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

Journal name:
Nature Photonics
Volume:
9,
Pages:
608–614
Year published:
DOI:
doi:10.1038/nphoton.2015.150
Received
Accepted
Published online

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.

At a glance

Figures

  1. Experimental observation of spectrum evolution in normal and anomalous dispersion fibres.
    Figure 1: Experimental observation of spectrum evolution in normal and anomalous dispersion fibres.

    a, Experimental set-up. b, Initial spectrum and spectrum after propagation in 100 km of LEAF and SMF-28 fibres. Power launched into each fibre = 1.5 W. OSA: optical spectrum analyser; RFL: Raman fibre laser.

  2. Spectrum shape after signal propagation in LEAF fibre.
    Figure 2: Spectrum shape after signal propagation in LEAF fibre.

    a, Experiment and b, simulation. P0(0) = 1.5 W, L = 100 km.

  3. Evolution of the signal spectrum and temporal shape along the fibre.
    Figure 3: Evolution of the signal spectrum and temporal shape along the fibre.

    a, Computed power spectrum density evolution along the LEAF fibre, demonstrating a transition to very stable propagation with a distinctive asymptotic spectrum. b, Corresponding spatiotemporal dynamics over an interval of 800 ps. Here, the fluctuating c.w. power P(t,z) is normalized by the distance-dependent factor Pnorm(z)  = P(0)exp(αz), where α = 0.25 dB km–1 is the fibre loss. The two figures illustrate that although the temporal field structure is irregular, the spectrum propagation demonstrates remarkable stability.

  4. Signal gain spectra as a function of pump wavelength spacing.
    Figure 4: Signal gain spectra as a function of pump wavelength spacing.

    a, Four-wave model, P0(0) = 1.5 W, L = 1 km. The unsaturated single-pass gain for signal G3 is shown. Black lines show the corresponding wavelengths of the pumps. b, NLSE model, P0(0) = 1.5 W, P3(0) = 300 mW, P4(0) = 0, L = 1 km. The projection at the top is related to the normal dispersion case: black solid line, deterministic phases of waves; grey circles, averaging over 600 sets of random phases.

  5. Estimate of FWM product during signal amplification.
    Figure 5: Estimate of FWM product during signal amplification.

    Top: dependence of signal gain G (in dB) on relative phase difference θ(0) and wavelength spacing between two pumps Δλ. Bottom: dependence of F = ΔPs/PFWM on relative phase difference θ(0) and wavelength spacing between two pumps Δλ.

  6. Theoretical evolution of the spectral broadening factor.
    Figure 6: Theoretical evolution of the spectral broadening factor.

    a, Dependence of the broadening factor Δλoutλin on the initial spectrum width Δλin after 100 km of LEAF, P0 = 1.5 W, lossless fibre. Inset: spectrum shapes before and after signal propagation in 100 km of LEAF, corresponding to the points marked 1 and 2. b, Dependence of the broadening factor Δλoutλin on pump power, corresponding to the points marked 1 and 2, L = 100 km. c, Dependence of the broadening factor Δλoutλin on group delay dispersion, corresponding to the points marked 1 and 2, L = 100 km, P0 = 1.5 W. d, Dependence of the broadening factor Δλoutλin on fibre length, corresponding to the points marked 1 and 2, P0 = 1.5 W. e, Scaling of Ld/LNL along the propagation distance (P0 = 1.5 W). f,g, Experimentally measured input and output spectra of 1,276 nm light propagating in 100 km of SMF-28 versus input power with P0 = 0.7 W (f) and P0 = 1.3 W (g).

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Author information

Affiliations

  1. Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET, UK

    • Sergei K. Turitsyn
  2. Novosibirsk State University, Novosibirsk 630090, Russia

    • Sergei K. Turitsyn,
    • Anastasia E. Bednyakova &
    • Mikhail P. Fedoruk
  3. Institute of Computational Technologies, SB RAS, Novosibirsk 630090, Russia

    • Anastasia E. Bednyakova &
    • Mikhail P. Fedoruk
  4. MPB Communications Inc., Montreal, Quebec H9R 1E9, Canada

    • Serguei B. Papernyi &
    • Wallace R. L. Clements

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.

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The authors declare no competing financial interests.

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