The phenomenon of synchronization occurs universally across the natural sciences and provides critical insight into the behaviour of coupled nonlinear dynamical systems. It also offers a powerful approach to robust frequency or temporal locking in diverse applications including communications, superconductors and photonics. Here, we report the experimental synchronization of two coupled soliton mode-locked chip-based frequency combs separated over distances of 20 m. We show that such a system obeys the universal Kuramoto model for synchronization and that the cavity solitons from the microresonators can be coherently combined, which overcomes the fundamental power limit of microresonator-based combs. This study could significantly expand the applications of microresonator combs, and with its capability for massive integration it offers a chip-based photonic platform for exploring complex nonlinear systems.

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

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  1. 1.

    Strogatz, S. H. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143, 1–20 (2000).

  2. 2.

    Buck, J. Synchronous rhythmic flashing of fireflies. II. Q. Rev. Biol. 63, 265–289 (1988).

  3. 3.

    Michaels, D. C., Matyas, E. P. & Jalife, J. Mechanisms of sinoatrial pacemaker synchronization: a new hypothesis. Circ. Res. 61, 704–714 (1987).

  4. 4.

    Wiesenfeld, K., Colet, P. & Strogatz, S. H. Synchronization transitions in a disordered Josephson series array. Phys. Rev. Lett. 76, 404–407 (1996).

  5. 5.

    York, R. A. & Compton, R. C. Quasi-optical power combining using mutually synchronized oscillator arrays. IEEE Trans. Microwave Theory Tech. 39, 1000–1009 (1991).

  6. 6.

    Ramirez, J. P., Olvera, L. A., Nijmeijer, H. & Alvarez, J. The sympathy of two pendulum clocks: beyond Huygens observations. Sci. Rep. 6, 23580 (2016).

  7. 7.

    Kuramoto, Y. Self-entrainment of a population of coupled non-linear oscillators. In Proc. Int. Symp. Mathematical Problems in Theoretical Physics (ed. Araki, H.) 420–422 (Springer, Berlin, 1975).

  8. 8.

    Nixon, M. et al. Controlling synchronization in large laser networks. Phys. Rev. Lett. 108, 214101 (2012).

  9. 9.

    Cheo, P. K., Liu, A. & King, G. G. A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array. IEEE Photon. Technol. Lett. 13, 439–441 (2001).

  10. 10.

    Udem, T., Holzwarth, R. & Hänsch, T. W. Optical frequency metrology. Nature 416, 233–237 (2002).

  11. 11.

    Cundiff, S. T. & Ye, J. Colloquium: femtosecond optical frequency combs. Rev. Mod. Phys. 75, 325–342 (2003).

  12. 12.

    Dudley, J. M., Genty, G. & Coen, S. Supercontinuum generation in photonic crystal fiber. Rev. Mod. Phys. 78, 1135 (2006).

  13. 13.

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

  14. 14.

    Del’Haye, P. et al. Optical frequency comb generation from a monolithic microresonator. Nature 450, 1214–1217 (2007).

  15. 15.

    Savchenkov, A. A. et al. Tunable optical frequency comb with a crystalline whispering gallery mode resonator. Phys. Rev. Lett. 101, 093902 (2008).

  16. 16.

    Levy, J. S. et al. CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects. Nat. Photon. 4, 37–40 (2010).

  17. 17.

    Razzari, L. et al. CMOS-compatible integrated optical hyper-parametric oscillator. Nat. Photon. 4, 41–45 (2010).

  18. 18.

    Herr, T. et al. Universal formation dynamics and noise of Kerr-frequency combs in microresonators. Nat. Photon. 6, 480–487 (2012).

  19. 19.

    Leo, F., Gelens, L., Emplit, P., Haelterman, M. & Coen, S. Dynamics of one-dimensional Kerr cavity solitons. Opt. Express 21, 9180–9191 (2013).

  20. 20.

