Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Optomechanical dissipative solitons

A Publisher Correction to this article was published on 24 January 2022

This article has been updated

Abstract

Nonlinear wave–matter interactions may give rise to solitons, phenomena that feature inherent stability in wave propagation and unusual spectral characteristics. Solitons have been created in a variety of physical systems and have had important roles in a broad range of applications, including communications, spectroscopy and metrology1,2,3,4. In recent years, the realization of dissipative Kerr optical solitons in microcavities has led to the generation of frequency combs in a chip-scale platform5,6,7,8,9,10. Within a cavity, photons can interact with mechanical modes. Cavity optomechanics has found applications for frequency conversion, such as microwave-to-optical or radio-frequency-to-optical11,12,13, of interest for communications and interfacing quantum systems operating at different frequencies. Here we report the observation of mechanical micro-solitons excited by optical fields in an optomechanical microresonator, expanding soliton generation in optical resonators to a different spectral window. The optical field circulating along the circumference of a whispering gallery mode resonator triggers a mechanical nonlinearity through optomechanical coupling, which in turn induces a time-varying periodic modulation on the propagating mechanical mode, leading to a tailored modal dispersion. Stable localized mechanical wave packets—mechanical solitons—can be realized when the mechanical loss is compensated by phonon gain and the optomechanical nonlinearity is balanced by the tailored modal dispersion. The realization of mechanical micro-solitons driven by light opens up new avenues for optomechanical technologies14 and may find applications in acoustic sensing, information processing, energy storage, communications and surface acoustic wave technology.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Mechanism of acoustic-wave propagation in an optomechanical resonator.
Fig. 2: Generation of an optomechanical soliton.
Fig. 3: Localized periodic phonon pulses in the cnoidal wave regime and soliton regime.
Fig. 4: Detection of a low-frequency vibration of a cantilever tip by an optomechanical soliton.

Data availability

The datasets generated during and/or analysed in this study are available from the corresponding author upon reasonable request.

Change history

References

  1. Holzwarth, R. et al. Optical frequency synthesizer for precision spectroscopy. Phys. Rev. Lett. 85, 2264–2267 (2000).

    ADS  CAS  PubMed  Google Scholar 

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

    ADS  CAS  PubMed  Google Scholar 

  3. Haus, H. A. & Wong, W. S. Solitons in optical communications. Rev. Mod. Phys. 68, 423–444 (1996).

    ADS  Google Scholar 

  4. Kippenberg, T. J., Holzwarth, R. & Diddams, S. A. Microresonator-based optical frequency combs. Science 332, 555–559 (2011).

    ADS  CAS  PubMed  Google Scholar 

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

    ADS  CAS  Google Scholar 

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

    PubMed  Google Scholar 

  7. Brasch, V. et al. Photonic chip-based optical frequency comb using soliton Cherenkov radiation. Science 351, 357–360 (2016).

    ADS  MathSciNet  CAS  MATH  PubMed  Google Scholar 

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

    ADS  CAS  PubMed  Google Scholar 

  9. Suh, M.-G., Yang, Q.-F., Yang, K. Y., Yi, X. & Vahala, K. J. Microresonator soliton dual-comb spectroscopy. Science 354, 600–603 (2016).

    ADS  CAS  PubMed  Google Scholar 

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

    ADS  CAS  Google Scholar 

  11. Shao, L. et al. Microwave-to-optical conversion using lithium niobate thin-film acoustic resonators. Optica 6, 1498–1505 (2019).

    ADS  CAS  Google Scholar 

  12. Forsch, M. et al. Microwave-to-optics conversion using a mechanical oscillator in its quantum ground state. Nat. Phys. 16, 69–74 (2020).

    CAS  Google Scholar 

  13. Yamazaki, R. et al. Radio-frequency-to-optical conversion using acoustic and optical whispering-gallery modes. Phys. Rev. A 101, 053839 (2020).

    ADS  CAS  Google Scholar 

  14. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    ADS  Google Scholar 

  15. Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).

