Stochastic perturbation of dispersion-managed optical solitons

The stochastic perturbation of dispersion-managed optical solitons is studied in this paper, in addition to deterministic preturbation terms, by the aid of soliton perturbation theory. The super-Gaussian pulses are considered and the corresponding Langevin equations are derived and analyzed. It is shown that in presence of the perturbation terms, the soliton propagates down the fiber with a fixed mean energy.OCIS Codes: 060.2310; 060.4510; 060.5530; 190.4370     

Physics and mathematics of dispersion-managed optical solitons

We review the main physical and mathematical properties of dispersion-managed (DM) optical solitons. Theory of DM solitons can be presented at two levels of accuracy: first, simple, but nevertheless, quantitative models based on ordinary differential equations governing evolution of the soliton width and phase parameter (the so-called chirp); and second, a comprehensive path-average theory that is capable of describing in detail both the fine structure of DM soliton form and its evolution along the fiber line. An analogy between DM soliton and a macroscopic nonlinear quantum oscillator model is also discussed. To cite this article: S.K. Turitsyn et al., C. R. Physique 4 (2003).     

Quasi-soliton propagation in dispersion-managed optical fibers

Combination of programmed chirp and dispersion profiles produced a solitonlike nonlinear pulse with a stationary structure (quasi-soliton). The quasi-soliton has more attractive properties than those of a soliton because of its reduced interaction and smaller peak power than a soliton and allows ~100-Gbit / s transmission over a 125-dispersion distance with reasonable power.     

Interactions of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines

We investigate interactions between pulses in dispersion-managed multichannel wavelength-division-multiplexed soliton systems, using an improved variational approximation. The frequency shifts are found to be smallest for moderate, i.e., relatively short-scale, dispersion management. The position shifts increase monotonically with map strength.     

Soliton interaction in strongly dispersion-managed optical fibers

We derive an expression for the speed with which neighboring solitons attract or repel each other in dispersion-managed fiber systems. We show that the collapse distance can be increased by an order of magnitude by use of quasi-solitons.     

Short optical solitons in fibers

The dynamics of short (of the order of a few wave periods) intense optical pulses and interaction of short optical solitons in fibers are considered within the framework of the third-order nonlinear Schrodinger equation. It is shown that an initial pulse tends to one or a few short solitons plus a linear quasiperiodic wave when the third-order linear dispersion and nonlinear dispersion have parameters of the same sign. The number and parameters of the solitons depend on the magnitudes of initial pulse parameters. Interaction of short optical solitons having different amplitudes is accompanied by radiation of part of the wave field from the area of interaction, by an increase of the soliton with larger amplitude, and a decrease of the soliton with a smaller one. (c) 2000 American Institute of Physics.     

Heat dissipative solitons in optical fibers

We propose a one-dimensional model governing the propagation of heat waves in an optical fiber (the “fiber fuse”). The model has solutions in the form of high temperature localized waves moving towards the input end of the fiber, fueled by the laser power. These waves can be ignited by local heating at any point along the fiber. The effect of such a wave is irreversible damage to the fiber core. The phenomenon was observed earlier by Hand and Russell, when locally heating a fiber through which CW light of modest intensity was propagating. This induced self-destruction of the optical fiber core.     

Radiating and nonradiating dispersion-managed solitons

Using spectral analysis, we present the salient features of the radiating behavior of optical solitons in dispersion-managed fiber systems. Depending on the map strength of the system, we find a rich variety of dynamic states that includes weak, moderate, and strong radiation states. We establish the existence of a critical map strength at which a Gaussian-shaped light pulse with a large initial dressing undergoes highly stable nonradiative propagation over transoceanic distances.     

Velocity of heat dissipative solitons in optical fibers

In the fiber fuse, a pulse of high temperature travels toward the input end of the fiber, where high-power laser light is launched into the fiber. At any point along the fiber, the soliton can be ignited. The fiber core is damaged in the process so that light cannot propagate beyond the hot spot. This phenomenon is an example of a dissipative soliton that can exist only in the presence of an external energy supply and internal loss. We analyze this phenomenon, derive an expression for the velocity of the soliton, and determine its width as functions of the physical parameters of the laser and the fiber material.     

Black solitons in dispersion-managed fiber transmission systems

In an ideal continuous exponential varying-dispersion fiber, black solitons, like their bright counterparts, can propagate over long distances without being broadened when the weakened nonlinearity that is due to the fiber loss is compensated for by the decreasing dispersion. It is found, however, that in a practical stepwise decreasing-dispersion fiber with N steps the number of steps N required for well-behaved evolution of black solitons in a lossy fiber with negligible distortion and broadening is fewer than for bright solitons. This finding indicates that the stepwise-varying-dispersion in fibers can be more effective for extending the amplifier spacing or reducing amplifier numbers in the high-bit-rate black soliton transmission system than in the corresponding bright soliton transmission system.     

