matter interactions in atoms, molecules and solids. At the mid-infrared wavelength, the Keldysh parameter could be much smaller than unity even at relatively modest laser intensities, enabling the study of the strong-field sub-cycle electron dynamics in solids without damage. Here we report a high-energy sub-cycle pulse synthesiser based on a mid-infrared optical parametric amplifier and its application to high-harmonic generation in solids. The signal and idler combined spectrum spans from 2.5 to 9.0 µm. We coherently synthesise the passively carrier-envelope phase-stable signal and idler pulses to generate 33 μJ, 0.88-cycle, multi-gigawatt pulses centred at ~4.2 μm, which is further energy scalable. The mid-infrared sub-cycle pulse is used for driving high-harmonic generation in thin silicon samples, producing harmonics up to ~19th order with a continuous spectral coverage due to the isolated emission by the sub-cycle driver.


Supplementary Figure 5:
Cross-referencing f-3f spectral interferometry for characterizing shot-to-shot carrier-envelope phase stability of idler pulses. (a) The setup schematic of the cross-referencing spectral interferometery (SI) measurement (colour online). The 2.1-µm polarization-rotated residual pump pulse (purple color), which is found to have narrower spectrum than the original pump spectrum, is focused to a 1-mm-thick ZGP crystal for the moderate spectral broadening through self-phase modulation (blue color), together with the collinear idler pulse (yellow color) spanning from 4.4 to 9 µm. The collinear pulses are then focused to another 0.5-mm-thick ZGP to generate the third-harmonic (TH) of the idler in the wavelength of 1.7 to 2.4 µm (red color), with the optimized phase-matching angle of the ZGP crystal. The spectrally overlapped TH of the idler and the broadened pump pulses are coupled into a spectrometer with InGaAs detectors (Ocean Optics, Inc.) for the SI measurement. The polarization of the 2.1-µm polarization-rotated residual pump and the idler pulses is marked by concentric circles. (b) The spectra of the spectrally broadened, 2.1-µm residual pump pulse (blue) and the TH of the idler pulse (red). (c) The interference spectrum of the broadened polarizationrotated pump and the TH of the idler pulses with 1 ms of integration time for the single-shot measurement. idler pulses is recorded over 2 hours using a pyroelectric detector (Molectron, Coherent Inc.). The pump energy is ~0.65 mJ and the 3-11 µm filter (~80% transmission) is used for blocking background optical noises. The shot-to-shot energy fluctuation is measured as ~2.7% rms over 10,000 shots, while the intermediate-term oscillation of the mean pulse energy is measured as ~7% peak-to-peak over ~10 minutes of period which corresponds to the on/off operation of the air conditioner in the laboratory. However, there is no long-term drift of the pulse energy observed over several hours. The significant drop of the pulse energy at ~90 minutes of time is due to the manual adjustment of the beam pointing stabilizers in the cryogenic Yb:YAG pump laser and the 2.1 µm optical parametric chirped pulse amplifier when they go out of the range, which occasionally happens.

Supplementary Note 1: CEP control of the synthesized pulse
The absolute carrier-envelope phase (CEP) of the synthesized pulse can be shifted using a low-dispersive wedge pair.
For example, we can use a 1.2-mm-thick wedge pair made of caesium iodide (CsI) which has very flat dispersion from 2 to 10 µm to change the CEP by 2π while the sub-cycle duration is maintained, as shown in Supplementary Fig. 10 below. However, due to the ultrabroad spectral bandwidth, it is challenging to shift the CEP much more than 2π without distorting the pulse shape with sub-cycle duration. Figure 10: Calculated CEP change of the synthesized pulse with regard to the thickness of CsI. The CEP of signal and idler pulses before a CsI window is preset to be 1.5π and 0π, respectively, as shown in (a). The CEP of the combined pulse can be shifted up to 2π using the 1.2-mm-thick CsI window (e) while the sub-cycle pulse duration is maintained. However, the groupdelay dispersion (GDD) and third-order dispersion (TOD) eventually broadens and distorts the pulse shape if the excessive thickness is used for CEP shift.

Supplementary
Besides the CEP shift of the synthesized pulse, the individual CEP of the signal and idler pulses can simultaneously be accessed via the CEP adjustment of the pump pulse before and after the white light generation (WLG) stage, respectively. We discuss how we can access the individual CEP as below.
Since the signal pulse has a constant relative phase to the pump pulse in the WLG process, the signal CEP is changed accordingly with the CEP shift of the pump pulse. It is relatively straightforward to change the CEP of the CEP-stable 26 fs, 2.1 µm pump pulse before the WLG stage using the techniques basically the same as what has been known for near-IR lasers, i.e., CEP-stable Ti:sapphire laser amplifiers. Here, we suggest two specific methods: 1) the use of a thin wedge pair made of low-dispersion BaF2 which has zero dispersion at ~1.9 µm and 2) the use of an acousto-optic programmable dispersive filter (AOPDF; Dazzler, Fastlite) installed in our 2.1 µm optical parametric chirped pulse amplifier. Since the phase of RF pulse driving the Dazzler is locked to the mode-locked pulse train, the RF phase can be transferred to the optical pulse in the process of acousto-optic pulse shaping. Unlike a wedge pair we don't need to add any optical component to change the pump CEP. We actually tested the second method and observed the CEPdependence of solid-state HHG results which are under further investigations. In either way, changing the signal CEP provides a partialcontrol knob for accessing the CEP of synthesized pulse and also allows presetting the signal CEP to a certain value.
On the other hand, the idler CEP is determined by the relative phase between the signal and pump pulses. Therefore, by adding another thin BaF2 wedge pair for the pump after the WLG stage to control the relative phase between the pump and signal pulses, we can change the idler CEP without affecting the signal CEP. It should be noted that a precise compensation of delay between the pump and signal pulses is required for not affecting the OPA performance whenever this wedge pair is tuned. This additional wedge pair enables to access and preset the CEP of the idler pulse without changing the signal CEP.
Based on the above arguments, we come up with a procedure of controlling the CEP of combined (synthesized) pulse as follows: -First, we optimize the OPA to obtain the shortest pulse duration and minimal pedestal (which is the case of current research), by properly adjusting the individual CEP of the signal and idler pulses in addition to the pump-signal delay. Once we find an optimal condition (say, "preset" condition), we do not change the individual CEP of signal and idler pulses.
-Second, we shift the CEP of the combined pulse using a CsI wedge pair, as shown in Supplementary Fig. 10, for the application experiments like HHG.
In summary, we show that the CEP control of the demonstrated pulse synthesis system is feasible.