Dispersion-managed Systems Research Articles

Long-Haul WDM IMDD Transmission at 10.7 Gbit/s in a Dispersion-Managed Multispan System Using MLSE Receivers

We compare by simulation the performance of a maximum likelihood sequence estimation (MLSE) receiver with that of a standard optimized threshold receiver in a dispersion-managed multispan WDM transmission system at 10.7 Gbit/s in the presence of fiber nonlinearities. We found that the use of MLSE receivers helps to significantly increase the tolerance of the dispersion map design and may improve overall system performance.

ANALYTICAL SOLUTIONS FOR THE VARIATIONAL EQUATIONS DERIVED FOR THE NONLINEAR SCHRÖDINGER EQUATION: DISPERSION-MANAGED FIBER SYSTEM

We consider the nonlinear Schrödinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse, we derive the variational equations. For a particular case of DM fiber systems when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses, we show through numerical simulations that the analytically calculated energy (for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.

Design of dispersion-managed fiber systems for transmitting chirp-free Gaussian pulses

We present a general method to analytically design a dispersion-managed (DM) fiber system for any desired fiber (dispersion, nonlinearity and losses) and pulse (width and energy) parameters. This analytical design allows one to transmit chirp-free Gaussian pulses (for very long distances) in almost all kinds of DM fiber systems that have appeared so far in the literature, including systems with dispersion map length greater, equal or shorter with respect to the amplification period.

Soliton stability against polarization-mode-dispersion in dispersion-managed systems

We study the dynamics of two-component solitons in a dispersion-managed (DM) system, built as a periodic concatenation of segments of optical fibers with anomalous and normal group-velocity dispersion (GVD). The model includes, in addition to the usual GVD and nonlinear terms, birefringence and polarization-mode-dispersion (PMD), in the form of the polarization scrambling (random rotation of the polarization) taking place at randomly distributed defects. We propose a numerical algorithm for finding optimized DM solitons in such a system, which secure stable transmission over a large distance. The analysis includes effects of the PMD-induced noise, together with the noise due to the spontaneous amplifier emission, and the input-source noise. It is concluded that, if the group-velocity birefringence is not excessively large, the use of the optimized solitons makes it possible to tolerate the PMD effects in the long-haul DM link.

Optimization of the Net Residual Dispersion for Self-Phase Modulation-Impaired Systems by Perturbation Theory

The performance of self-phase modulation (SPM)-impaired systems can be improved significantly by adjusting the net residual dispersion (NRD) of the systems. In this paper, we propose a novel approach to optimize the NRD for SPM-impaired systems. We find that in SPM-impaired system, the optimal NRD can be obtained by minimizing the output distortion of a single pulse. Using a perturbation theory, a semianalytical expression is derived to calculate the output distortion of a single pulse. With the obtained expression, the NRD of SPM-impaired dispersion-managed systems can be optimized conveniently. Compared to previous methods, the present method is simple and fast. The validity of this method is verified by numerical simulations for various SPM-impaired systems

Twin families of bisolitons in dispersion-managed systems

We calculate bisoliton solutions by using a slowly varying stroboscopic equation. The system is characterized in terms of a single dimensionless parameter. We find two branches of solutions and describe the structure of the tails for the lower-branch solutions.

Analytic Multi-Solitonic Solutions of Variable-Coefficient Higher-Order Nonlinear Schrödinger Models by Modified Bilinear Method with Symbolic Computation

In this paper, the physically interesting variable-coefficient higher-order nonlinear Schr¨odinger models in nonlinear optical fibers with varying higher-order effects such as third-order dispersion, self-steepening, delayed nonlinear response and gain or absorption are investigated. The bilinear transformation method is modified for constructing the analytic solutions of these models directly with sets of parametric conditions. With the aid of symbolic computation, the explicit analytic multisolitonic solutions of the variable-coefficient higher-order nonlinear Schr¨odinger models are presented by employing the modified bilinear transformation method. The one- and two-solitonic solutions in explicit form are given in detail. Finally, solutions are illustrated and discussed through adjusting the parameters, so different dispersion management systems can be obtained.

Generalized Riccati equation rational expansion method and its application

By directly extending the Riccati equation rational expansion method, a new method is developed for constructing a series of exact analytical solutions of an averaged dispersion-managed fiber system equation (ADmE), including some new rational formal soliton-like solutions, triangle-like solutions and rational solutions.

