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The time-programmable frequency comb and its use in quantum-limited ranging


Two decades after its invention, the classic self-referenced frequency comb laser is an unrivalled ruler for frequency, time and distance metrology owing to the rigid spacing of its optical output1,2. As a consequence, it is now used in numerous sensing applications that require a combination of high bandwidth and high precision3,4,5. Many of these applications, however, are limited by the trade-offs inherent in the rigidity of the comb output and operate far from quantum-limited sensitivity. Here we demonstrate an agile programmable frequency comb where the pulse time and phase are digitally controlled with ±2-attosecond accuracy. This agility enables quantum-limited sensitivity in sensing applications as the programmable comb can be configured to coherently track weak returning pulse trains at the shot-noise limit. To highlight its capabilities, we use this programmable comb in a ranging system, reducing the required power to reach a given precision by about 5,000-fold compared with a conventional dual-comb system. This enables ranging at a mean photon per pulse number of 1/77 while retaining the full accuracy and precision of a rigid frequency comb. Beyond ranging and imaging6,7,8,9,10,11,12, applications in time and frequency metrology1,2,5,13,14,15,16,17,18,19,20,21,22,23, comb-based spectroscopy24,25,26,27,28,29,30,31,32, pump–probe experiments33 and compressive sensing34,35 should benefit from coherent control of the comb-pulse time and phase.

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Fig. 1: A time-programmable frequency comb.
Fig. 2: Illustration and characterization of the time programmability of the TPFC through LOS.
Fig. 3: Dual-comb ranging with a time-programmable frequency comb.
Fig. 4: Ranging and velocity data to a moving retroreflector.
Fig. 5: Comparison of conventional and tracking dual-comb ranging.

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Data availability

The data for the figures in this paper are available for download at

Code availability

The mathematics and algorithms necessary to create a time-programmable frequency comb are described between the main text and Methods.


  1. Hänsch, T. W. Nobel Lecture: Passion for precision. Rev. Mod. Phys. 78, 1297–1309 (2006).

    Article  ADS  Google Scholar 

  2. Hall, J. L. Nobel Lecture: Defining and measuring optical frequencies. Rev. Mod. Phys. 78, 1279–1295 (2006).

    Article  ADS  Google Scholar 

  3. Newbury, N. R. Searching for applications with a fine-tooth comb. Nat. Photon. 5, 186–188 (2011).

    Article  ADS  CAS  Google Scholar 

  4. Fortier, T. & Baumann, E. 20 years of developments in optical frequency comb technology and applications. Commun. Phys. 2, 153 (2019).

    Article  Google Scholar 

  5. Diddams, S. A., Vahala, K. & Udem, T. Optical frequency combs: coherently uniting the electromagnetic spectrum. Science 369, eaay3676 (2020).

    Article  CAS  PubMed  Google Scholar 

  6. Zhu, Z. & Wu, G. Dual-comb ranging. Engineering 4, 772–778 (2018).

    Article  Google Scholar 

  7. Coddington, I., Swann, W. C., Nenadovic, L. & Newbury, N. R. Rapid and precise absolute distance measurements at long range. Nat. Photon. 3, 351–356 (2009).

    Article  ADS  CAS  Google Scholar 

  8. Kim, W. et al. Absolute laser ranging by time-of-flight measurement of ultrashort light pulses. J. Opt. Soc. Am. A 37, B27–B35 (2020).

    Article  ADS  CAS  Google Scholar 

  9. Minoshima, K. & Matsumoto, H. High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser. Appl. Opt. 39, 5512–5517 (2000).

    Article  ADS  CAS  PubMed  Google Scholar 

  10. Vicentini, E., Wang, Z., Van Gasse, K., Hänsch, T. W. & Picqué, N. Dual-comb hyperspectral digital holography. Nat. Photon. 15, 890–894 (2021).

