Abstract
Recently, the field of optical frequency combs experienced a major development of new sources. They are generally much smaller in size (on the scale of millimetres) and can extend frequency comb emission to other spectral regions, in particular towards the mid- and far-infrared regions. Unlike classical pulsed frequency combs, their mode-locking mechanism relies on four-wave-mixing nonlinear processes, yielding a non-trivial phase relation among the modes and an uncommon emission time profile. Here, by combining dual-comb multi-heterodyne detection with Fourier-transform analysis, we show how to simultaneously acquire and monitor over a wide range of timescales the phase pattern of a generic (unknown) frequency comb. The technique is applied to characterize both a mid-infrared and a terahertz quantum cascade laser frequency comb, conclusively proving the high degree of coherence and the remarkable long-term stability of these sources. Moreover, the technique allows also the reconstruction of the electric field, intensity profile and instantaneous frequency of the emission.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.
References
Jones, D. J. et al. Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis. Science 288, 635–639 (2000).
Diddams, S. A. et al. Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb. Phys. Rev. Lett. 84, 5102–5105 (2000).
Holzwarth, R. et al. Optical frequency synthesizer for precision spectroscopy. Phys. Rev. Lett. 85, 2264–2267 (2000).
Udem, T., Holzwarth, R. & Hänsch, T. W. Optical frequency metrology. Nature 416, 233–237 (2002).
Diddams, S. A. The evolving optical frequency comb. J. Opt. Soc. Am. B 27, B51 (2010).
Faist, J. et al. Quantum cascade laser. Science 264, 553–556 (1994).
Beck, M. et al. Continuous wave operation of a mid-infrared semiconductor laser at room temperature. Science 295, 301–305 (2002).
Köhler, R. et al. Terahertz semiconductor-heterostructure laser. Nature 417, 156–159 (2002).
Tombez, L. et al. Wavelength tuning and thermal dynamics of continuous-wave mid-infrared distributed feedback quantum cascade lasers. Appl. Phys. Lett. 103, 031111 (2013).
Consolino, L., Cappelli, F., Siciliani de Cumis, M. & De Natale, P. QCL-based frequency metrology from the mid-infrared to the THz range: a review. Nanophotonics 8, 181–204 (2018).
Faist, J. Quantum Cascade Lasers (Oxford Univ. Press, 2013).
Hugi, A., Villares, G., Blaser, S., Liu, H. C. & Faist, J. Mid-infrared frequency comb based on a quantum cascade laser. Nature 492, 229–233 (2012).
Malara, P. et al. External ring-cavity quantum cascade lasers. Appl. Phys. Lett. 102, 141105 (2013).
Faist, J. et al. Quantum cascade laser frequency combs. Nanophotonics 5, 272–291 (2016).
Wang, C. Y. et al. Mode-locked pulses from mid-infrared quantum cascade lasers. Opt. Express 17, 12929–12943 (2009).
Revin, D. G., Hemingway, M., Wang, Y., Cockburn, J. W. & Belyanin, A. Active mode locking of quantum cascade lasers in an external ring cavity. Nat. Commun. 7, 11440 (2016).
Barbieri, S. et al. Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis. Nat. Photon. 5, 306–313 (2011).
Wang, F. et al. Short terahertz pulse generation from a dispersion compensated modelocked semiconductor laser. Laser Photon. Rev. 11, 1700013 (2017).
Riedi, S., Hugi, A., Bismuto, A., Beck, M. & Faist, J. Broadband external cavity tuning in the 3−4 μm window. Appl. Phys. Lett. 103, 031108 (2013).
Riedi, S. et al. Broadband superluminescence, 5.9 μm to 7.2 μm, of a quantum cascade gain device. Opt. Express 23, 7184–7189 (2015).
Burghoff, D. et al. Terahertz laser frequency combs. Nat. Photon. 8, 462–467 (2014).
Rösch, M., Scalari, G., Beck, M. & Faist, J. Octave-spanning semiconductor laser. Nat. Photon. 9, 42–47 (2014).
Friedli, P. et al. Four-wave mixing in a quantum cascade laser amplifier. Appl. Phys. Lett. 102, 222104 (2013).
DeLong, K. W., Trebino, R., Hunter, J. & White, W. E. Frequency-resolved optical gating with the use of second-harmonic generation. J. Opt. Soc. Am. B 11, 2206–2215 (1994).
Freeman, J. R. et al. Electric field sampling of modelocked pulses from a quantum cascade laser. Opt. Express 21, 16162–16169 (2013).
Villares, G., Hugi, A., Blaser, S. & Faist, J. Dual-comb spectroscopy based on quantum-cascade-laser frequency combs. Nat. Commun. 5, 5192 (2014).
Cappelli, F. et al. Frequency stability characterization of a quantum cascade laser frequency comb. Laser Photon. Rev. 10, 623–630 (2016).
Cappelli, F., Villares, G., Riedi, S. & Faist, J. Intrinsic linewidth of quantum cascade laser frequency combs. Optica 2, 836–840 (2015).
Burghoff, D. et al. Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs. Opt. Express 23, 1190–1202 (2015).