Timing Jitter and Frequency Shift in Dispersion-Managed Soliton Systems with Raman Scattering Effect

We have studied the timing jitter in dispersion-managed soliton systems with a Gaussian pulse by two methods. Firstly, the timing jitter expressions for dispersion-managed soliton are derived by use of the perturbed variational method. By analyzing and simulating the timing jitter expressions, one can find that the timing jitter is induced by the amplifier spontaneous emission noise, the frequency shift, etc. The chirp sign, the soliton self-frequency shift, and the filters action also have effects on the timing jitter. Secondly, the timing jitter is calculated and analyzed by the moment method. The results of the two methods are proved to be consistent.

Dispersion-Compensating Graded Index Multiclad Fiber: Optimization for Dispersion-Managed WDM Transmission Systems

This work reports the design optimization of a single-mode graded index multiclad dispersion-compensating fiber (DCF) with a central dip, for broadband wavelength division multiplexing (WDM) system in the C- and L-bands of an operating wavelength zone. The index profile parameters of this fiber have been adjusted to simultaneously achieve high figure of merit (FOM) as well as considerably high value of effective core areas of the fiber to minimize the nonlinear effects like self-phase modulation or cross-phase modulation. At 1,550 nm operating wavelength, an effective core area (A eff ) of 46 μm2, which is very large compared to other reported values of DCFs, is obtained here. The average dispersion of the DCFs, in combination with conventional single-mode fiber (CSF) and small dispersion fiber (SDF), are found out to be considerably flat in the entire C- and L-band zone of operating wavelength.

Dual-soliton dense dispersion-managed system with BL product of 2x10^15 b/s km

A two-channel long-haul soliton propagation system is demonstrated. Extensive variations of system parameters were numerically studied to provide the optimized system reported. In this system each soliton carries 80 Gb/s pseudo-random bit signal over 14,000 km. Key system parameters, such as the input peak power, the non linear coefficient, average dispersion and the number of sections of fiber in one amplifier length, are optimized, while the Q factor is monitored. As the Q factor falls below the threshold of 6.0 (corresponding to a BER of one error in a billion bits) the propagation distance is noted. For this optimized system a Q-factor threshold distance of 12700 km was obtained. This yields a bit-rate-distance (BL) product in excess of 210(15)b/s km.

Reduction of Gordon-Mollenauer phase noise in dispersion-managed systems using in-line spectral inversion

The influence of spectral inversion on the phase jitter of a soliton propagating in single-channel arbitrary dispersion-managed systems is studied with a semianalytic moment method. The results are similar to those previously observed in constant-dispersion links and show that the transmission-system reach can significantly be increased.

Soliton-like pulse timing jitter in dispersion-managed systems

In this paper, the timing jitter in dispersion-managed soliton-like systems with the Gaussian pulse is studied by using two methods. Firstly, the derivation of the dynamic equations for the evolution of soliton-like parameters and the timing jitter expressions for the dispersion-managed soliton-like systems are carried out by the perturbed variational method. By analysing and simulating these timing jitter expressions, one can find that the timing jitter is induced by the amplified spontaneous emission noise and the frequency shift, etc. Nonlinear gain can suppress the timing jitter. The chirp sign and the filters action have also effects on the total timing jitter. Secondly, the timing jitter is calculated and analysed by using the moment method. The results of the two methods prove to be consistent with each other.

Characterization and optimization of optical pulse differentiation using spectral interferometry

A simple fiber-based spectral interferometry setup is implemented for characterizing and monitoring the amplitude and phase of ultrafast temporal waveforms generated by optical differentiation with a long-period fiber grating (LPFG). In particular, the system is applied to characterize subpicosecond odd-symmetry Hermite-Gaussian (HG) pulses, consisting of two pi phase-shifted temporal lobes, obtained by temporal differentiation of Gaussian-like pulses. This technique is ideally suited for optimizing the experiment conditions (e.g., wavelength shifting between the input pulse and LPFG transmission characteristic) so as to achieve a nearly ideal odd-symmetry HG temporal waveform (with a sharp discrete pi phase shift at its center), of potential interest as a higher order soliton in dispersion-managed optical communication systems

