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:

Extreme waveform compression with a nonlinear temporal focusing mirror

Nature Photonics volume 16, pages 822–827 (2022)Cite this article

Subjects

Abstract

Dealing with the increase in digital optical data transmission rates requires innovative approaches for stretching or compressing optical waveforms beyond the bandwidth limitations inherent in conventional electro‐optical systems. To this aim, photonic platforms exploiting ultrafast nonlinear phenomena have been successfully applied to the temporal stretching of optical waveforms. However, the inverse process, that is, the temporal compression of arbitrary lightwaves, has remained largely unexploited so far. Here we present an experimental demonstration of the extreme temporal compression of optical waveforms, including non‐trivial on‐demand time reversal. The method is based on counterpropagating degenerate four‐photon interaction in birefringent optical fibres. We demonstrate the performance of this system by generating the ultrafast replica of data packets with record temporal compression factors ranging from 4,350 to 13,000. This approach is scalable and offers great promise for ultrafast arbitrary optical waveform generation and related applications.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Fig. 1: Temporal compression system.
Fig. 2: Experimental demonstration of temporal compression of a 10.0 Mbit s–1 10‑bit‑long sequence into a 43.5 Gbit s–1 replica.
Fig. 3: Temporal compression factor M versus fibre birefringence.
Fig. 4: Experimental result of temporal compression of a MHz-bandwidth arbitrary waveform into a multi-gigahertz replica.
Fig. 5: Numerical results showing the temporal compression of an analogue optical waveform for different values of fibre birefringence.

Similar content being viewed by others

Data availability

All data generated in the present study as well as simulation codes are available from the corresponding author on reasonable request.

References

  1. Wong, T. et al. Asymmetric-detection time-stretch optical microscopy (ATOM) for ultrafast high-contrast cellular imaging in flow. Sci. Rep. 4, 3656 (2014).

    Article  Google Scholar 

  2. Roussel, E. et al. Observing microscopic structures of a relativistic object using a time-stretch strategy. Sci. Rep. 5, 10330 (2015).

    Article  ADS  Google Scholar 

  3. 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 

  4. Lei, M., Zou, W., Li, X. & Chen, J. Ultrafast FBG interrogator based on time-stretch method. IEEE Photon. Technol. Lett. 28, 778–781 (2016).

    Article  ADS  Google Scholar 

  5. Palushani, E. et al. All-optical OFDM demultiplexing by spectral magnification and band-pass filtering. Opt. Express 22, 136–144 (2014).

    Article  ADS  Google Scholar 

  6. Bennett, C. V., Scott, R. P. & Kolner, B. H. Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope. Appl. Phys. Lett. 65, 2513–2515 (1994).

    Article  ADS  Google Scholar 

  7. Foster, M. A. et al. Silicon-chip-based ultrafast optical oscilloscope. Nature 456, 81–84 (2008).

    Article  ADS  Google Scholar 

  8. Mahjoubfar, A. et al. Time stretch and its applications. Nat. Photon. 11, 341–351 (2017).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Kolner, B. H. Space-time duality and the theory of temporal imaging. IEEE J. Quantum Electron. 30, 1951–1963 (1994).

    Article  ADS  Google Scholar 

  11. Azaña, J. Time-to-frequency conversion using a single time lens. Opt. Commun. 217, 205–209 (2003).

    Article  ADS  Google Scholar 

  12. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. 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 

  16. 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 

  17. Meng, F. et al. Intracavity incoherent supercontinuum dynamics and rogue waves in a broadband dissipative soliton laser. Nat. Commun. 12, 5567 (2021).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Herink, G., Jalali, B., Ropers, C. & Solli, D. 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 

  20. 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 

  21. Asghari, M. H. & Jalali, B. Experimental demonstration of optical real-time data compression. Appl. Phys. Lett. 104, 111101 (2014).

    Article  ADS  Google Scholar 

  22. Jalali, B., Chan, J. & Asghari, M. H. Time-bandwidth engineering. Optica 1, 23–31 (2014).

    Article  ADS  Google Scholar 

  23. Rangarajan, S., Poulsen, H. N. & Blumenthal, D. J. All-optical packet compression of variable length packets from 40 to 1500 B using a gated fibre loop. IEEE Photon. Technol. Lett. 18, 322–324 (2006).

