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.

  • Article
  • Published:

Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser

Nature Photonics volume 12, pages 221–227 (2018)Cite this article

Subjects

Abstract

Dissipative solitons are remarkably localized states of a physical system that arise from the dynamical balance between nonlinearity, dispersion and environmental energy exchange. They are the most universal form of soliton that can exist, and are seen in far-from-equilibrium systems in many fields, including chemistry, biology and physics. There has been particular interest in studying their properties in mode-locked lasers, but experiments have been limited by the inability to track the dynamical soliton evolution in real time. Here, we use simultaneous dispersive Fourier transform and time-lens measurements to completely characterize the spectral and temporal evolution of ultrashort dissipative solitons as their dynamics pass through a transient unstable regime with complex break-up and collisions before stabilization. Further insight is obtained from reconstruction of the soliton amplitude and phase and calculation of the corresponding complex-valued eigenvalue spectrum. These findings show how real-time measurements provide new insights into ultrafast transient dynamics in optics.

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
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Direct photodetector measurement of transient laser dynamics.
Fig. 2: Experimental setup.
Fig. 3: Real-time spectral and temporal characterization near stability.
Fig. 4: Real-time spectral and temporal characterization of complex dynamics.
Fig. 5: Eigenvalue content of unstable solitons.

Similar content being viewed by others

References

  1. French, P. M. W. The generation of ultrashort laser pulses. Rep. Prog. Phys. 58, 169–267 (1995).

    Article  ADS  Google Scholar 

  2. Keller, U. Recent developments in compact ultrafast lasers. Nature 424, 831–838 (2003).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. Abraham, D., Nagar, R., Mikhelashvili, V. & Eisenstein, G. Transient dynamics in a self-starting passively mode-locked fiber-based soliton laser. Appl. Phys. Lett. 63, 2857–2859 (1993).

    Article  ADS  Google Scholar 

  5. Dudley, J. M., Loh, C. M. & Harvey, J. D. Stable and unstable operation of a mode-locked argon laser. Quantum Semiclass. Opt. 8, 1029–1039 (1996).

    Article  ADS  Google Scholar 

  6. Hönninger, C., Paschotta, R., Morier-Genoud, F., Moser, M. & Keller, U. Q-switching stability limits of continuous wave passive mode locking. J. Opt. Soc. Am. B 16, 46–56 (1999).

    Article  ADS  Google Scholar 

  7. Akhmediev, N. & Ankiewicz, A. (eds) Dissipative Solitons, Lecture Notes in Physics, Vol. 661 (Springer-Verlag, Berlin, Germany, 2005).

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

    Article  ADS  Google Scholar 

  9. Grelu, P. (ed.) Nonlinear Optical Cavity Dynamics: From Microresonators to Fiber Lasers (Wiley, Berlin, Germany, 2016).

  10. Turitsyn, S. K. et al. Dissipative solitons in fiber lasers. Phys. Usp. 59, 642–668 (2016).

    Article  ADS  Google Scholar 

  11. Flynn, M. B., O’Faolain, L. & Krauss, T. F. An experimental and numerical study of Q-switched mode-locking in monolithic semiconductor diode lasers. IEEE J. Quant. Electron. 40, 1008–1013 (2004).

    Article  ADS  Google Scholar 

  12. Schlatter, A., Zeller, S. C., Grange, R., Paschotta, R. & Keller, U. Pulse-energy dynamics of passively mode-locked solid-state lasers above the Q-switching threshold. J. Opt. Soc. Am. B 21, 1469–1478 (2004).

    Article  ADS  Google Scholar 

  13. Lecaplain, C., Grelu, P., Soto-Crespo, J. M. & Akhmediev, N. Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser. Phys. Rev. Lett. 108, 233901 (2012).

    Article  ADS  Google Scholar 

  14. Goda, K. & Jalali, B. Dispersive Fourier transformation for fast continuous single-shot measurements. Nat. Photon. 7, 102–112 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Godin, T. et al. Real time noise and wavelength correlations in octave-spanning supercontinuum generation. Opt. Express 21, 18452–18460 (2013).

    Article  ADS  Google Scholar 

  17. Solli, D. R., Herink, G., Jalali, B. & Ropers, C. Fluctuations and correlations in modulation instability. Nat. Photon. 6, 463–468 (2012).

    Article  ADS  Google Scholar 

  18. Wetzel, B. et al. Real-time full bandwidth measurement of spectral noise in supercontinuum generation. Sci. Rep. 2, 882 (2012).

