^{1}Laboratoire de Physique de la Matière Condensée, Unité de Recherche Associée Centre National de la Recherche Scientifique, Université de Nice–Sophia Antipolis, Parc Valrose, F-06108 Nice Cedex,
France

^{2}Institute of Automation and Electrometry, Siberian Branch, Academy of Sciences, 630090 Novosibirsk,
Russia

Carlos Montes and Alexander M. Rubenchik, "Stimulated Brillouin scattering from trains of solitons in optical fibers: information degradation," J. Opt. Soc. Am. B 9, 1857-1875 (1992)

The limitation on information flux in soliton-based optical-fiber communication that is due to stimulated Brillouin scattering (SBS) is analyzed by means of the space–time three-wave resonant model for SBS. We show that a continuous train of well-separated solitons excites SBS above a bit-rate threshold f_{bit}^{thd} and that SBS degrades the information after some critical transmission length L_{c}. General simple formulas give f_{bit}^{thd}, the SBS gain, and L_{c} as functions of the fiber characteristics. A large range of threshold values is obtained, depending principally on the soliton phase distribution and on the fiber dispersion. For trains of solitons in phase, f_{bit}^{thd} is ∼0.7 Gbit/s for normally dispersive (n.d.) fibers and ∼3.3 Gbits/s for dispersion-shifted (d.-s.) fibers, whereas for trains of solitons uncorrelated in phase the bit-rate threshold goes from ∼21 Gbits/s for n.d. fibers to ∼440 Gbits/s for d.-s. fibers.

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The system uses a monomode laser at λ = 1.55 μm and a normal dispersive [D = 21(ps/nm)km] single-mode silica fiber of effective cross section S = 25 μm^{2}. Adjacent solitons of the form sech(t/τ_{p}) have FWHM value (for the intensity) τ_{FWHM} = 1.76 τ_{p} = 3.75 × 10^{−4}τ_{B}, where τ_{B} = (KE_{p})^{−1} is the coherent SBS characteristic time and K = 20.8 m s^{−1} V^{−1} is the SBS coupling constant. The dimensionless width of the hyperbolic secant is τ_{p}/τ_{B} − a/π = 2.13 × 10^{−4} [cf. Eq. (24)]. In order to minimize the soliton interaction,28 we separated the pulses by Δt_{p}/τ_{p} = π (a + b)/a = 20 [cf. expression (26)], i.e., Δt_{p} = 11.36τ_{FWHM} (or Δt_{p}/τ_{B} ≃ 1/235 = 4.26 × 10^{− 1}. The soliton bit rate is f_{bit} 1/Δt_{p}= 1/(20τ_{p}) = 0.088/τ_{FWHM} [expression (25)]. For these parameters, the peak power P required to support the N = 1 soliton is related to its width by expression (3b) with D = 21 ps/(nm/km), and the values of P correspond to the low-gain regime of low input intensities [cf. Eqs. (39) and (40)]. P, peak pump power coupled into the fiber [expressions (3a), (3b), (23a), and (23b)].

Table 2

SBS Limitation for Transmission Capacity in Soliton-Based Optical-Fiber Communication^{a}

Solitons Correlated, In Phase (δω_{p} ≪ γ_{a})

Case (c), Solitons with Distributed Random Phases δω_{p} ∼ f_{bit} ≫ γ_{a}

Case (a), In-Phase Low-Gain γ_{0}a/(a + b) < γ_{a}

Case (b), Alternate-Phase High-Gain γ_{0}a/(a + b) > γ_{a}

General formulas (valid for different fiber parameters, peak pump powers, and bit rates) of the bit-rate threshold f_{bit}^{thd}, time amplitude growth rate γ, gain G, information damage length L_{c} (or effective length), length–bit-rate product L_{c}f_{bit} and number of solitons N_{bit} transmitted without SBS damage for the three different phase cases (a), (b), and (c):

δω_{p}, spectral width for the soliton train (cf. Section 2);

The system uses a monomode laser at λ = 1.55 μm and a normal dispersive [D = 21(ps/nm)km] single-mode silica fiber of effective cross section S = 25 μm^{2}. Adjacent solitons of the form sech(t/τ_{p}) have FWHM value (for the intensity) τ_{FWHM} = 1.76 τ_{p} = 3.75 × 10^{−4}τ_{B}, where τ_{B} = (KE_{p})^{−1} is the coherent SBS characteristic time and K = 20.8 m s^{−1} V^{−1} is the SBS coupling constant. The dimensionless width of the hyperbolic secant is τ_{p}/τ_{B} − a/π = 2.13 × 10^{−4} [cf. Eq. (24)]. In order to minimize the soliton interaction,28 we separated the pulses by Δt_{p}/τ_{p} = π (a + b)/a = 20 [cf. expression (26)], i.e., Δt_{p} = 11.36τ_{FWHM} (or Δt_{p}/τ_{B} ≃ 1/235 = 4.26 × 10^{− 1}. The soliton bit rate is f_{bit} 1/Δt_{p}= 1/(20τ_{p}) = 0.088/τ_{FWHM} [expression (25)]. For these parameters, the peak power P required to support the N = 1 soliton is related to its width by expression (3b) with D = 21 ps/(nm/km), and the values of P correspond to the low-gain regime of low input intensities [cf. Eqs. (39) and (40)]. P, peak pump power coupled into the fiber [expressions (3a), (3b), (23a), and (23b)].

Table 2

SBS Limitation for Transmission Capacity in Soliton-Based Optical-Fiber Communication^{a}

Solitons Correlated, In Phase (δω_{p} ≪ γ_{a})

Case (c), Solitons with Distributed Random Phases δω_{p} ∼ f_{bit} ≫ γ_{a}

Case (a), In-Phase Low-Gain γ_{0}a/(a + b) < γ_{a}

Case (b), Alternate-Phase High-Gain γ_{0}a/(a + b) > γ_{a}

General formulas (valid for different fiber parameters, peak pump powers, and bit rates) of the bit-rate threshold f_{bit}^{thd}, time amplitude growth rate γ, gain G, information damage length L_{c} (or effective length), length–bit-rate product L_{c}f_{bit} and number of solitons N_{bit} transmitted without SBS damage for the three different phase cases (a), (b), and (c):

δω_{p}, spectral width for the soliton train (cf. Section 2);