    Article  ADS  Google Scholar 

  24. Deng, K.-L., Kang, K. I., Glesk, I., Prucnal, P. R. & Shin, S. Optical packet compressor for ultra-fast packet-switched optical networks. Electron. Lett. 33, 1237–1238 (1997).

    Article  ADS  Google Scholar 

  25. Toda, H., Nakada, F., Suzuki, M. & Hasegawa, A. An optical packet compressor based on a fibre delay loop. IEEE Photon. Technol. Lett. 12, 708–710 (2000).

    Article  ADS  Google Scholar 

  26. Toliver, P., Deng, K.-L., Glesk, I. & Prucnal, P. R. Simultaneous optical compression and decompression of 100-Gb/s OTDM packets using a single bidirectional optical delay line lattice. IEEE Photon. Technol. Lett. 11, 1183–1185 (1999).

    Article  ADS  Google Scholar 

  27. Sotobayashi, H., Kitayama, K. & Ozeki, T. 40 Gbit/s photonic packet compression and decompression by supercontinuum generation. Electron. Lett. 37, 110–111 (2001).

    Article  ADS  Google Scholar 

  28. Almeida, P. J., Petropoulos, P., Thomsen, B. C., Ibsen, M. & Richardson, D. J. All-optical packet compression based on time-to-wavelength conversion. IEEE Photon. Technol. Lett. 16, 1688–1690 (2004).

    Article  ADS  Google Scholar 

  29. Foster, M. et al. Ultrafast waveform compression using a time-domain telescope. Nat. Photon. 3, 581–585 (2009).

    Article  ADS  Google Scholar 

  30. Cundiff, S. & Weiner, A. Optical arbitrary waveform generation. Nat. Photon. 4, 760–766 (2010).

    Article  ADS  Google Scholar 

  31. Wang, J. et al. Reconfigurable radio-frequency arbitrary waveforms synthesized in a silicon photonic chip. Nat. Commun. 6, 5957 (2015).

    Article  ADS  Google Scholar 

  32. Rouskas, G. N. & Xu L. Optical packet switching. in Emerging Optical Network Technologies (eds Sivalingam K. M. & Subramaniam S.) (Springer, 2005).

  33. Yoshida, Y. et al. SDN-based network orchestration of variable-capacity optical packet switching network over programmable flexi-grid elastic optical path network. J. Lightwave Technol. 33, 609–617 (2015).

    Article  ADS  Google Scholar 

  34. Wohlleben, W., Buckup, T., Herek, J. L. & Motzkus, M. Coherent control for spectroscopy and manipulation of biological dynamics. ChemPhysChem 6, 850–857 (2005).

    Article  Google Scholar 

  35. Wu, H., Zhu, W., Pang, J. & Cheng, Z. Research on superconducting qubit manipulation based on arbitrary waveform generator. J. Phys.: Conf. Ser. 1650, 022112 (2020).

  36. Ng, W., Rockwood, T., Sefler, G. & Valley, G. Demonstration of a large stretch-ratio (M = 41) photonic analog-to-digital converter with 8 ENOB for an input signal bandwidth of 10 GHz. IEEE Photon. Technol. Lett. 24, 1185–1187 (2012).

    Article  ADS  Google Scholar 

  37. Goda, K., Tsia, K. K. & Jalali, B. Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena. Nature 458, 1145–1149 (2009).

    Article  ADS  Google Scholar 

  38. Khilo, A. et al. Photonic ADC: overcoming the bottleneck of electronic jitter. Opt. Express 20, 4454–4469 (2012).

    Article  ADS  Google Scholar 

  39. Starodumov, A. N. Pulse train compression up to terabit rates using four-wave mixing in birefringent fibre. Opt. Commun. 124, 365–372 (1996).

    Article  ADS  Google Scholar 

  40. Kaplan, A. E. Optical bistability that is due to mutual self-action of counterpropagating beams of light. Opt. Lett. 6, 360–362 (1981).

    Article  ADS  Google Scholar 

  41. Guasoni, M. et al. Line of polarization attraction in highly birefringent optical fibres. J. Opt. Soc. Am. B 31, 572–580 (2014).

    Article  ADS  Google Scholar 

  42. Gauthier, D. J., Malcuit, M. S., Gaeta, A. L. & Boyd, R. W. Polarization bistability of counterpropagating laser beams. Phys. Rev. Lett. 64, 1721 (1990).

