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Versatile optical frequency division with Kerr-induced synchronization at tunable microcomb synthetic dispersive waves

Abstract

Kerr-induced synchronization (KIS) provides a key tool for the control and stabilization of a dissipative Kerr soliton (DKS) frequency comb, enabled by the capture of a comb tooth by an injected reference laser. Efficient KIS relies on large locking bandwidth, meaning both the comb tooth and intracavity reference power need to be sufficiently large. Although KIS can theoretically occur at any comb tooth, large modal separations from the main pump to achieve large optical frequency division factors are often difficult or unfeasible due to cavity dispersion. While tailoring the dispersion to generate dispersive waves can support on-resonance KIS far from the main pump, this approach restricts synchronization to specific wavelengths. Here we demonstrate an alternative KIS method that allows efficient synchronization at arbitrary modes by multi-pumping a microresonator. This creates a multicolour DKS with a main and an auxiliary comb, the latter enabling the creation of a synthetic dispersive wave. As cross-phase modulation leads to a unique group velocity for both the soliton comb and the auxiliary comb, repetition rate disciplining of the auxiliary comb through KIS automatically controls the DKS microcomb. We explore this colour-KIS phenomenon theoretically and experimentally, showing control and tuning of the soliton microcomb repetition rate, resulting in optical frequency division independent of the main pump noise properties.

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Fig. 1: Concept of colour KIS.
Fig. 2: Theoretical study of the colour-KIS effect.
Fig. 3: DKS and new DW generated via auxiliary pumping.
Fig. 4: Repetition rate control and OFD through colour KIS.
Fig. 5: Colour-KIS noise OFD onto the DKS repetition rate.
Fig. 6: Tunability of the secondary colour comb tooth for colour-KIS frequency versatility.

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Data availability

The data that supports the plots within this paper and other findings of this study are available from the corresponding authors upon request.

Code availability

The simulation code is available from the authors through the pyLLE package available online38, with a modification that is available upon reasonable request, using the inputs and parameters presented in this work.

References

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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  3. Spencer, D. T. et al. An optical-frequency synthesizer using integrated photonics. Nature 557, 81–85 (2018).

    Article  ADS  MATH  Google Scholar 

  4. Newman, Z. L. et al. Architecture for the photonic integration of an optical atomic clock. Optica 6, 680 (2019).

    Article  ADS  MATH  Google Scholar 

  5. Oelker, E. et al. Demonstration of 4.8 × 10−17 stability at 1 s for two independent optical clocks. Nat. Photon. 13, 714–719 (2019).

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

    Article  ADS  MATH  Google Scholar 

  7. Caldwell, E. D. et al. Quantum-limited optical time transfer for future geosynchronous links. Nature 618, 721–726 (2023).

    Article  ADS  MATH  Google Scholar 

  8. Tetsumoto, T. et al. Optically referenced 300 GHz millimetre-wave oscillator. Nat. Photon. 15, 516–522 (2021).

    Article  ADS  Google Scholar 

  9. Xie, X. et al. Photonic microwave signals with zeptosecond-level absolute timing noise. Nat. Photon. 11, 44–47 (2017).

    Article  ADS  MATH  Google Scholar 

  10. Riemensberger, J. et al. Massively parallel coherent laser ranging using a soliton microcomb. Nature 581, 164–170 (2020).

    Article  ADS  MATH  Google Scholar 

  11. Kippenberg, T. J., Gaeta, A. L., Lipson, M. & Gorodetsky, M. L. Dissipative Kerr solitons in optical microresonators. Science 361, eaan8083 (2018).

    Article  MATH  Google Scholar 

  12. Liu, J. et al. High-yield, wafer-scale fabrication of ultralow-loss, dispersion-engineered silicon nitride photonic circuits. Nat. Commun. 12, 2236 (2021).

    Article  ADS  MATH  Google Scholar 

  13. Wildi, T., Gaafar, M. A., Voumard, T., Ludwig, M. & Herr, T. Dissipative Kerr solitons in integrated Fabry–Perot microresonators. Optica 10, 650–656 (2023).

    Article  ADS  Google Scholar 

  14. Stern, B., Ji, X., Okawachi, Y., Gaeta, A. L. & Lipson, M. Battery-operated integrated frequency comb generator. Nature 562, 401–405 (2018).

    Article  ADS  Google Scholar 

  15. Fortier, T. M. et al. Generation of ultrastable microwaves via optical frequency division. Nat. Photon. 5, 425–429 (2011).

    Article  ADS  MATH  Google Scholar 

  16. Liu, K. et al. 36 Hz integral linewidth laser based on a photonic integrated 4.0 m coil resonator. Optica 9, 770–775 (2022).

    Article  ADS  MATH  Google Scholar 

  17. Kudelin, I. et al. Photonic chip-based low-noise microwave oscillator. Nature 627, 534–539 (2024).

    Article  ADS  MATH  Google Scholar 

  18. Sun, S. et al. Integrated optical frequency division for microwave and mmWave generation. Nature 627, 540–545 (2024).

    Article  ADS  MATH  Google Scholar 

  19. Moille, G. et al. Kerr-induced synchronization of a cavity soliton to an optical reference. Nature 624, 267–274 (2023).

    Article  ADS  Google Scholar 

  20. Wildi, T., Ulanov, A., Englebert, N., Voumard, T. & Herr, T. Sideband injection locking in microresonator frequency combs. APL Photon. 8, 120801 (2023).

    Article  ADS  Google Scholar 

  21. Sun, S. et al. Kerr optical frequency division with integrated photonics for stable microwave and mmWave generation. Preprint at https://arxiv.org/abs/2402.11772v1 (2024).

  22. Moille, G. et al. Frontiers in Optics and Laser Science Report No. FTh3E-2 (Optica Publishing Group, 2023).

  23. Shen, B. et al. Integrated turnkey soliton microcombs. Nature 582, 365–369 (2020).

    Article  ADS  Google Scholar 

  24. Ulanov, A. E. et al. Synthetic reflection self-injection-locked microcombs. Nat. Photon. 18, 294–299 (2024).

    Article  ADS  Google Scholar 

  25. Voloshin, A. S. et al. Dynamics of soliton self-injection locking in optical microresonators. Nat. Commun. 12, 235 (2021).

    Article  ADS  MATH  Google Scholar 

  26. Moille, G. et al. Ultra-broadband Kerr microcomb through soliton spectral translation. Nat. Commun. 12, 7275 (2021).

    Article  ADS  MATH  Google Scholar 

  27. Zhang, S., Silver, J. M., Bi, T. & Del’Haye, P. Spectral extension and synchronization of microcombs in a single microresonator. Nat. Commun. 11, 6384 (2020).

    Article  ADS  MATH  Google Scholar 

  28. Wang, Y. et al. Universal mechanism for the binding of temporal cavity solitons. Optica 4, 855 (2017).

    Article  ADS  MATH  Google Scholar 

  29. Qureshi, P. C. et al. Soliton linear-wave scattering in a Kerr microresonator. Commun. Phys. 5, 123 (2022).

    Article  MATH  Google Scholar 

  30. Taheri, H., Matsko, A. B. & Maleki, L. Optical lattice trap for Kerr solitons. Eur. Phys. J. D 71, 153 (2017).

    Article  ADS  MATH  Google Scholar 

  31. Moille, G. et al. Two-dimensional nonlinear mixing between a dissipative Kerr soliton and continuous waves for a higher-dimension frequency comb. Preprint at https://arxiv.org/abs/2303.10026 (2023).

  32. Shandilya, P. H., Moille, G., D’Aguanno, G., Srinivasan, K. & Menyuk, C. R. Frontiers in Optics and Laser Science Report No. JW4A-48 (Optica Publishing Group, 2023).

  33. Moille, G. et al. Broadband resonator–waveguide coupling for efficient extraction of octave-spanning microcombs. Opt. Lett. 44, 4737 (2019).

    Article  ADS  MATH  Google Scholar 

  34. Yang, Q.-F., Yi, X., Yang, K. Y. & Vahala, K. Counter-propagating solitons in microresonators. Nat. Photon. 11, 560–564 (2017).

    Article  MATH  Google Scholar 

  35. Zhou, H. et al. Soliton bursts and deterministic dissipative Kerr soliton generation in auxiliary-assisted microcavities. Light Sci. Appl. 8, 50 (2019).

    Article  ADS  MATH  Google Scholar 

  36. Zhang, S. et al. Sub-milliwatt-level microresonator solitons with extended access range using an auxiliary laser. Optica 6, 206 (2019).

    Article  ADS  MATH  Google Scholar 

  37. Stone, J. R. & Papp, S. B. Harnessing dispersion in soliton microcombs to mitigate thermal noise. Phys. Rev. Lett. 125, 153901 (2020).

    Article  ADS  Google Scholar 

  38. Moille, G., Li, Q., Xiyuan, L. & Srinivasan, K. pyLLE: a fast and user friendly Lugiato–Lefever equation solver. J. Res. NIST 124, 124012 (2019).

    Article  Google Scholar 

  39. Crameri, F. Scientific colour maps. Zenodo https://doi.org/10.5281/zenodo.8409685 (2023).

  40. Crameri, F., Shephard, G. E. & Heron, P. J. The misuse of colour in science communication. Nat. Commun. 11, 5444 (2020).

    Article  ADS  MATH  Google Scholar 

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Acknowledgements

The scientific colour map batlow39 and subsequent colour set is used in this study to prevent visual distortion of the data and exclusion of readers with colour-vision deficiencies40. We acknowledge partial funding support from the Space Vehicles Directorate of the Air Force Research Laboratory, the Atomic-Photonic Integration programme of the Defense Advanced Research Projects Agency, and the NIST-on-a-chip programme of the National Institute of Standards and Technology. P.S. and C.M. acknowledge support from the Air Force Office of Scientific Research (grant number FA9550-20-1-0357) and the National Science Foundation (grant number ECCS-18-07272). We thank S. Krzyzewski and M. Davanço for insightful feedback. G.M. also thanks T.B.M.

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Contributions

G.M. and K.S. led the project. G.M. designed the resonators and performed the measurements and simulations. P.S. and C.M. helped with the theoretical and numerical understanding. A.N. and G.C. helped with the experimental understanding. K.S. helped with data analysis. G.M. and K.S. wrote the paper, with input from all authors. All the authors contributed to and discussed the content of this paper.

Corresponding authors

Correspondence to Grégory Moille or Kartik Srinivasan.

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Competing interests

G.M., C.M. and K.S have submitted a provisional patent application based on aspects of the work presented in this paper. The other authors declare no competing interests.

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Nature Photonics thanks Mengxi Tan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Sections 1–4, Figs. 1–4 and References.

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Moille, G., Shandilya, P., Niang, A. et al. Versatile optical frequency division with Kerr-induced synchronization at tunable microcomb synthetic dispersive waves. Nat. Photon. 19, 36–43 (2025). https://doi.org/10.1038/s41566-024-01540-w

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