Dynamics of nonstationary return-to-zero pulses in dispersion-managed systems

We describe an analytical framework for return-to-zero (RZ) propagation in dispersion-managed fiber systems. The pulses may generally not follow the same periodicity as that of the dispersion map (i.e., nonstationary evolution), which can complicate the design and monitoring of such systems. We show that a phase-plane representation of pulses is useful in identifying as well as predicting the salient features of this multiscale and nonlinear evolutionary behavior. Numerical calculations of RZ pulse-train propagation over 4000 km are carried out to demonstrate the correspondence of theory and simulation

Statistical characteristics and effects of polarization mode dispersion in dispersion managed soliton systems

Firstly, the JME (Jones matrix eigen) method is used to simulate the statistical characteristics of first- and second-order PMD in dispersion management system. Then, with help of the CNLSE (coupled nonlinear Schrodinger equations), the effects of PMD on DMS (dispersion managed soliton) transmission is studied with a variatioal method. The simplified relationships of the statistical parameters of second-order and first-order of PMD in dispersion management system have been gotten, from which the detailed information of second-order can be obtained, if the condition of DGD is given. The results have shown that the first and second-order PMD (polarization mode dispersion) vectors influence the evolution of energy and Mean square of time displacement of DMS in high-speed bit rates systems. WhenDPMD1 st>0.3 ps/km1/2, we must consider some means of control (for example the filter) the restrain the PMD.

Analytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems

Dispersion management is an effective technique to suppress the nonlinear impairment in fiber transmission systems, which includes tuning the amounts of precompensation, residual dispersion per span (RDPS), and net residual dispersion (NRD) of the systems. For self-phase modulation (SPM)-limited systems, optimizing the NRD is necessary because it can greatly improve the system performance. In this paper, an analytical method is presented to optimize NRD for SPM-limited dispersion-managed systems. The method is based on the correlation between the nonlinear impairment and the output pulse broadening of SPM-limited systems; therefore, dispersion-managed systems can be optimized through minimizing the output single-pulse broadening. A set of expressions is derived to calculate the output pulse broadening of the SPM-limited dispersion-managed system, from which the analytical result of optimal NRD is obtained. Furthermore, with the expressions of pulse broadening, how the nonlinear impairment depends on the amounts of precompensation and RDPS can be revealed conveniently.

Higher bit rates for dispersion-managed soliton communication systems via constrained coding

Constrained coding as a method to increase the data rate in dispersion-managed soliton (DMS) communication systems is proposed. This approach is well known and widely used in the context of magnetic and optical recording systems. This paper shows that it is also applicable to DMS systems due to certain similarities between the underlying physical channels. Since timing jitter is an important error-generating mechanism for solitons, a coding scheme specifically designed to combat pulse shifts is also presented, and its properties in the framework of a particular information-theoretic channel model are analyzed. A connection between the model used and the real physical channel is then established. Next, the coded system is compared with the original one from the channel capacity point of view with the help of numerical examples. Finally, the fact that the application of constrained coding may alleviate soliton pulse-to-pulse interaction is exploited. This, in turn, opens the door to the usage of higher-than-usual map strengths and ultimately leads to a significant increase of up to 50% in the bit rate

Chirped soliton-like solutions for nonlinear Schrödinger equation with variable coefficients

The exact chirped bright and dark soliton-like solutions of generalized nonlinear Schrödinger equation including linear and nonlinear gain(loss) with variable coefficients describing dispersion-management or soliton control is obtained detailedly in this paper. To begin our numerical studies of the stability of the solutions, we present a periodically distributed dispersion management or soliton control system as an example. It is found that both the bright and dark soliton-like solutions are stable during propagation in the given system. The numerical results are well in accordance with those obtained by analytical methods.

Unsymmetric map of dispersion-managed soliton transmission system with lumped amplifiers

A dispersion-managed soliton transmission using an unsymmetric dispersion map in a lumped amplifier system is investigated. For a soliton dispersion management system with equal-length segments of both normal and anomalous dispersion fibers, it is shown that the initial fiber length of the unsymmetric dispersion map must be shorter than that of the symmetric map to attain a chirp-free pulse at the beginning of a dispersion management unit cell. By properly adjusting the initial fiber length of the unsymmetric dispersion map, the dispersive wave is reduced and the allowed transmission distance can be increased when compared to the symmetric map system with optimum prechirping.