Sub-cycle millijoule-level parametric waveform synthesizer for attosecond science


The availability of high-energy pulses with durations shorter than the period of their carrier frequency (sub-cycle) will reveal new regimes of strong-field light–matter interactions. Parametric waveform synthesis (that is, the coherent combination of carrier-envelope-phase-stable pulses that emerge from different optical parametric amplifiers) is a promising technology for the realization of tailored optical waveforms with scalable spectral bandwidth, energy and average power. Here we use parametric waveform synthesis to generate phase-controlled sub-cycle waveforms at the millijoule energy level with excellent stability. Full control over the synthesized waveforms (currently spanning 1.7 octaves with full-width at half-maximum durations down to 2.8 fs, that is, 0.6 optical cycles at a central wavelength of 1.4 μm) enables the creation of extreme ultraviolet isolated attosecond pulses via high-harmonic generation without the need for additional gating techniques. The synthesized electric field is directly measured by attosecond-resolution sampling, which also showcases the waveform stability.

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Fig. 1: Optical scheme of the PWS.
Fig. 2: Spectro-temporal pulse characterization.
Fig. 3: Waveform stabilization and control.
Fig. 4: A CEP-controlled EUV spectrum and IAP energy stability.
Fig. 5: Attosecond streaking and extracted waveform.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

Code availability

The code that supports the plots within this paper and other findings of this study is available from the corresponding author on reasonable request.


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We gratefully acknowledge support from Deutsches Elektronen-Synchrotron (DESY) of the Helmholtz Association, from the Cluster of Excellence ‘CUI: Advanced Imaging of Matter’ of the Deutsche Forschungsgemeinschaft (DFG)—EXC 2056—project ID 390715994 and from the priority programme ‘Quantum Dynamics in Tailored Intense Fields’ (QUTIF) (SPP1840 SOLSTICE) of the DFG. We thank H. Cankaya and L. Wang for many valuable discussions and theory support.

Author information




G.M.R. and R.E.M. designed and implemented the optical/mechanical set-up and its waveform stabilization/control infrastructure. Y.Y. designed and implemented the attosecond beamline. F.S. and M.A.S.-T. contributed to the pulse characterization and analysis of the streaking data jointly with P.D.K. S.-H.C. and F.X.K. designed the dichroic/chirped mirrors. G.M.R., R.E.M., Y.Y., F.S. and M.A.S.-T. conducted the experiments. G.M.R., R.E.M. and Y.Y. co-wrote the paper with contributions from all authors. F.X.K. conceived the initial parallel synthesizer scheme and first implementations were worked out jointly with C.M., G. Cirmi, G. Cerullo, O.D.M. and S.F. The PWS project was supervised by G. Cirmi and F.X.K.

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Correspondence to Giulio Maria Rossi.

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Rossi, G.M., Mainz, R.E., Yang, Y. et al. Sub-cycle millijoule-level parametric waveform synthesizer for attosecond science. Nat. Photonics (2020).

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