    ADS  CAS  PubMed  Google Scholar 

  16. LIGO Scientific Collaboration and Virgo Collaboration. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016).

    ADS  MathSciNet  Google Scholar 

  17. Grudinin, I. S., Lee, H., Painter, O. & Vahala, K. J. Phonon laser action in a tunable two-level system. Phys. Rev. Lett. 104, 083901 (2010).

    ADS  PubMed  Google Scholar 

  18. Jing, H. et al. PT-symmetric phonon laser. Phys. Rev. Lett. 113, 053604 (2014).

    ADS  CAS  PubMed  Google Scholar 

  19. Zhang, J. et al. A phonon laser operating at an exceptional point. Nat. Photon. 12, 479–484 (2018).

    ADS  CAS  Google Scholar 

  20. Carmon, T., Cross, M. C. & Vahala, K. J. Chaotic quivering of micron-scaled onchip resonators excited by centrifugal optical pressure. Phys. Rev. Lett. 98, 167203 (2007).

    ADS  PubMed  Google Scholar 

  21. Monifi, F. et al. Optomechanically induced stochastic resonance and chaos transfer between optical fields. Nat. Photon. 10, 399–405 (2016).

    ADS  CAS  Google Scholar 

  22. Gan, J.-H., Xiong, H., Si, L.-G., Lü, X.-Y. & Wu, Y. Solitons in optomechanical arrays. Opt. Lett. 41, 2676–2679 (2016).

    ADS  PubMed  Google Scholar 

  23. Xiong, H., Gan, J. H. & Wu, Y. Kuznetsov–Ma soliton dynamics based on the mechanical effect of light. Phys. Rev. Lett. 119, 153901 (2017).

    ADS  PubMed  Google Scholar 

  24. Xiong, H. & Wu, Y. Optomechanical Akhmediev breathers. Laser Photon. Rev. 12, 1700305 (2018).

    ADS  Google Scholar 

  25. Ganesan, A., Do, C. & Seshia, A. Phononic frequency comb via intrinsic three-wave mixing. Phys. Rev. Lett. 118, 033903 (2017).

    ADS  PubMed  Google Scholar 

  26. Butsch, A., Koehler, J. R., Noskov, R. E. & Russell, P. St. J. CW-pumped single-pass frequency comb generation by resonant optomechanical nonlinearity in dual-nanoweb fiber. Optica 1, 158–163 (2014).

    ADS  Google Scholar 

  27. Savchenkov, A. A., Matsko, A. B., Ilchenko, V. S., Seidel, D. & Maleki, L. Surface acoustic wave opto-mechanical oscillator and frequency comb generator. Opt. Lett. 36, 3338–3340 (2011).

    ADS  CAS  PubMed  Google Scholar 

  28. Miri, M.-A., D’Aguanno, G. & Alù, A. Optomechanical frequency combs. New J. Phys. 20, 043013 (2018).

    ADS  Google Scholar 

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

    ADS  PubMed  Google Scholar 

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

    ADS  PubMed  Google Scholar 

  31. Rueda, A., Sedlmeir, F., Kumari, M., Leuchs, G. & Schwefel, H. G. L. Resonant electro-optic frequency comb. Nature 568, 378–381 (2019); correction 569, E11 (2019).

    ADS  CAS  PubMed  Google Scholar 

  32. Zhang, M. et al. Broadband electro-optic frequency comb generation in a lithium niobate microring resonator. Nature 568, 373–377 (2019).

    ADS  CAS  PubMed  Google Scholar 

  33. Li, Q. et al. Stably accessing octave-spanning microresonator frequency combs in the soliton regime. Optica 4, 193–203 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  34. Cao, L. S., Qi, D. X., Peng, R. W., Wang, M. & Schmelcher, P. Phononic frequency combs through nonlinear resonances. Phys. Rev. Lett. 112, 075505 (2014).

