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.
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References
Stolen, R. H. The early years of fiber nonlinear optics. J. Lightw. Technol. 26, 1021–1031 (2008).
Agrawal, G. P. Nonlinear Fiber Optics (Academic, 2007).
Boyd, R. W. Nonlinear Optics (Academic, 2003).
Toulouse, J. Optical nonlinearities in fibers: review, recent examples, systems applications. J. Lightw. Technol. 23, 3625–3641 (2005).
Dudley, J. M. & Taylor, J. R. Ten years of nonlinear optics in photonic crystal fibre. Nature Photon. 3, 85–90 (2009).
Garmire, E. Nonlinear optics in daily life. Opt. Express 21, 30532–30544 (2013).
Solli, D. R., Ropers, C., Koonath, P. & Jalali, B. Optical rogue waves. Nature 450, 1054–1057 (2007).
Turitsyna, E. G. et al. The laminar–turbulent transition in a fibre laser. Nature Photon. 7, 783–786 (2013).
Kibler, B. et al. The Peregrine soliton in nonlinear fibre optics. Nature Phys. 6, 790–795 (2010).
Turitsyn, S. K. et al. Random distributed feedback fibre laser. Nature Photon. 4, 231–235 (2010).
Turitsyn, S. K., Bale, B. & Fedoruk, M. P. Dispersion-managed solitons in fibre systems and lasers. Phys. Rep. 521, 135–203 (2012).
Turitsyn, S. K. et al. Random distributed feedback fibre lasers. Phys. Rep. 542, 133–193 (2014).
Picozzi, A. et al. Optical wave turbulence: toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics. Phys. Rep. 542, 1–132 (2014).
Stolen, R. H. Phase-matched-stimulated four-photon mixing in silica-fiber waveguides. IEEE J. Quantum Electron. 11, 100–103 (1975).
Marhic, M. E. Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge Univ. Press, 2007).
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).
Radic, S. & McKinstrie, C. J. Two-pump fiber parametric amplifiers. Opt. Fiber Technol. 9, 7–23 (2003).
McKinstrie, C. & Radic, S. Phase-sensitive amplification in a fiber. Opt. Express 12, 4973–4979 (2004).
McKinstrie, C. J., Radic, S. & Gnauck, A. H. All-optical signal processing by fiber-based parametric devices. Opt. Photon. News 18, 34–40 (2007).
Marhic, M. E. et al. Fiber optical parametric amplifiers in optical communication systems. Laser Photon. Rev. 9, 50–74 (2015).
Tong, Z. et al. Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers. Nature Photon. 5, 430–436 (2011).
Slavik, R. et al. All-optical phase and amplitude regenerator for next-generation telecommunications systems. Nature Photon. 4, 690–695 (2010).
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).
Bouteiller, J-C. Spectral modeling of Raman fiber lasers. Photon. Technol. Lett. 15, 1698–1700 (2003).
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).
Turitsyn, S. K. et al. Modeling of CW Yb-doped fiber lasers with highly nonlinear cavity dynamics. Opt. Express 19, 8394–8405 (2011).
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).
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).
Babin, S. et al. Turbulent broadening of optical spectra in ultralong Raman fiber lasers. Phys. Rev. A 77, 033803 (2008).
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).
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).
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).
Churkin, D., Smirnov, S. & Podivilov, E. Statistical properties of partially coherent cw fiber lasers. Opt. Lett. 35, 3288–3290 (2010).
Churkin, D. V. et al. Wave kinetics of random fibre lasers. Nature Commun. 6, 6214 (2015).
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).
Cundiff, S. T. et al. Propagation of highly chirped pulses in fiber-optic communications systems. J. Lightw. Technol. 17, 811–816 (1999).
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).
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).
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).
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).
Preda, C. E., Fotiadi, A. A. & Mégret, P. Numerical approximation for Brillouin fiber ring resonator. Opt. Express 20, 5783–5788 (2012).
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.
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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.
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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
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DOI: https://doi.org/10.1038/nphoton.2015.150
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