    Parra-Rivas, P., Gomila, D., Matías, M. A., Coen, S. & Gelens, L. Dynamics of localized and patterned structures in the Lugiato–Lefever equation determine the stability and shape of optical frequency combs. Phys. Rev. A 89, 043813 (2014).

  21. 21.

    Anderson, M., Leo, F., Coen, S., Erkintalo, M. & Murdoch, S. G. Observation of spatiotemporal instabilities of temporal cavity solitons. Optica 3, 1071–1074 (2016).

  22. 22.

    Bao, C. et al. Observation of Fermi–Pasta–Ulam recurrence induced by breather solitons in an optical microresonator. Phys. Rev. Lett. 117, 163901 (2016).

  23. 23.

    Yu, M. et al. Breather soliton dynamics in microresonators. Nat. Commun. 8, 14569 (2017).

  24. 24.

    Lucas, E., Karpov, M., Guo, H., Gorodetsky, M. L. & Kippenberg, T. J. Breathing dissipative solitons in optical microresonators. Nat. Commun. 8, 736 (2017).

  25. 25.

    Leo, F. et al. Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer. Nat. Photon. 4, 471–476 (2010).

  26. 26.

    Saha, K. et al. Modelocking and femtosecond pulse generation in chip-based frequency combs. Opt. Express 21, 1335–1343 (2013).

  27. 27.

    Herr, T. et al. Temporal solitons in optical microresonators. Nat. Photon. 8, 145–152 (2014).

  28. 28.

    Jang, J. K., Erkintalo, M., Coen, S. & Murdoch, S. G. Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons. Nat. Commun. 6, 7370 (2015).

  29. 29.

    Del’Haye, P. et al. Phase steps and resonator detuning measurements in microresonator frequency combs. Nat. Commun. 6, 5668 (2015).

  30. 30.

    Liang, W. et al. High spectral purity Kerr frequency comb radio frequency photonic oscillator. Nat. Commun. 6, 7957 (2015).

  31. 31.

    Yi, X., Yang, Q.-F., Yang, K. Y., Suh, M.-G. & Vahala, K. Soliton frequency comb at microwave rates in a high-Q silica microresonator. Optica 2, 1078–1085 (2015).

  32. 32.

    Joshi, C. et al. Thermally controlled comb generation and soliton modelocking in microresonators. Opt. Lett. 41, 2565–2568 (2016).

  33. 33.

    Wang, P.-H. et al. Intracavity characterization of micro-comb generation in the single-soliton regime. Opt. Express 24, 10890–10897 (2016).

  34. 34.

    Webb, K. E., Erkintalo, M., Coen, S. & Murdoch, S. G. Experimental observation of coherent cavity soliton frequency combs in silica microspheres. Opt. Lett. 41, 4613–4616 (2016).

  35. 35.

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

  36. 36.

    Joshi, C. et al. Counter-rotating cavity solitons in a silicon nitride microresonator. Opt. Lett. 43, 547–550 (2018).

  37. 37.

    Papp, S. B., Del’Haye, P. & Diddams, S. A. Parametric seeding of a microresonator optical frequency comb. Opt. Express 21, 17615–17624 (2013).

  38. 38.

    Obrzud, E., Lecomte, S. & Herr, T. Temporal solitons in microresonators driven by optical pulses. Nat. Photon. 11, 600–607 (2017).

  39. 39.

    Wen, Y. H., Lamont, M. R. E. & Gaeta, A. L. Synchronization of multiple parametric frequency combs. OSA Technical Digest Paper FW1D.4 (2014).

  40. 40.

    Munns, J. H. D., Walmsley, I. A. & Wen, Y. H. Novel interactions of dissipative Kerr solitons in nonlinear cavity networks. In Proc. European Conf. Lasers and Electro-Optics and European Quantum Electronics Conferences EF_1_1 (OSA, Washington DC, 2017).

  41. 41.