    ADS  CAS  PubMed  Google Scholar 

  35. Czaplewski, D. A. et al. Bifurcation generated mechanical frequency comb. Phys. Rev. Lett. 121, 244302 (2018).

    ADS  CAS  PubMed  Google Scholar 

  36. Hao, H. Y. & Maris, H. J. Experiments with acoustic solitons in crystalline solids. Phys. Rev. B 64, 064302 (2001).

    ADS  Google Scholar 

  37. Hereman, W. Shallow water waves and solitary waves. In Encyclopedia of Complexity and Systems Science (ed. Meyers, R. A.) 480 (Springer, 2009); https://doi.org/10.1007/978-0-387-30440-3_480.

  38. Barland, S. et al. Temporal localized structures in optical resonators. Adv. Phys. X 2, 496–517 (2017).

    CAS  Google Scholar 

  39. Lugiato, L., Prati, F. & Brambilla, M. Nonlinear Optical Systems (Cambridge Univ. Press, 2015).

  40. Jang, J. K., Erkintalo, M., Murdoch, S. G. & Coen, S. Ultraweak long-range interactions of solitons observed over astronomical distances. Nat. Photon. 7, 657–663 (2013).

    ADS  CAS  Google Scholar 

  41. Barland, S. et al. Cavity solitons as pixels in semiconductor microcavities. Nature 419, 699–702 (2002).

    ADS  CAS  PubMed  Google Scholar 

  42. 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).

    ADS  CAS  Google Scholar 

  43. Grelu, P. & Akhmediev, N. Dissipative solitons for mode-locked lasers. Nat. Photon. 6, 84–92 (2012).

    ADS  CAS  Google Scholar 

  44. Korteweg, D. J. & de Vries, G. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philos. Mag. 39, 422–443 (1895).

    MathSciNet  MATH  Google Scholar 

  45. Boyd, J. P. The double cnoidal wave of the Korteweg–de Vries equation: an overview. J. Math. Phys. 25, 3390–3401 (1984).

    ADS  MathSciNet  MATH  Google Scholar 

  46. Nayanov, V. I. Surface acoustic cnoidal waves and solitons in a LiNbO3-(SiO film) structure. JETP Lett. 44, 314–317 (1986); translated from Pis’ma Zh. Eksp. Teor. Fiz. 44, 245–247 (1986).

    ADS  Google Scholar 

  47. Fiore, V. et al. Storing optical information as a mechanical excitation in a silica optomechanical resonator. Phys. Rev. Lett. 107, 133601 (2011).

    ADS  PubMed  Google Scholar 

  48. Carmon, T., Rokhsari, H., Yang, L., Kippenberg, T. J. & Vahala, K. J. Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode. Phys. Rev. Lett. 94, 223902 (2005).

    ADS  PubMed  Google Scholar 

Download references

Acknowledgements

The project is supported by the NSF grant number EFMA1641109 and ARO grant numbers W911NF1710189 and W911NF1210026. J.Z. is supported by the NSFC under grant numbers 61622306 and 11674194. Y.-x.L. is supported by the NSFC under grant number 61025022. Y.-x.L. and J.Z. are supported by the National Basic Research Program of China (973 Program) under grant number 2014CB921401, the Tsinghua University Initiative Scientific Research Program, and the Tsinghua National Laboratory for Information Science and Technology (TNList) Cross-discipline Foundation. L.L. is supported by the NSFC under grant number. 61925307. S.K. and A.A. are supported by the Office of Naval Research and the Air Force Office of Scientific Research.

Author information

Authors and Affiliations

Authors

Contributions

J.Z., B.P., F.M. and L.Y. conceived the idea. L.Y. designed the experiments. J.Z. performed the experiments and processed the data with the help of X.J., Y.L., P.Y. and L.L. J.Z. and S.K. provided theoretical analysis under the guidance of Y.-x.L. and A.A. J.Z. and L.Y. wrote the manuscript with contributions from all authors. L.Y. supervised the project.

Corresponding author

Correspondence to Lan Yang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

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 supplementary text, supplementary equations, supplementary sections S1–S8 and supplementary references.

Peer Review File

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Peng, B., Kim, S. et al. Optomechanical dissipative solitons. Nature 600, 75–80 (2021). https://doi.org/10.1038/s41586-021-04012-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-021-04012-1

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing