Dispersion-managed Optical Fiber Research Articles

Modulational instability in randomly dispersion-managed optical fiber links

Modulational instability in randomly dispersion-managed optical fiber links

Bright, dark and Gaussons optical solutions for fourth-order Schrödinger equations with cubic–quintic and logarithmic nonlinearities

This work addresses two nonlinear Schrödinger equations with fourth-order dispersion and cubic–quintic nonlinearity for the first one, and logarithmic nonlinearity for the second. The proposed methods retrieve bright and dark optical soliton solutions for the first equation, whereas Gausson soliton solutions will be obtained for the logarithmic Schrödinger equation. The obtained Gaussons are characterized by no soliton radiation, and propagate through dispersion-managed optical fibers. In addition, with some certain constraints on the parameters, other solutions are derived. The obtained results may be helpful in understanding the solitons features in optical fiber.

Semi-analytical method for designing finite sets of discriminated solitons and soliton molecules in fibres

ABSTRACTAn infinite number of solitons, as well as soliton molecules belonging different families, are allowed to propagate stably along a given dispersion-managed optical fibre. In this paper, we propose a semi-analytical method to systematically find a finite number of solitons and two-soliton molecules. Determined solitons and soliton molecules present a greatest power gap between them, to make them sufficiently distinct symbols for encoding several bits of information per symbol in a multilevel modulation format in fibre-optic transmission systems. Furthermore, for illustrative purposes, we discuss the possibility of encoding three bits per symbol.

Optical Gaussons for nonlinear logarithmic Schrödinger equations via the variational iteration method

In this work, we study the logarithmic Schrödinger equation, with and without a detuning term. We derive optical Gaussons, named for their Gaussian shape, for these logarithmic models via using the variational iteration method. The obtained Gaussons are characterized by no soliton radiation, and propagate through dispersion-managed optical fibers. The physical structures of the derived Gaussons, namely, its amplitude and width will be examined for a variety numerical values of the parameters.

Adiabatic exponential midpoint rule for the dispersion-managed nonlinear Schrödinger equation

Abstract Modeling long-haul data transmission through dispersion-managed optical fiber cables leads to a nonlinear Schrödinger equation where the linear part is multiplied by a large, discontinuous and rapidly changing coefficient function. Typical solutions oscillate with high frequency and have low regularity in time, such that traditional numerical methods suffer from severe step size restrictions and typically converge only with low order. We construct and analyse a norm-conserving, uniformly convergent time-integrator called the adiabatic exponential midpoint rule by extending techniques developed in Jahnke & Mikl (2018, Adiabatic midpoint rule for the dispersion-managed nonlinear Schrödinger equation. Numer. Math., 138, 975–1009). This method is several orders of magnitude more accurate than standard schemes for a relevant set of parameters. In particular, we prove that the accuracy of the method improves considerably if the step size is chosen in a special way.

Many-soliton bound states in dispersion-managed optical fiber: Possibility of fiber-optic transmission of three bits per clock period

We study the stability and the dynamics of many-soliton molecules in dispersion-managed (DM) optical fibers with focus on five-and seven-soliton molecules by analytical and numerical means. In particular we calculate the binding force, pulse durations and equilibrium separations using a variational approach. Predicted pulse shapes are in good agreement with those found by numerical simulations of the underlying nonlinear Schrödinger equation. Within limitations, soliton molecules with up to seven solitons possibly allow to encode three bits of data per clock period.

Evaluation of the impact of higher-order energy enhancement characteristics of solitons in strongly dispersion-managed optical fibers

We study the propagation properties of nonlinear pulses with periodic evolution in a dispersion-managed transmission link by means of a variational approach. We fit the energy enhancement required for stable propagation of a single soliton in a prototypical commercial link to a polynomial approximation that describes the dependence of the energy on the map strength of the normalized unit cell. We present an improvement of a relatively old and essential result, namely, the dependence of the energy-enhancement factor of dispersion-management solitons with the square of the map strength of the fiber link. We find that adding additional corrections to the conventional quadratic formula up to the fourth order results in an improvement in the accuracy of the description of the numerical results obtained with the variational approximation. Even a small error in the energy is found to introduce large deviations in the pulse parameters during its evolution. The error in the evaluation of the interaction distance between two adjacent time division multiplexed pulses propagating in the same channel in a prototypical submarine link is of the same order as the error in the energy.