    Lugiato, L. A. & Lefever, R. Spatial dissipative structures in passive optical systems. Phys. Rev. Lett. 58, 2209 (1987).

  42. 42.

    Wabnitz, S. Suppression of interactions in a phase-locked soliton optical memory. Opt. Lett. 18, 601–603 (1993).

  43. 43.

    Coen, S., Randle, H. G., Sylvestre, T. & Erkintalo, M. Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato–Lefever model. Opt. Lett. 38, 37–39 (2013).

  44. 44.

    Chembo, Y. K. & Menyuk, C. R. Spatiotemporal Lugiato–Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators. Phys. Rev. A 87, 053852 (2013).

  45. 45.

    Levy, J. S. et al. High-performance silicon-nitride-based multiple-wavelength source. IEEE Photon. Technol. Lett. 24, 1375–1377 (2012).

  46. 46.

    Marin-Palomo, P. et al. Microresonator-based solitons for massively parallel coherent optical communications. Nature 546, 274–279 (2017).

  47. 47.

    Carmon, T., Yang, L. & Vahala, K. J. Dynamical thermal behavior and thermal self-stability of microcavities. Opt. Express 12, 4742–4750 (2004).

  48. 48.

    Adler, R. A study of locking phenomena in oscillators. Proc. IRE 34, 351–357 (1946).

  49. 49.

    Del’Haye, P., Beha, K., Papp, S. B. & Diddams, S. A. Self-injection locking and phase-locked states in microresonators-based optical frequency combs. Phys. Rev. Lett. 112, 043905 (2014).

  50. 50.

    Taheri, H., Eftekhar, A. A., Wiesenfeld, K. & Adibi, A. Anatomy of phase locking in hyperparametric oscillations based on Kerr nonlinearity. IEEE Photon. J. 9, 6100911 (2017).

  51. 51.

    Trebino, R. Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Springer, New York, 2000)..

  52. 52.

    Xue, X. et al. Thermal tuning of Kerr frequency combs in silicon nitride microring resonators. Opt. Express 24, 687–698 (2016).

  53. 53.

    Wen, Y. H., Lamont, M. R. E., Strogatz, S. H. & Gaeta, A. L. Self-organization in Kerr-cavity-soliton formation in parametric frequency combs. Phys. Rev. A 94, 063843 (2016).

  54. 54.

    Taheri, H., Del’Haye, P., Eftekhar, A. A., Wiesenfeld, K. & Adibi, A. Self-synchronization phenomena in the Lugiato–Lefever equation. Phys. Rev. A 96, 013828 (2017).

  55. 55.

    Ji, X. et al. Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold. Optica 4, 619–624 (2017).

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This work was supported by the Air Force Office of Scientific Research (AFOSR) (grant no. FA9550-15-1-0303), the National Science Foundation (NSF) (grant no. CCF-1640108) and the Semiconductor Research Corporation (SRC) (grant no. SRS 2016-EP-2693-A). The authors also thank K. Bergman and R. Polster for lending the high-resolution optical spectrum analyser and autocorrelator.

Author information


  1. Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA

    • Jae K. Jang
    • , Alexander Klenner
    • , Yoshitomo Okawachi
    •  & Alexander L. Gaeta
  2. School of Electrical and Computer Engineering, Cornell University, Ithaca, NY, USA

    • Xingchen Ji
  3. Department of Electrical Engineering, Columbia University, New York, NY, USA

    • Xingchen Ji
    •  & Michal Lipson


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J.K.J. and A.K. performed experiment. J.K.J carried out theoretical analysis and numerical simulation, and wrote the manuscript with inputs from all authors. J.K.J., A.K., Y.O. and A.L.G. contributed to the interpretation of data. X.J. fabricated the devices under the supervision of M.L. A.L.G. supervised the overall project.

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The authors declare no competing interests.

Corresponding author

Correspondence to Alexander L. Gaeta.

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