    Article  Google Scholar 

  19. Runge, A. F. J., Aguergaray, C., Broderick, N. G. R. & Erkintalo, M. Coherence and shot-to-shot spectral fluctuations in noise-like ultrafast fiber lasers. Opt. Lett. 38, 4327–4330 (2013).

    Article  ADS  Google Scholar 

  20. Runge, A. F. J., Broderick, N. G. R. & Erkintalo, M. Observation of soliton explosions in a passively mode-locked fiber laser. Optica 2, 36–39 (2015).

    Article  Google Scholar 

  21. 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 

  22. 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 

  23. Kolner, B. H. & Nazarathy, M. Temporal imaging with a time lens. Opt. Lett. 14, 630–632 (1989).

    Article  ADS  Google Scholar 

  24. Suret, P. et al. Single-shot observation of optical rogue waves in integrable turbulence using time microscopy. Nat. Commun. 7, 13136 (2016).

    Article  ADS  Google Scholar 

  25. Närhi, M. et al. Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability. Nat. Commun. 7, 13675 (2016).

    Article  ADS  Google Scholar 

  26. Billet, C., Dudley, J. M., Joly, N. & Knight, J. C. Intermediate asymptotic evolution and photonic bandgap fiber compression of optical similaritons around 1550 nm. Opt. Express 13, 3236–3241 (2005).

    Article  ADS  Google Scholar 

  27. Soto-Crespo, J. M., Akhmediev, N. & Town, G. Continuous-wave versus pulse regime in a passively mode-locked laser with a fast saturable absorber. J. Opt. Soc. Am. B 19, 234–242 (2002).

    Article  ADS  Google Scholar 

  28. Schreiber, T., Ortaç, B., Limpert, J. & Tünnermann, A. On the study of pulse evolution in ultra-short pulse mode-locked fiber lasers by numerical simulations. Opt. Express 15, 8252–8262 (2007).

    Article  ADS  Google Scholar 

  29. Sarukura, N. & Ishida, Y. Pulse evolution dynamics of a femtosecond passively mode-locked Ti:sapphire laser. Opt. Lett. 17, 61–63 (1992).

    Article  ADS  Google Scholar 

  30. Vodonos, B. et al. Experimental study of the stochastic nature of the pulsation self-starting process in passive mode locking. Opt. Lett. 30, 2787–2789 (2005).

    Article  ADS  Google Scholar 

  31. Li, H., Ouzounov, D. G. & Wise, F. W. Starting dynamics of dissipative-soliton fiber laser. Opt. Lett. 35, 2403–2405 (2010).

    Article  ADS  Google Scholar 

  32. Zinkiewicz, Ł., Ozimek, F. & Wasylczyk, P. Witnessing the pulse birth-transient dynamics in a passively mode-locked femtosecond laser. Laser Phys. Lett. 10, 125003 (2013).

    Article  ADS  Google Scholar 

  33. Ghiu Lee, C., Kim, J., Kim, S. & Petropoulos, P. Transient response of a passively mode-locked Er-doped fiber ring laser. Opt. Commun. 356, 161–165 (2015).

    Article  ADS  Google Scholar 

  34. Wang, Z. et al. Q-switched-like soliton bunches and noise-like pulses generation in a partially mode-locked fiber laser. Opt. Express 24, 14709–14716 (2016).

    Article  ADS  Google Scholar 

  35. Gerchberg, R. W. & Saxton, W. O. A practical algorithm for the determination of the phase from image and diffraction plane pictures. Optik 35, 237–246 (1972).

    Google Scholar 

  36. Trebino, R. Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Wiley, Berlin, Germany, 2000).

  37. Grelu, P. & Soto-Crespo, J. M. in Dissipative Solitons: From Optics to Biology and Medicine, Lecture Notes in Physics, Vol. 751 (eds Akhmediev, N. & Ankiewicz, A.) 137–173 (Springer, Berlin, Heidelberg, 2008).

  38. 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 

  39. Tang, D. Y., Zhao, B., Zhao, L. M. & Tam, H. Y. Soliton interaction in a fiber ring laser. Phys. Rev. E 72, 16616 (2005).

    Article  ADS  Google Scholar 

  40. Roy, V., Olivier, M. & Piché, M. Pulse interactions in the stretched-pulse fiber laser. Opt. Express 13, 9217–9223 (2005).

    Article  ADS  Google Scholar 

  41. Akhmediev, N., Soto-Crespo, J. M., Grapinet, M. & Grelu, P. Dissipative soliton interactions inside a fiber laser cavity. Opt. Fib. Tech. 11, 209–228 (2005).

    Article  Google Scholar 

  42. Akhmediev, N., Soto-Crespo, J. M. & Town, G. Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: complex Ginzburg-Landau equation approach. Phys. Rev. E 63, 56602 (2001).

    Article  ADS  Google Scholar 

  43. Zakharov, V. E. & Shabat, A. B. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62–69 (1972).

    ADS  MathSciNet  Google Scholar 

  44. Akhmediev, N. & Ankiewicz, A. Solitons: Non-linear Pulses and Beams (Chapman and Hall, London, UK, 1997).

  45. Osborne, A. R. Nonlinear Ocean Waves and the Inverse Scattering Transform (Elsevier, London, UK, 2010).

  46. Agrawal, G. P. Nonlinear Fiber Optics (Elsevier, Oxford, UK, 2013).

  47. Turitsyn, S. K. & Derevyanko, S. A. Soliton-based discriminator of noncoherent optical pulses. Phys. Rev. A 78, 063819 (2008).

    Article  ADS  Google Scholar 

  48. Randoux, S., Suret, P. & El, G. Inverse scattering transform analysis of rogue waves using local periodization procedure. Sci. Rep. 6, 29238 (2016).

    Article  ADS  Google Scholar 

  49. Turitsyn, S. K. et al. Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives. Optica 4, 307–322 (2017).

    Article  Google Scholar 

  50. 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).

    Article  ADS  Google Scholar 

  51. Iaconis, C. & Walmsley, I. A. Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses. Opt. Lett. 23, 792–794 (1998).

    Article  ADS  Google Scholar 

  52. Tikan, A., Bielawski, S., Szwaj, C., Randoux, S. & Suret, P. Phase and amplitude single-shot measurement by using heterodyne time-lens and ultrafast digital time-holography. Nat. Photon. https://doi.org/10.1038/s41566-018-0113-8 (2018).

  53. Salem, R., Foster, M. A. & Gaeta, A. L. Application of space–time duality to ultrahigh-speed optical signal processing. Adv. Opt. Photon. 5, 274–317 (2013).

    Article  Google Scholar 

  54. Sugavanam, S., Kamalian, M., Peng, J., Prilepsky, J. E. & Turitsyn, S. K. Experimentally characterized nonlinear fourier transform of a mode-locked fibre laser. In Conference on Lasers and Electro-Optics Europe and the European Quantum Electronics Conference EF-2.6 (Optical Society of America, 2017).

  55. Narhi, M., Ryczkowski, P., Billet, C., Genty, G. & Dudley, J. M. Ultrafast simultaneous real time spectral and temporal measurements of fibre laser modelocking dynamics. In Conference on Lasers and Electro-Optics Europe and the European Quantum Electronics Conference EE-3.5 (Optical Society of America, 2017).

  56. Reddy, K. V. et al. A turnkey 1.5 μm picosecond Er/Yb fiber laser. In Conference on Optical Fiber Communication (OFC), OSA Technical Digest Series PD17 (Optical Society of America, 1993).

  57. Wahls, S. & Poor, H. V. Fast numerical nonlinear Fourier transforms. IEEE Trans. Inf. Theory 6, 6957–6974 (2015).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the Agence Nationale de la Recherche project LABEX ACTION ANR11-LABX-0001-01, the Region of Franche-Comté Project CORPS and the Academy of Finland (Grants 267576 and 298463). The authors also thank K. V. Reddy for providing technical details concerning the soliton operating regime of the Pritel laser used in these experiments.

Author information

Author notes

  1. These authors contributed equally: P. Ryczkowski, M. Närhi and C. Billet.

Authors and Affiliations

  1. Laboratory of Photonics, Tampere University of Technology, Tampere, Finland

    P. Ryczkowski, M. Närhi & G. Genty

  2. Institut FEMTO-ST, UMR 6174 CNRS-Université Bourgogne Franche-Comté, Besançon, France

    C. Billet, J.-M. Merolla & J. M. Dudley

Authors
  1. P. Ryczkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Närhi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Billet
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J.-M. Merolla
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. G. Genty
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. J. M. Dudley
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors participated in all the experimental work and data analysis reported, and in the writing and review of the final manuscript. G.G. and J.M.D. planned the research project and provided overall supervision.

Corresponding author

Correspondence to J. M. Dudley.

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

Phase retrieval algorithm and nonlinear Fourier transform of typical pulse shapes.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ryczkowski, P., Närhi, M., Billet, C. et al. Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser. Nature Photon 12, 221–227 (2018). https://doi.org/10.1038/s41566-018-0106-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-018-0106-7

This article is cited by

Search

Advanced 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