    Article  ADS  Google Scholar 

  43. Dawes, A. M. C., Illing, L., Clark, S. M. & Gauthier, D. J. All-optical switching in rubidium vapor. Science 308, 672–674 (2005).

    Article  ADS  Google Scholar 

  44. Beltrán-Mejía, F. et al. Ultrahigh-birefringent squeezed lattice photonic crystal fiber with rotated elliptical air holes. Opt. Lett. 35, 544–546 (2010).

    Article  ADS  Google Scholar 

  45. Jung, Y., Brambilla, G., Oh, K. & Richardson, D. J. Highly birefringent silica microfiber. Opt. Lett. 35, 378–380 (2010).

    Article  ADS  Google Scholar 

  46. Yang, T. et al. High birefringence photonic crystal fiber with high nonlinearity and low confinement loss. Opt. Express 23, 8329–8337 (2015).

    Article  ADS  Google Scholar 

  47. Zhou, J. et al. Electro-optically switchable optical true delay lines of meter-scale lengths fabricated on lithium niobate on insulator using photolithography assisted chemo-mechanical etching. Chinese Phys. Lett. 37, 084201 (2020).

    Article  ADS  Google Scholar 

  48. Zhang, H., Bigot-Astruc, M., Bigot, L., Sillard, P. & Fatome, J. Multiple modal and wavelength conversion process of a 10-Gbit/s signal in a 6-LP-mode fibre. Opt. Express 27, 15413–15425 (2019).

    Article  ADS  Google Scholar 

  49. Li, B. et al. Reaching fiber-laser coherence in integrated photonics. Opt. Lett. 46, 5201–5204 (2021).

    Article  ADS  Google Scholar 

  50. Agrawal, G. P. Nonlinear Fibre Optics 5th edn (Academic Press, 2013).

Download references

Acknowledgements

We acknowledge A. Picozzi, P. Béjot, M. Guasoni, B. Kibler, C. Finot, A. Parriaux, G. Millot, H. Zhang, F. Leo and S. Pitois for fruitful discussions. We also acknowledge T. Villedieu from iXblue for providing the fibre parameters. J.F. acknowledges financial support from the CNRS, IRP Wall-IN project (CNRS research collaboration agreement no. 241655) and financial support from the Conseil Régional de Bourgogne Franche-Comté, International Mobility Program. This work is supported by la délégation régionale à la recherche et à la technologie and the European Union through the PO FEDER-FSE Bourgogne 2014/2020 programs. This work has benefited from the facilities of the SMARTLIGHT platform in Bourgogne Franche-Comté (EQUIPEX + ANR-21-ESRE-0040). S.C. and M.E. acknowledge financial support from The Royal Society of New Zealand, in the form of Marsden Funding (18-UOA-310) and Rutherford Discovery Fellowships.

Author information

Authors and Affiliations

  1. Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS Université Bourgogne Franche-Comté, Dijon, France

    Nicolas Berti & Julien Fatome

  2. Department of Physics, The University of Auckland, Auckland, New Zealand

    Stéphane Coen, Miro Erkintalo & Julien Fatome

  3. The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand

    Stéphane Coen, Miro Erkintalo & Julien Fatome

Authors
  1. Nicolas Berti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stéphane Coen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Miro Erkintalo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Julien Fatome
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.F. and N.B. designed the experimental setup. J.F. and N.B. performed the experiments. N.B. and J.F. performed the numerical simulations. S.C. and M.E. provided theoretical assistance. All the authors have contributed to the interpretation of the results. J.F., S.C. and M.E. wrote the paper.

Corresponding author

Correspondence to Julien Fatome.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

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

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Sections 1–4 and Figs. 1–3.

Supplementary Video 1

Numerical simulation of the temporal compression of a data sequence.

Supplementary Video 2

Same data as in Supplementary Video 1, but the incident data sequence is replaced by an arbitrary-shaped waveform.

Supplementary Video 3

Spatiotemporal evolution of the temporal compression of a data sequence and the simultaneous temporal inversion.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Berti, N., Coen, S., Erkintalo, M. et al. Extreme waveform compression with a nonlinear temporal focusing mirror. Nat. Photon. 16, 822–827 (2022). https://doi.org/10.1038/s41566-022-01072-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-022-01072-1

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