Phase fluctuations of linearly chirped solitons in a noisy optical fiber channel with varying dispersion, nonlinearity, and gain

Shihua Chen, Y. H. Yang, Lin Yi, Peixiang Lu, and Dong-Sheng Guo

Phys. Rev. E 75, 036617 – Published 29 March 2007

Abstract

The phase fluctuations of arbitrarily nonlinearity- and dispersion-managed solitons propagating in a noisy fiber channel are studied both analytically and numerically. We begin by discussing the stability problem of such linearly chirped solitons with a full linear stability analysis. It is shown that these sophisticated solitons possess an enhanced stability against perturbations and therefore hold promise for applications in optical telecommunications. We then make an approach to the phase statistics of these solitons, which stems from an inevitable random walk in phase evolutions due to amplified spontaneous emission noise. By using the variational approach together with impulse-response (Green) functions, an elegant closed-form expression for the phase variance is derived based on an unconstrained self-similar soliton ansatz in which the effect of chirp fluctuations has been critically taken into account as well as the dispersive and nonlinear effects. An inspection of the intriguing subtleties of the interplay among these effects reveals that the chirp fluctuations effect does play an important role in the control of nonlinear phase noise via fiber dispersion, independently of whether the input solitons are initially chirped or not. Our analytical result also offers many possibilities of optimally manipulating nonlinear phase noise with engineered fiber parameters that may lead to the steady pulse propagation, broadening, or compression under favorable parametric conditions. Last, we demonstrate our result by several convincible examples and show an excellent agreement between analytical predictions and numerical simulations.

Received 28 October 2006

DOI:https://doi.org/10.1103/PhysRevE.75.036617

Authors & Affiliations

Shihua Chen^1,2, Y. H. Yang¹, Lin Yi², Peixiang Lu³, and Dong-Sheng Guo^3,4

¹Department of Physics, Southeast University, Nanjing 210096, China
²Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
³Wuhan National Laboratory for Optoelectronics, Wuhan 430074, China
⁴Department of Physics, Southern University, Baton Rouge, Louisiana 70813, USA

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Vol. 75, Iss. 3 — March 2007

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Images

Figure 1
(Color online) Schematic structure of the spectra of the linear eigenvalue problem (6) with the shaded regimes corresponding to the discrete “0” and continuums $∣ λ ∣ > 1 ∕ 2$ .Reuse & Permissions
Figure 2
(Color online) (a) Phase variances of an initially unchirped $17.6 ps$ (FWHM), $0.2 pJ$ soliton in an optical fiber with constant dispersion and nonlinearity within the propagation of $10 Mm$ for different frequency shifts $(b_{0} = 0, 0.1)$ . The solid lines and circles represent the analytical results and the corresponding numerical simulations. Meanwhile, the analytical oscillating phase variance (together with two bounded lines) and the pulse evolutions simulated under different frequency shifts are plotted in the insets as well. (b) Phase variances of the same soliton $(b_{0} = 0)$ under identical parametric conditions within $200 km$ . The dotted line denotes the approximate phase variance given by Eq. (70). The other symbols are the same as described in (a).Reuse & Permissions
Figure 3
(Color online) Pulse evolutions and phase variances for an initially chirped soliton $(c_{0} = 5 \times 10^{- 3} {THz}^{2})$ propagating in an optical fiber with exponentially increasing dispersion and constant nonlinearity within $30 km$ . [(a) and (c)] Pulse evolutions for $b_{0} = 0$ and $b_{0} = 0.05$ ; [(b) and (d)] the corresponding phase variances (bold lines: analytical; red circles: numerical) together with the changes of pulse width (thin lines). The other parameters have been specified in the text.Reuse & Permissions
Figure 4
(Color online) The same as in Fig. 3 except that $c_{0} = - 5 \times 10^{- 3} {THz}^{2}$ and $σ > 0.1 {km}^{- 1}$ , which corresponds to a positively chirped soliton propagating in an optical fiber with exponentially decreasing dispersion and constant $γ (z)$ .Reuse & Permissions
Figure 5
(Color online) Pulse evolutions and phase variances for an initially unchirped $3.5 ps$ (FWHM) soliton propagating in a cosinoidally managed optical fiber. [(a) and (b)] $b_{0} = 0$ . [(c) and (d)] $b_{0} = 0.05$ . Bold lines and red circles stand for analytical results and the corresponding numerical simulations. In (b) the approximate phase variance (91) (see text) under existing conditions is also plotted (thin line).Reuse & Permissions
Figure 6
(Color online) Comparison of phase variances for an initially unchirped $10.6 ps$ (FWHM) soliton (taking $b_{0} = 0$ ) propagating in two cosinoidally varying systems, which correspond to $∣ ν_{0} ∕ α ∣ = 0.884$ and $0.018$ , respectively. The relevant parameters have been specified in the text. Bold lines: exact analytical result (53). Thin crossed lines: approximate result (91). Red circles: numerical simulations.Reuse & Permissions

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