    Article  ADS  CAS  Google Scholar 

  11. Kato, T., Uchida, M. & Minoshima, K. No-scanning 3D measurement method using ultrafast dimensional conversion with a chirped optical frequency comb. Sci. Rep. 7, 3670 (2017).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  12. Hase, E. et al. Scan-less confocal phase imaging based on dual-comb microscopy. Optica 5, 634–643 (2018).

    Article  ADS  Google Scholar 

  13. Deschênes, J.-D. et al. Synchronization of distant optical clocks at the femtosecond level. Phys. Rev. X 6, 021016 (2016).

    Google Scholar 

  14. Giorgetta, F. R. et al. Optical two-way time and frequency transfer over free space. Nat. Photon. 7, 434–438 (2013).

    Article  ADS  CAS  Google Scholar 

  15. Xin, M., Şafak, K. & Kärtner, F. X. Ultra-precise timing and synchronization for large-scale scientific instruments. Optica 5, 1564–1578 (2018).

    Article  ADS  CAS  Google Scholar 

  16. Shen, Q. et al. Experimental simulation of time and frequency transfer via an optical satellite–ground link at 10−18 instability. Optica 8, 471–476 (2021).

    Article  ADS  Google Scholar 

  17. Boulder Atomic Clock Optical Network (BACON) Collaboration Frequency ratio measurements at 18-digit accuracy using an optical clock network. Nature 591, 564–569 (2021).

    Article  ADS  Google Scholar 

  18. Clivati, C. et al. Common-clock very long baseline interferometry using a coherent optical fiber link. Optica 7, 1031–1037 (2020).

    Article  ADS  CAS  Google Scholar 

  19. Bergeron, H. et al. Femtosecond time synchronization of optical clocks off of a flying quadcopter. Nat. Commun. 10, 1819 (2019).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  20. Bodine, M. I. et al. Optical time-frequency transfer across a free-space, three-node network. APL Photon. 5, 076113 (2020).

    Article  ADS  CAS  Google Scholar 

  21. Dix-Matthews, B. P. et al. Point-to-point stabilized optical frequency transfer with active optics. Nat. Commun. 12, 515 (2021).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  22. Gozzard, D. R. et al. Ultrastable free-space laser links for a global network of optical atomic clocks. Phys. Rev. Lett. 128, 020801 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  23. Shen, Q. et al. 113 km free-space time-frequency dissemination at the 19th decimal instability. Preprint at (2022).

  24. Coddington, I., Newbury, N. & Swann, W. Dual-comb spectroscopy. Optica 3, 414–426 (2016).

    Article  ADS  Google Scholar 

  25. Cossel, K. C. et al. in Advances in Spectroscopic Monitoring of the Atmosphere (eds Chen, W. et al.) 27–93 (Elsevier, 2021);

  26. Picqué, N. & Hänsch, T. W. Frequency comb spectroscopy. Nat. Photon. 13, 146–157 (2019).

    Article  ADS  Google Scholar 

  27. Lomsadze, B., Smith, B. C. & Cundiff, S. T. Tri-comb spectroscopy. Nat. Photon. 12, 676–680 (2018).

    Article  ADS  CAS  Google Scholar 

  28. Friedlein, J. T. et al. Dual-comb photoacoustic spectroscopy. Nat. Commun. 11, 3152 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  29. Wildi, T., Voumard, T., Brasch, V., Yilmaz, G. & Herr, T. Photo-acoustic dual-frequency comb spectroscopy. Nat. Commun. 11, 4164 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  30. Ideguchi, T. et al. Coherent Raman spectro-imaging with laser frequency combs. Nature 502, 355–358 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  31. Rieker, G. B. et al. Frequency-comb-based remote sensing of greenhouse gases over kilometer air paths. Optica 1, 290–298 (2014).

    Article  ADS  CAS  Google Scholar 

  32. Voumard, T. et al. AI-enabled real-time dual-comb molecular fingerprint imaging. Opt. Lett. 45, 6583–6586 (2020).

    Article  ADS  PubMed  Google Scholar 

  33. Marian, A., Stowe, M. C., Lawall, J. R., Felinto, D. & Ye, J. United time-frequency spectroscopy for dynamics and global structure. Science 306, 2063–2068 (2004).

