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.

  • Letter
  • Published:

Resonant excitation and all-optical switching of femtosecond soliton molecules

Abstract

The emergence of confined structures and pattern formation are exceptional manifestations of nonlinear interactions found in a variety of physical, chemical and biological systems1. Facilitated by optical nonlinearities, solitons enable ultrashort temporal confinement of light and stable propagation despite the presence of dispersion. Such particle-like structures can assemble in stable arrangements, forming ‘soliton molecules’2,3. Recent work has revealed oscillatory internal motions of these bound states, akin to molecular vibrations4,5,6,7,8,9, raising the question of how far the ‘molecular’ analogy reaches, that is, whether further concepts from molecular spectroscopy apply and whether such intramolecular dynamics can be externally driven or manipulated. Here, we probe and control ultrashort bound states in an optical oscillator, using real-time spectral interferometry and time-dependent excitation. For a frequency-swept pump modulation, we analyse the nonlinear response and resolve anharmonicities in soliton interactions that lead to generation of overtones and sub-harmonics. Applying stronger stimuli, we demonstrate all-optical switching between states with different binding separations. These results could be applied to rapid pulse-pair generation and may stimulate the development of future instruments for ultrafast science.

This is a preview of subscription content, access via your institution

Access options

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

Fig. 1: Optical control scheme of soliton molecules.
Fig. 2: Driven soliton molecule.
Fig. 3: Numerical simulation of resonant behaviour.
Fig. 4: All-optical switching of soliton molecules.

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 author upon reasonable request.

Code availability

The data processing and simulation codes that were used to generate the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Cross, M. C. & Hohenberg, P. C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993).

    Article  ADS  Google Scholar 

  2. Mitschke, F. M. & Mollenauer, L. F. Experimental observation of interaction forces between solitons in optical fibers. Opt. Lett. 12, 355–357 (1987).

    Google Scholar 

  3. Stratmann, M., Pagel, T. & Mitschke, F. Experimental observation of temporal soliton molecules. Phys. Rev. Lett. 95, 143902 (2005).

    Article  ADS  Google Scholar 

  4. Soto-Crespo, J. M., Grelu, P., Akhmediev, N. & Devine, N. Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs. Phys. Rev. E 75, 016613 (2007).

    Article  ADS  Google Scholar 

  5. Zavyalov, A., Iliew, R., Egorov, O. & Lederer, F. Dissipative soliton molecules with independently evolving or flipping phases in mode-locked fiber lasers. Phys. Rev. A 80, 3827–3829 (2009).

    Article  Google Scholar 

  6. Ortaç, B. et al. Observation of soliton molecules with independently evolving phase in a mode-locked fiber laser. Opt. Lett. 35, 1578–1580 (2010).

    Article  Google Scholar 

  7. Herink, G., Kurtz, F., Jalali, B., Solli, D. R. & Ropers, C. Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules. Science 356, 50–54 (2017).

    Article  ADS  Google Scholar 

  8. Krupa, K., Nithyanandan, K., Andral, U., Tchofo-Dinda, P. & Grelu, P. Real-time observation of internal motion within ultrafast dissipative optical soliton molecules. Phys. Rev. Lett. 118, 243901 (2017).

    Article  ADS  Google Scholar 

  9. Shi, H., Song, Y., Wang, C., Zhao, L. & Hu, M. Observation of subfemtosecond fluctuations of the pulse separation in a soliton molecule. Opt. Lett. 43, 1623–1626 (2018).

    Google Scholar 

  10. Becker, C. et al. Oscillations and interactions of dark and dark–bright solitons in Bose–Einstein condensates. Nat. Phys. 4, 496–501 (2008).

    Article  Google Scholar 

  11. Cole, D. C., Lamb, E. S., Del’Haye, P., Diddams, S. A. & Papp, S. B. Soliton crystals in Kerr resonators. Nat. Photon. 11, 671–676 (2017).

    Article  ADS  Google Scholar 

  12. Husakou, A. V. & Herrmann, J. Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers. Phys. Rev. Lett. 87, 203901 (2001).

    Article  ADS  Google Scholar 

  13. Solli, D. R., Ropers, C., Koonath, P. & Jalali, B. Optical rogue waves. Nature 450, 1054–1057 (2007).

    Article  ADS  Google Scholar 

  14. Dudley, J. M., Dias, F., Erkintalo, M. & Genty, G. Instabilities, breathers and rogue waves in optics. Nat. Photon. 8, 755–764 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Balakireva, I. V. & Chembo, Y. K. A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity. Phil. Trans. R. Soc. Math. Phys. Eng. Sci. 376, 20170381 (2018).

    Article  ADS  Google Scholar 

  17. Hause, A., Hartwig, H., Böhm, M. & Mitschke, F. Binding mechanism of temporal soliton molecules. Phys. Rev. A 78, 063817 (2008).

    Article  ADS  Google Scholar 

  18. Lai, M., Nicholson, J. & Rudolph, W. Multiple pulse operation of a femtosecond Ti:sapphire laser. Opt. Commun. 142, 45–49 (1997).

    Article  ADS  Google Scholar 

  19. Akhmediev, N. N., Ankiewicz, A. & Soto-Crespo, J. M. Stable soliton pairs in optical transmission lines and fiber lasers. J. Opt. Soc. Am. B 15, 515 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  20. Liu, X. Dynamic evolution of temporal dissipative-soliton molecules in large normal path-averaged dispersion fiber lasers. Phys. Rev. A 82, 063834 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. Li, X., Wang, Y., Zhang, W. & Zhao, W. Experimental observation of soliton molecule evolution in Yb-doped passively mode-locked fiber lasers. Laser Phys. Lett. 11, 075103 (2014).

    Article  ADS  Google Scholar 

  23. Wei, Y., Li, B., Wei, X., Yu, Y. & Wong, K. K. Y. Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser. Appl. Phys. Lett. 112, 081104 (2018).

    Article  ADS  Google Scholar 

  24. Ryczkowski, P. et al. Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser. Nat. Photon. 12, 221–227 (2018).

    Article  ADS  Google Scholar 

  25. Klein, A. et al. Ultrafast rogue wave patterns in fiber lasers. Optica 5, 774 (2018).

    Article  ADS  Google Scholar 

  26. Herink, G., Jalali, B., Ropers, C. & Solli, D. R. Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate. Nat. Photon. 10, 321–326 (2016).

    Article  ADS  Google Scholar 

  27. Fano, U. Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124, 1866–1878 (1961).

    Article  ADS  Google Scholar 

  28. Grapinet, M. & Grelu, P. Vibrating soliton pairs in a mode-locked laser cavity. Opt. Lett. 31, 2115 (2006).

    Article  ADS  Google Scholar 

  29. Matos, L., Mücke, O. D., Chen, J. & Kärtner, F. X. Carrier-envelope phase dynamics and noise analysis in octave-spanning Ti:sapphire lasers. Opt. Express 14, 2497–2511 (2006).

    Article  ADS  Google Scholar 

  30. Prosperetti, A. Application of the subharmonic threshold to the measurement of the damping of oscillating gas bubbles. J. Acoust. Soc. Am. 61, 11–16 (1977).

    Article  ADS  Google Scholar 

  31. Sanchez, F. et al. Manipulating dissipative soliton ensembles in passively mode-locked fiber lasers. Opt. Fiber Technol. 20, 562–574 (2014).

    Article  ADS  Google Scholar 

  32. Pang, M., He, W., Jiang, X. & Russell, P. S. J. All-optical bit storage in a fibre laser by optomechanically bound states of solitons. Nat. Photon. 10, 454–458 (2016).

    Article  ADS  Google Scholar 

  33. Yu, Y., Wei, X., Kang, J., Li, B. & Wong, K. K. Y. Pulse-spacing manipulation in a passively mode-locked multipulse fiber laser. Opt. Express 25, 13215 (2017).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

F.K. is part of the Max Planck School of Photonics supported by BMBF, Max Planck Society and Fraunhofer Society. We thank D. R. Solli for valuable discussions.

Author information

Authors and Affiliations

Authors

Contributions

All authors were closely involved in this study and contributed to the ideas, realization of the experiments, data analysis and interpretation, and the writing of the paper.

Corresponding author

Correspondence to G. Herink.

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. 1–4.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kurtz, F., Ropers, C. & Herink, G. Resonant excitation and all-optical switching of femtosecond soliton molecules. Nat. Photonics 14, 9–13 (2020). https://doi.org/10.1038/s41566-019-0530-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-019-0530-3

This article is cited by

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