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.

Inverse four-wave mixing and self-parametric amplification in optical fibre

Abstract

An important group of nonlinear processes in optical fibre involve the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and those arising from self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect—self-parametric amplification—which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. Self-parametric amplification and the observed stable nonlinear spectral propagation with a random temporal waveform can find applications in optical communications and high-power fibre lasers with nonlinear intracavity dynamics.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Experimental observation of spectrum evolution in normal and anomalous dispersion fibres.
Figure 2: Spectrum shape after signal propagation in LEAF fibre.
Figure 3: Evolution of the signal spectrum and temporal shape along the fibre.
Figure 4: Signal gain spectra as a function of pump wavelength spacing.
Figure 5: Estimate of FWM product during signal amplification.
Figure 6: Theoretical evolution of the spectral broadening factor.

References

  1. Stolen, R. H. The early years of fiber nonlinear optics. J. Lightw. Technol. 26, 1021–1031 (2008).

    Article  ADS  Google Scholar 

  2. Agrawal, G. P. Nonlinear Fiber Optics (Academic, 2007).

    MATH  Google Scholar 

  3. Boyd, R. W. Nonlinear Optics (Academic, 2003).

    Google Scholar 

  4. Toulouse, J. Optical nonlinearities in fibers: review, recent examples, systems applications. J. Lightw. Technol. 23, 3625–3641 (2005).

    Article  ADS  Google Scholar 

  5. Dudley, J. M. & Taylor, J. R. Ten years of nonlinear optics in photonic crystal fibre. Nature Photon. 3, 85–90 (2009).

    Article  ADS  Google Scholar 

  6. Garmire, E. Nonlinear optics in daily life. Opt. Express 21, 30532–30544 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Turitsyna, E. G. et al. The laminar–turbulent transition in a fibre laser. Nature Photon. 7, 783–786 (2013).

    Article  ADS  Google Scholar 

  9. Kibler, B. et al. The Peregrine soliton in nonlinear fibre optics. Nature Phys. 6, 790–795 (2010).

    Article  ADS  Google Scholar 

  10. Turitsyn, S. K. et al. Random distributed feedback fibre laser. Nature Photon. 4, 231–235 (2010).

    Article  ADS  Google Scholar 

  11. Turitsyn, S. K., Bale, B. & Fedoruk, M. P. Dispersion-managed solitons in fibre systems and lasers. Phys. Rep. 521, 135–203 (2012).

    Article  ADS  Google Scholar 

  12. Turitsyn, S. K. et al. Random distributed feedback fibre lasers. Phys. Rep. 542, 133–193 (2014).

    Article  ADS  Google Scholar 

  13. Picozzi, A. et al. Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics. Phys. Rep. 542, 1–132 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  14. Stolen, R. H. Phase-matched-stimulated four-photon mixing in silica-fiber waveguides. IEEE J. Quantum Electron. 11, 100–103 (1975).

    Article  ADS  Google Scholar 

  15. Marhic, M. E. Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge Univ. Press, 2007).

    Book  Google Scholar 

  16. Hansryd, J., Andrekson, P. A., Westlund, M., Li, J. & Hedekvist, P. O. Fiber-based optical parametric amplifiers and their applications. J. Sel. Top. Quantum Electron. 8, 506–520 (2002).

    Article  Google Scholar 

  17. Radic, S. & McKinstrie, C. J. Two-pump fiber parametric amplifiers. Opt. Fiber Technol. 9, 7–23 (2003).

    Article  ADS  Google Scholar 

  18. McKinstrie, C. & Radic, S. Phase-sensitive amplification in a fiber. Opt. Express 12, 4973–4979 (2004).

    Article  ADS  Google Scholar 

  19. McKinstrie, C. J., Radic, S. & Gnauck, A. H. All-optical signal processing by fiber-based parametric devices. Opt. Photon. News 18, 34–40 (2007).

    Article  ADS  Google Scholar 

  20. Marhic, M. E. et al. Fiber optical parametric amplifiers in optical communication systems. Laser Photon. Rev. 9, 50–74 (2015).

    Article  ADS  Google Scholar 

  21. Tong, Z. et al. Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers. Nature Photon. 5, 430–436 (2011).

    Article  ADS  Google Scholar 

  22. Slavik, R. et al. All-optical phase and amplitude regenerator for next-generation telecommunications systems. Nature Photon. 4, 690–695 (2010).

    Article  ADS  Google Scholar 

  23. Karpov, V. I., Clements, W. R. L., Dianov, E. M. & Papernyi, S. B. High-power 1.48 μm phosphoro-silicate-fiber-based laser pumped by laser diodes. Can. J. Phys. 78, 407–413 (2000).

    Article  ADS  Google Scholar 

  24. Bouteiller, J-C. Spectral modeling of Raman fiber lasers. Photon. Technol. Lett. 15, 1698–1700 (2003).

    Article  ADS  Google Scholar 

  25. Suret, P. & Randoux, S. Influence of spectral broadening on steady characteristics of Raman fiber lasers: from experiments to questions about the validity of usual models. Opt. Commun. 237, 201–212 (2004).