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Giorgetta, F. R. et al. Fiber laser based dual-comb spectroscopy with dynamically controlled spectral resolution. In Conference on Lasers and Electro-Optics (2021) AM3E.4 (Optical Society of America, 2021).

  35. Kawai, A., Kageyama, T., Horisaki, R. & Ideguchi, T. Compressive dual-comb spectroscopy. Sci. Rep. 11, 13494 (2021).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  36. Martin, B., Feneyrou, P., Dolfi, D. & Martin, A. Performance and limitations of dual-comb based ranging systems. Opt. Express 30, 4005 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  37. Ellis, J. L. et al. Scaling up frequency-comb-based optical time transfer to long terrestrial distances. Phys. Rev. Appl. 15, 034002 (2021).

    Article  ADS  CAS  Google Scholar 

  38. Schliesser, A., Brehm, M., Keilmann, F. & van der Weide, D. Frequency-comb infrared spectrometer for rapid, remote chemical sensing. Opt. Express 13, 9029–9038 (2005).

    Article  ADS  CAS  PubMed  Google Scholar 

  39. Tourigny-Plante, A., Guay, P. & Genest, J. Apodization in dual-comb spectroscopy for rapid measurement. In Optical Sensors and Sensing Congress (2020) LTu3C.2 (Optical Society of America, 2020).

  40. Shi, Y. et al. High speed time-of-flight displacement measurement based on dual-comb electronically controlled optical sampling. Opt. Express 30, 8391–8398 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  41. Antonucci, L., Solinas, X., Bonvalet, A. & Joffre, M. Asynchronous optical sampling with arbitrary detuning between laser repetition rates. Opt. Express 20, 17928–17937 (2012).

    Article  ADS  PubMed  Google Scholar 

  42. Trocha, P. et al. Ultrafast optical ranging using microresonator soliton frequency combs. Science 359, 887–891 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  43. Mitchell, T., Sun, J., Sun, J. & Reid, D. T. Dynamic measurements at up to 130-kHz sampling rates using Ti:sapphire dual-comb distance metrology. Opt. Express 29, 42119–42126 (2021).

    Article  ADS  CAS  Google Scholar 

  44. Suh, M.-G. & Vahala, K. J. Soliton microcomb range measurement. Science 359, 884–887 (2018).

    Article  ADS  CAS  PubMed  Google Scholar 

  45. Kalisz, J. Review of methods for time interval measurements with picosecond resolution. Metrologia 41, 17–32 (2004).

    Article  ADS  Google Scholar 

  46. Fabre, C. & Treps, N. Modes and states in quantum optics. Rev. Mod. Phys. 92, 035005 (2020).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  47. Ansari, V. et al. Achieving the ultimate quantum timing resolution. PRX Quantum 2, 010301 (2021).

    Article  Google Scholar 

  48. Sinclair, L. C. et al. Synchronization of clocks through 12 km of strongly turbulent air over a city. Appl. Phys. Lett. 109, 151104 (2016).

    Article  ADS  PubMed  Google Scholar 

  49. Barber, Z. W., Dahl, J. R., Sharpe, T. L. & Erkmen, B. I. Shot noise statistics and information theory of sensitivity limits in frequency-modulated continuous-wave ladar. J. Opt. Soc. Am. A 30, 1335–1341 (2013).

    Article  ADS  Google Scholar 

  50. Baumann, E. et al. Comb-calibrated frequency-modulated continuous-wave ladar for absolute distance measurements. Opt. Lett. 38, 2026–2028 (2013).

    Article  ADS  PubMed  Google Scholar 

  51. Crouch, S. & Barber, Z. W. Laboratory demonstrations of interferometric and spotlight synthetic aperture ladar techniques. Opt. Express 20, 24237 (2012).

    Article  ADS  PubMed  Google Scholar 

  52. Caldwell, E. D. et al. Photon efficient optical time transfer. In 2022 Joint Conference of the European Frequency and Time Forum & the IEEE International Frequency Control Symposium Paris, France (2022).