A scheme for pre-shaping of dispersion-managed solitons

We demonstrate efficacy of shaping Gaussian pulses into dispersion-managed (DM) solitons by dint of a device which includes two fibers with the same group-velocity-dispersion (GVD) coefficients as in the DM system, a frequency-domain filter, and an amplifier. The shaping of a given input pulse is optimized by adjusting values of four free parameters of the cell, viz., lengths of the two fibers, filtering coefficient, and amplification gain, with the objective to achieve the best fit of the transformed pulse to the (numerically found) DM soliton, including systems with the third-order GVD, and with three-step DM maps. Launching reshaped pulses into the DM system, we demonstrate, in direct simulations, their complete stability over indefinitely long propagation distances. We examine sensitivity of the reshaping to deviations of the control parameters from their optimum values, a noteworthy results being very weak dependence on variations of the filtering strength. The dependence of the four control parameters on the width and chirp of the Gaussian input signal is also studied in detail.     

FWM minimization in WDM optical communication systems using the asymmetrical dispersion-managed fibers

Four wave mixing (FWM) induced power penalty is investigated theoretically for asymmetrical dispersion-managed fibers in wavelength division multiplexing (WDM) systems. The power penalty in these fibers is analyzed for various values of channel spacing, maximum dispersion and number of sections in different channels. Using numerical simulations, it is illustrated that the FWM induced power penalty is minimized for the case of two fiber sections with unequally special lengths and symmetrical dispersion values.     

Carrier-envelope phase slip of ultrashort dispersion-managed solitons

The carrier-envelope phase slip of an ultrashort pulse circulating in a mode-locked Ti:sapphire laser is analyzed. The laser cavity is modeled by a dispersion- and nonlinearity-managed nonlinear Schr?dinger equation. The combined contributions to the phase slip induced by nonlinear phase and nonlinear dispersion are found to approach zero for strong dispersion maps. The dependence of the slip on third-order dispersion is found as well. The analytical results are verified using numerical simulations.     

Scheme for the characterization of dispersion-managed solitons

We give a simple new derivation of the ordinary differential equations that describe approximately the behavior of dispersion-managed solitons, and a new scheme for their solution in which the nonlinear dispersive and spectral effects are clearly apparent.     

Perturbation of higher-order solitons by fourth-order dispersion in optical fibers

We study analytically and numerically how the radiation emitted by fundamental solitons in the form of dispersive waves is affected by the third and fourth-order dispersions when a higher-order soliton undergoes the fission process inside an optical fiber. Our results show that two dispersive wave sidebands appear in the output spectrum on opposite sides of the input spectrum. The frequencies of these sidebands are set by the relative magnitudes of the third- and fourth-order dispersion parameters, but are not affected much by the Raman process. A well defined phase-matching condition accurately predicts these conjugate frequencies of dispersive wave. The relative amplitudes of these two sidebands are not equal because of the asymmetry induced by the third-order dispersion and higher-order nonlinearities. It is found that with increasing fourth-order dispersion the amplitude of both spectral components eventually saturate and the relative power level associated with one of the components can exceed 10% of the launched power under suitable conditions. This component is the one that will form even in the absence of fourth-order dispersion and its wavelength may lie on the red or the blue side of the launched wavelength depending on the sign of the dispersion slope at this wavelength. It is also observed that soliton order itself significantly influence the peak amplitude of the radiation and play a minor role in determining radiation frequencies. We believe, these results should be of relevance for applications requiring an ultrabroadband optical source and understanding the interesting facts of supercontinuum generation.     

Instability of dispersion-managed solitons in a system with filtering

Unstable behavior of dispersion-managed (DM) solitons in a system with lumped filtering is numerically studied. A variational analysis shows that the system cannot have stable fixed DM soliton solutions when the filter location is improperly chosen. This is because of the unique dynamics of the spectral behavior of DM solitons, which differs from that of standard solitons in fibers with constant dispersion. The instability is confirmed by numerical simulations with and without sliding center frequencies of the filters.     

Family of multi-hump solitons propagating in dispersion-managed optical fiber transmission system and their existent parameter ranges

Multi-hump soliton which consists of plural pulses can propagate in a dispersion-managed optical fiber transmission system with maintaining the pulse-to-pulse spacings. In this paper, the family members of multi-hump soliton are systematically introduced using a family tree. The system parameter ranges in which multi-hump soliton can exist are studied by a numerical averaging scheme. The dependency of pulse energy and pulse-to-pulse spacing on the system parameter is also investigated to show the robustness of anti-phase bi-soliton against imposed perturbations.