Dispersive wave generation by solitons in microstructured optical fibers

Ilaria Cristiani; Riccardo Tediosi; Luca Tartara; Vittorio Degiorgio

doi:10.1364/OPEX.12.000124

Optics Express
Vol. 12,
Issue 1,
pp. 124-135
(2004)
•https://doi.org/10.1364/OPEX.12.000124

Dispersive wave generation by solitons in microstructured optical fibers

Ilaria Cristiani, Riccardo Tediosi, Luca Tartara, and Vittorio Degiorgio

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Ilaria Cristiani, Riccardo Tediosi, Luca Tartara, and Vittorio Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124-135 (2004)

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Abstract

We study the nonlinear propagation of femtosecond pulses in the anomalous dispersion region of microstructured fibers, where soliton fission mechanisms play an important role. The experiment shows that the output spectrum contains, besides the infrared supercontinuum, a narrow-band 430-nm peak, carrying about one fourth of the input energy. By combining simulation and experiments, we explore the generation mechanism of the visible peak and describe its properties. The simulation demonstrates that the blue peak is generated only when the input pulse is so strongly compressed that the short-wavelength tail of the spectrum includes the wavelength predicted for the dispersive wave. In agreement with simulation, intensity-autocorrelation measurements show that the duration of the blue pulse is in the picosecond time range, and that, by increasing the input intensity, satellite pulses of lower intensity are generated.

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Fig. 1. Output spectrum showing highly efficient visible light generation in a 40-cm MF. See Ref. 9 for experimental details.

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Fig. 2. Phase matching condition for the dispersive wave. The red line refers to the case in which the nonlinear dephasing is taken into account (P_o =5 kW)

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Fig. 3. Experimental output spectrum obtained using different pump wavelengths λ₀ =810 nm (blue line), λ₀ =890 nm (green line) and λ₀ =760 nm (red line)

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Fig. 4. Comparison between the experimental output spectrum (pump wavelengths λ0=810 nm, fiber length L=40 cm) and the simulation results

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Fig. 5. Picture of the first centimeters of fiber. The input pulse generates blue light after a very short propagation distance

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Fig. 6. Spectrum evolution of a fourth-order-soliton on half-soliton period. Coupling between dispersive radiation and soliton occurs in correspondence with the first temporal contraction.

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Fig. 7. (a) Temporal evolution of the launched pulse on half soliton period; (b) Corresponding spectral evolution; (c) Temporal behaviour of the dispersive wave, by filtering the complete spectrum 150 <Ω< 200 THz.

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Fig. 8. Temporal behaviour of the dispersive radiation obtained by numerically filtering the output spectrum of a fifth order soliton at different fiber length. The plots are presented in log-scale to highlight the presence of the satellite pulses that have an intensity much lower than that of the main pulse, because the simulation is performed at low intensity.

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Fig. 9. Measured intensity autocorrelation of the dispersive radiation. a) L=33 cm and the input power P=90 mW, b) L=33 cm and P=50 mW, c) L=18 cm and P=50 mW.

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Equations (13)

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Δ κ = β (ω) - β (ω_{o}) - (ω - ω_{o}) ⁄ u_{g} - γ P_{o} = 0

β (ω) = \sum_{k = 0}^{\infty} \frac{β_{k}}{k!} Ω^{k}

β (ω) = \sum_{n \geq 2}^{\infty} \frac{β_{k}}{n!} Ω^{n - 2} ≅ 0

\frac{\partial A}{\partial z} + \frac{α}{2} A - \sum_{n \geq 2} \frac{i^{n + 1}}{n!} β_{n} \frac{\partial^{n} A}{\partial T^{n}} = i γ (1 + \frac{i}{ω_{0}} \frac{\partial}{\partial T}) A \cdot \int_{- \infty}^{+ \infty} R (T') {∣ A (z, T - T') ∣}^{2} s T'

A (0, T) = A_{o} sech (\frac{T}{T_{o}})

T = t - \frac{z}{u_{g} (ω_{o})}

R (T) = (1 - f_{r}) δ (T) + f_{r} h_{r} (T)

\frac{\partial A}{\partial z} = i γ (1 + \frac{i}{ω_{o}} \frac{\partial}{\partial T}) A \cdot [R (T) * {∣ A_{o} (z, T) ∣}^{2}]

A (z, T) = A_{o} \exp [i γ (R (T) * {∣ A_{o} (z, T) ∣}^{2}) z]

V (z, T) = A (z, T) \exp [i γ (R (T) * {∣ A_{o} ∣}^{2}) (z - z_{o})]

\frac{\partial V}{\partial z} = i γ V \cdot R (T) * ({∣ V_{o} ∣}^{2} + {∣ V ∣}^{2}) - γ \frac{1}{ω_{o}} \frac{\partial}{\partial T} (V \cdot R (T) * {∣ V ∣}^{2})

\frac{\partial V}{\partial z} = i γ V \cdot ℑ^{- 1} {R (Ω) \cdot ℑ ({∣ V_{o} ∣}^{2} + {∣ V ∣}^{2})} - γ \frac{1}{ω_{o}} \frac{\partial}{\partial T} (V \cdot ℑ^{- 1} {R (Ω) \cdot ℑ ({∣ V ∣}^{2})})

N^{2} = γ \frac{P_{o} T_{o}^{2}}{∣ β_{2} ∣}

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Equations (13)

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