    Article  ADS  Google Scholar 

  26. Turitsyn, S. K. et al. Modeling of CW Yb-doped fiber lasers with highly nonlinear cavity dynamics. Opt. Express 19, 8394–8405 (2011).

    Article  ADS  Google Scholar 

  27. Babin, S., Churkin, D., Ismagulov, A., Kablukov, S. & Podivilov, E. Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser. J. Opt. Soc. Am. B 24, 1729–1738 (2007).

    Article  ADS  Google Scholar 

  28. Turitsyn, S. K. et al. in Advances in Wave Turbulence Vol. 83 (eds Shrira, V. & Nazarenko, S.) Ch. 4, 113–164 (World Scientific Series on Nonlinear Science Series A, World Scientific, 2013).

    Book  Google Scholar 

  29. Babin, S. et al. Turbulent broadening of optical spectra in ultralong Raman fiber lasers. Phys. Rev. A 77, 033803 (2008).

    Article  ADS  Google Scholar 

  30. Paramonov, V. M., Kurkov, A. S., Medvedkov, O. I., Grukh, D. A. & Dianov, E. M. Two-frequency fibre Raman laser. Quantum Electron. 34, 213–215 (2004).

    Article  ADS  Google Scholar 

  31. Turitsyna, E. G., Falkovich, G., Mezentsev, V. K. & Turitsyn, S. K. Optical turbulence and spectral condensate in long-fiber lasers. Phys. Rev. A 80, 031804 (2009).

    Article  ADS  Google Scholar 

  32. Barviau, B., Randoux, S. & Suret, P. Spectral broadening of a multimode continuous-wave optical field propagating in the normal dispersion regime of a fiber. Opt. Lett. 31, 1696–1698 (2006).

    Article  ADS  Google Scholar 

  33. Churkin, D., Smirnov, S. & Podivilov, E. Statistical properties of partially coherent cw fiber lasers. Opt. Lett. 35, 3288–3290 (2010).

    Article  ADS  Google Scholar 

  34. Churkin, D. V. et al. Wave kinetics of random fibre lasers. Nature Commun. 6, 6214 (2015).

    Article  ADS  Google Scholar 

  35. Sidorov-Biryukov, D. A. et al. Spectral narrowing of chirp-free light pulses in anomalously dispersive, highly nonlinear photonic-crystal fibers. Opt. Express 16, 2502–2507 (2008).

    Article  ADS  Google Scholar 

  36. Cundiff, S. T. et al. Propagation of highly chirped pulses in fiber-optic communications systems. J. Lightw. Technol. 17, 811–816 (1999).

    Article  ADS  Google Scholar 

  37. Washburn, B. R., Buck, J. A. & Ralph, S. E. Transform-limited spectral compression due to self-phase modulation in fibers. Opt. Lett. 25, 445–447 (2000).

    Article  ADS  Google Scholar 

  38. Planas, S. A., Pires Mansur, N. L., Brito Cruz, C. H. & Fragnito, H. L. Spectral narrowing in the propagation of chirped pulses in single-mode fibers. Opt. Lett. 18, 699–701 (1993).

    Article  ADS  Google Scholar 

  39. Oberthaler, M. & Höpfel, R. A. Spectral narrowing of ultrashort laser pulses by self-phase modulation in optical fibers. Appl. Phys. Lett. 63, 1017–1019 (1993).

    Article  ADS  Google Scholar 

  40. Nishizawa, N., Takahashi, K., Ozeki, Y. & Itoh, K. Wideband spectral compression of wavelength-tunable ultrashort soliton pulse using comb-profile fiber. Opt. Express 18, 11700–11706 (2010).

    Article  ADS  Google Scholar 

  41. Preda, C. E., Fotiadi, A. A. & Mégret, P. Numerical approximation for Brillouin fiber ring resonator. Opt. Express 20, 5783–5788 (2012).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge financial support from the European Research Council project ULTRALASER (267763), the Ministry of Education and Science of the Russian Federation (14.B25.31.0003 and 14.578.21.0029) and the Russian Science Foundation (14-21-00110; work of A.E.B). The authors also thank E. V. Podivilov for fruitful discussions.

Author information

Authors and Affiliations

Authors

Contributions

S.B.P. initiated the study and carried out the experiments. A.E.B. designed and conducted the numerical modelling. S.K.T., A.E.B. and M.P.F. guided the theoretical and numerical studies. S.K.T., S.B.P., A.E.B., W.R.L.C and M.P.F. analysed the data. S.K.T., A.E.B., S.B.P. and W.R.L.C. wrote the paper.

Corresponding author

Correspondence to Sergei K. Turitsyn.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1584 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Turitsyn, S., Bednyakova, A., Fedoruk, M. et al. Inverse four-wave mixing and self-parametric amplification in optical fibre. Nature Photon 9, 608–614 (2015). https://doi.org/10.1038/nphoton.2015.150

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2015.150

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