Gaussian soliton solutions to a variety of nonlinear logarithmic Schrödinger equation

This work addresses a variety of Schrödinger equations with logarithmic nonlinearity, with and without an attenuation term. We show that the stationary and the time-dependent logarithmic models give Gaussian soliton solutions, or simply Gaussons, which are characterized by no soliton radiation, and propagate through dispersion-managed optical fibers. We examine the physical structures, especially the amplitude and width of the Gaussons which we will derive.

Averaged dynamics of soliton molecules in dispersion-managed optical fibers

The existence regimes and dynamics of soliton molecules in dispersion-managed (DM) optical fibers have been studied. Initially we develop a variational approximation (VA) for description of periodic dynamics of a soliton molecule within each unit cell of the dispersion map. The obtained system of coupled equations for the pulse width and chirp allows to find the parameters of DM soliton molecules for the given dispersion map and pulse energy. Then by means of a scaling transformation and averaging procedure we reduce the original nonlinear Schr\"odinger equation (NLSE) with piecewise-constant periodic dispersion to its counterpart with constant coefficients and additional parabolic potential. The obtained averaged NLSE with expulsive potential can explain the essential features of solitons and soliton molecules in DM fibers related to their energy loss during propagation. Also, the model of averaged NLSE predicts the instability of the temporal position of the soliton, which may lead to difficulty in holding the pulse in the middle of its time slot. All numerical simulations are performed using the parameters of the existing DM fiber setup, and illustrated via pertinent examples.

Intrachannel cross-phase modulation-induced phase shift in high-speed dispersion-managed optical fiber transmission system

We investigate the intrachannel cross-phase modulation (IXPM)-induced phase shift in optical return-to-zero pulse propagating in a periodically dispersion-managed long-haul optical fiber transmission line. Necessary dynamical equations for various pulse parameters have been derived using variational analysis to estimate the phase shift. These equations are solved by the Runge–Kutta method. The analytical result is verified by numerical simulation based on split-step Fourier method. We therefore explore the effects of various parameters, such as transmission distance, input power, duty cycle, dispersion map strength, and residual dispersion, on phase shift for a 40 Gb/s single-channel transmission system. We also check the impact of variation of bit rate on phase shift. We find that IXPM-induced phase shift can be mitigated by proper adjustment of dispersion management and different pulse parameters like duty cycle, dispersion map strength, and peak power.

Stability ofN-soliton molecules in dispersion-managed optical fibers

We investigate the stability of $N$-soliton molecules in dispersion-managed optical fibers with focus on the recently realized 2- and 3-soliton molecules. We calculate their binding energy using an averaged nonlinear Schr$\rm{\ddot o}$dinger equation. A combination of variational and numerical solutions to this equation shows that it describes well the intensity profiles and relative separations of the experimental molecules. Extending the calculation to larger values of $N$, the binding energy per soliton is found to saturate at N $N\ge7$.

Optimization strategy to find shapes of soliton molecules

Frequently, a certain solution of a nonlinear wave equation is of interest, but no analytic form is known, and one must work with approximations. We introduce a search strategy to find solutions of the propagation of soliton molecules in a dispersion-managed optical fiber and to determine their shape with some precision. The strategy compares shapes before and after propagation and invokes an optimization routine to minimize the difference. The scheme is designed to be implemented in an experiment so that all fiber parameters are taken into account. Here, we present a full numerical study and a verification of convergence; we validate the method with cases of known solutions. We also compare the performance of two optimization procedures, the Nelder–Mead simplex method and a genetic algorithm.

WDM Signal All-Optical Precompensation of Kerr Nonlinearity in Dispersion-Managed Fibers

Compensation of the Kerr nonlinearity in dispersion-managed optical fiber links is demonstrated for 100-GHz-spaced wavelength division multiplexing (WDM) 40-Gb/s return-to-zero-differential phase-shift keying signals using all-optical nonlinear predistortion and phase-conjugation at the transmitter. Measurements of the bit-error rate (BER) reveal a Q2-factor improvement from 1.3 to 2.9 dB for transmission of one to four WDM channels in a standard single-mode fiber link. Although signal distortion is primarily from intrachannel nonlinearity, the BER is also degraded by linear and nonlinear interchannel crosstalk.