  53. Schliesser, A., Picqué, N. & Hänsch, T. W. Mid-infrared frequency combs. Nat. Photon. 6, 440–449 (2012).

    Article  ADS  CAS  Google Scholar 

  54. Ycas, G. et al. High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm. Nat. Photon. 12, 202–208 (2018).

    Article  ADS  CAS  Google Scholar 

  55. Muraviev, A. V., Smolski, V. O., Loparo, Z. E. & Vodopyanov, K. L. Massively parallel sensing of trace molecules and their isotopologues with broadband subharmonic mid-infrared frequency combs. Nat. Photon. 12, 209–214 (2018).

    Article  ADS  CAS  Google Scholar 

  56. Sinclair, L. C. et al. Invited Article: A compact optically coherent fiber frequency comb. Rev. Sci. Instrum. 86, 081301 (2015).

    Article  ADS  CAS  PubMed  Google Scholar 

  57. Kingston, R. H. Detection of Optical and Infrared Radiation (Springer, 1978).

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We acknowledge J. Ellis, T. Fortier, K. Cossel, W. Swann, B. Stuhl and B. Washburn for discussions. We acknowledge funding from the National Institute of Standards and Technology.

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E.D.C., L.C.S., N.R.N. and J.-D.D. all contributed to the initial conception, the experiment design, the data acquisition, the analysis of the results and the writing of the manuscript.

Corresponding authors

Correspondence to Laura C. Sinclair or Nathan R. Newbury.

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Nature thanks Takuro Ideguchi, Xiaoxiao Xue and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Range deviation power comparison.

Range deviation (left axis) and time deviation (right axis) of dual-comb range measurements from a fixed reflection for signal-comb powers from 980 nW (bottom curve) down to 0.33 pW (top curve) with the following power levels ± 10%: 980 nW, 190 nW, 86 nW, 38 nW, 21 nW, 9.6 nW, 1.8 nW, 1.2 nW, 390 pW, 200 pW, 89 pW, 33 pW, 23 pW, 8.5 pW, 4.1 pW, 1.9 pW, 990 fW, 550 fW and 330 fW. The vertical dashed cyan line indicates the 200-ms averaging time for the data in Fig. 3c. Beyond 200-ms, the range deviation increases due to temperature-induced fluctuations in the fibre path up to the fixed reflection. In addition, the deviations for the difference between the absolute range from the tracking comb timing and the relative range from the unwrapped carrier phase shift, from Fig. 4, are shown for the time periods of 60 to 100 seconds at 3.2 pW (green squares) and 110 seconds to 150 seconds at 32 pW (green triangles). For these data, the differential chirp between the signal and TPFC pulses was larger, leading to an additional 1.5x penalty in C and thus lie slightly above the curves at the same power for ranging off the fixed reflection (solid circles). However, because the path-length variation is common mode, the difference continues to average down beyond 200 ms.

Extended Data Fig. 2 Range power spectral density.

Range power spectral density (PSD) for the data from Fig. 4 over the period of 60 s to 100 s at 3.2 pW return power for X(t) from the tracking comb (blue trace) and the unwrapped carrier phase \(\theta (t)\) (purple trace). Also shown is the noise floor for the unwrapped carrier phase (dark blue trace). The vibrations of the nominally immobile retroreflector can be clearly seen in the carrier-phase data. At the low average power of 3.2 pW, the tracking dual-comb range shot-noise limited noise floor lies just above the minimal vibrations seen here. The vertical magenta line indicates the maximum 10 Hz update rate of FMCW while the vertical dark green line indicates the 13 kHz cut-off imposed by the 26 kHz measurement rate for the range data.

Extended Data Table 1 Ranging modality comparison

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Caldwell, E.D., Sinclair, L.C., Newbury, N.R. et al. The time-programmable frequency comb and its use in quantum-limited ranging. Nature 610, 667–673 (2022).

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