Singleton, M., Jouy, P., Beck, M. & Faist, J. Evidence of linear chirp in mid-infrared quantum cascade lasers. Optica 5, 948–953 (2018).
Keilmann, F., Gohle, C. & Holzwarth, R. Time-domain mid-infrared frequency-comb spectrometer. Opt. Lett. 29, 1542–1544 (2004).
Coddington, I., Newbury, N. & Swann, W. Dual-comb spectroscopy. Optica 3, 414–426 (2016).
Chen, Z., Yan, M., Hänsch, T. & Picqué, N. A phase-stable dual-comb interferometer. Nat. Commun. 9, 3035 (2018).
Galli, I. et al. High-coherence mid-infrared frequency comb. Opt. Express 21, 28877–28885 (2013).
Galli, I. et al. Mid-infrared frequency comb for broadband high precision and sensitivity molecular spectroscopy. Opt. Lett. 39, 5050–5053 (2014).
Campo, G. et al. Shaping the spectrum of a down-converted mid-infrared frequency comb. J. Opt. Soc. Am. B 34, 2287–2294 (2017).
Consolino, L. et al. Phase-locking to a free-space terahertz comb for metrological-grade terahertz lasers. Nat. Commun. 3, 1040 (2012).
Bartalini, S. et al. Frequency-comb-assisted terahertz quantum cascade laser spectroscopy. Phys. Rev. X 4, 021006 (2014).
Benea-Chelmus, I.-C., Rösch, M., Scalari, G., Beck, M. & Faist, J. Intensity autocorrelation measurements of frequency combs in the terahertz range. Phys. Rev. A 96, 033821 (2017).
Wang, F. et al. Generating ultrafast pulses of light from quantum cascade lasers. Optica 2, 944–949 (2015).
Ferdous, F. et al. Spectral line-by-line pulse shaping of on-chip microresonator frequency combs. Nat. Photon. 5, 770–776 (2011).
Khurgin, J. B., Dikmelik, Y., Hugi, A. & Faist, J. Coherent frequency combs produced by self frequency modulation in quantum cascade lasers. Appl. Phys. Lett. 104, 081118 (2014).
Villares, G. & Faist, J. Quantum cascade laser combs: effects of modulation and dispersion. Opt. Express 23, 1651–1669 (2015).
Tzenov, P., Burghoff, D., Hu, Q. & Jirauschek, C. Time domain modeling of terahertz quantum cascade lasers for frequency comb generation. Opt. Express 24, 23232–23247 (2016).
Del’Haye, P., Beha, K., Papp, S. B. & Diddams, S. A. Self-injection locking and phase-locked states in microresonator-based optical frequency combs. Phys. Rev. Lett. 112, 043905 (2014).
Herr, T. et al. Temporal solitons in optical microresonators. Nat. Photon. 8, 145–152 (2013).
Mazzacurati, V., Benassi, P. & Ruocco, G. A new class of multiple dispersion grating spectrometers. J. Phys. E 21, 798–804 (1988).
Acknowledgements
The authors acknowledge financial support from the Ministero dell’Istruzione, dell’Università e della Ricerca (project PRIN-2015KEZNYM NEMO), the European Union’s Horizon 2020 research and innovation programme (Laserlab-Europe Project, grant no. 654148; CHIC Project, ERC grant no. 724344; ULTRAQCL Project, FET Open grant no 665158; Qombs Project, FET Flagship on Quantum Technologies grant no. 820419), the Italian ESFRI Roadmap (‘Extreme Light Infrastructure’—ELI Project) and the Swiss National Science Foundation (SNF200020-165639).
Author information
Authors and Affiliations
Contributions
F.C. and S.B. conceived the experiment. L.C., F.C., G.C., I.G., M.S.d.C., A.C., P.C.P. and R.E. performed the measurements. F.C., G.C., R.E. and S.B. analysed the data. L.C. and F.C. wrote the manuscript. G.C., D.M., M.S.d.C., P.C.P., R.E., S.B., G.S., J.F. and P.D.N. contributed to manuscript revision. J.F., G.S., M.R. and M.B. provided the quantum cascade lasers. L.C., F.C., D.M., P.C.P., R.E., S.B., G.S., J.F. and P.D.N. discussed the results. All work was performed under the joint supervision of P.D.N. and S.B.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
This file contains more information about the work and Supplementary Figs. 1–6.
Rights and permissions
About this article
Cite this article
Cappelli, F., Consolino, L., Campo, G. et al. Retrieval of phase relation and emission profile of quantum cascade laser frequency combs. Nat. Photonics 13, 562–568 (2019). https://doi.org/10.1038/s41566-019-0451-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41566-019-0451-1
This article is cited by
-
Dissipative Kerr solitons in semiconductor ring lasers
Nature Photonics (2022)
-
Phase Diversity Electro-optic Sampling: A new approach to single-shot terahertz waveform recording
Light: Science & Applications (2022)
-
Frequency comb ptychoscopy
Nature Communications (2021)
-
Femtosecond pulses from a mid-infrared quantum cascade laser
Nature Photonics (2021)
-
Quantum cascade laser based hybrid dual comb spectrometer
Communications Physics (2020)