Suppression of parabolic pulse-pair interaction using dispersion-managed fiber links with non-zero dispersion

We report on the suppression of the parabolic pulse-pair interaction by using the dispersion-managed optical fiber links with non-zero dispersion maps. The numerical results show that both the interaction and pulse splitting can be efficiently suppressed when the integrated dispersion is non-zero, and the pulse-pair can maintain their parabolic characteristics through the whole distance and turn to its original shape at the end of each map. Moreover, we numerically investigate the influence of the initial pulse width and chirp on the parabolic pulse pair propagation, which shows that the higher chirp is not conducive to pulse transmission.

Fundamental modes of a trapped probe photon in optical fibers conveying periodic pulse trains

Wave modes induced by cross-phase reshaping of a probe photon in the guiding structure of a periodic train of temporal pulses are investigated theoretically with emphasis on exact solutions to the wave equation for the probe. The study has direct connection with recent advances on the issue of light control by light, the focus being on the trapping of a low-power probe by a temporal sequence of periodically matched high-power pulses of a dispersion-managed optical fiber. The problem is formulated in terms of the nonlinear optical fiber equation with averaged dispersion, coupled to a linear equation for the probe including a cross-phase modulation term. Shape-preserving modes which are robust against the dispersion are shown to be induced in the probe, they form a family of mutually orthogonal solitons the characteristic features of which are determined by the competition between the self-phase and cross-phase effects. Considering a specific context of this competition, the theory predicts two degenerate modes representing a train of bright signals and one mode which describes a train of dark signals. When the walk-off between the pump and probe is taken into consideration, these modes have finite-momentum envelopes and none of them is totally transparent vis-\`a-vis the optical pump soliton.

Effective method of characterization of the phase and intensity profiles of asymmetrically distorted light pulses in optical fiber systems

We address the problem of characterization of light pulses that propagate in long-haul high-bit-rate optical communication systems, under strongly perturbed conditions. We show that the conventional technique for characterization of the phase and intensity profile of such pulses becomes qualitatively inconsistent when the pulse’s profile is asymmetrically distorted with respect to its center-of-mass. We resolve these inconsistencies by partially reformulating the conventional technique by means of appropriate pulse parameters, which we call upgraded parameters, which allow a fair characterization of the intensity and phase of all types of light pulses, including those which are asymmetrically distorted. We illustrate the effectiveness of the upgraded parameters by applying them to a meticulous characterization of light pulses in a dispersion-managed optical fiber system in which third-order dispersion is acting as a strong perturbation.

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.

Propagation of dark similaritons on the compact parabolic background in dispersion-managed optical fibers

The propagation of optical pulses inside dispersion-managed fibers is considered. It is found that the chirped compact parabolic pulse can propagate inside the dispersion-managed fibers self-similarly. Such a finite-width pulse can be served as the background for the propagation and interaction of dark similaritons. Approximate but highly accurate analytical methods are proposed to describe the interaction dynamics of multiple dark similaritons on the self-similar compact parabolic background.

Effective characterization of the phase and intensity profiles of asymmetrically distorted light pulses in optical fiber systems

We address the problem of characterization of light pulses that propagate in long-haul high-bit-rate optical communication systems under strongly perturbed conditions. We show that the conventional technique for characterization of the phase and intensity profile of such pulses becomes qualitatively inconsistent when the pulse's profile is asymmetrically distorted with respect to its center of mass. We resolve these inconsistencies by partially reformulating the conventional technique by means of appropriate pulse parameters, which we call upgraded parameters, that allow a fair characterization of the intensity and phase of all types of light pulses, including those that are asymmetrically distorted. We illustrate the effectiveness of the upgraded parameters by applying them to a meticulous characterization of light pulses in a dispersion-managed optical fiber system in which third-order dispersion is acting as a strong perturbation.

Effectiveness of Nonlinear Optical Loop Mirrors in Dispersion-Managed Fiber Communication Systems Compensated by Chirped Fiber Gratings With Group Delay Ripples

We examine the effectiveness of using nonlinear optical loop mirrors (NOLMs) to reduce the intersymbol interference in dispersion-managed (DM) fiber communication systems compensated by chirped fiber gratings (CFGs) with group delay ripples (GDR). We show that the use of NOLMs can enhance the transmission performance by more than one order of magnitude in the presence of amplifier noise and random variations in the parameters of the GDR in CFGs. We found that transoceanic transmissions can be achieved when NOLMs are included in the DM optical fiber transmission line compensated by CFGs with GDR whose parameters vary randomly along the transmission line.