Dispersion-managed Fiber Links Research Articles

Theory of optimal power budget in quasi-linear dispersion-managed fibre links

A theory of an optimal distribution of the gain of in-line amplifiers in dispersion-managed transmission systems is developed. As an example of the application of the general method, a design of the line with periodically imbalanced in-line amplification is proposed.

Complete analysis of sideband instability in chain of periodic dispersion-managed fiber link and its effect on higher order dispersion-managed long-haul wavelength-division multiplexed systems

We present for the first time a complete theoretical analysis of sideband instability (SI) that occurs when two kinds of fibers with different characteristics are concatenated to form a dispersion-managed fiber link. In the analysis, the following three cases are taken into account: case (a) when a dispersion-management period is larger than an amplification period, case (b) when the two lengths are equivalent, and case (c) when a dispersion-management period is smaller than an amplification period. We find that the SI gain peak appears at frequencies determined by the larger of the two variation periods. Moreover, for all three cases, the magnitude of the SI gain reduces with the increase in strength of dispersion management. Next, we focus on the fiber link using the combination of standard single-mode fiber and reverse dispersion fiber, which is widely used for simultaneously compensating second- and third-order dispersion. By computer simulation, it is shown that in wavelength-division-multiplexed systems, SI still induces significant degradation in channels located at frequencies where SI induced from other channels arises. By reallocating the channel frequency to avoid the SI frequency, the transmission performance is improved significantly.

Balance between birefringence and Kerr effect in zero-averaged-path dispersion-managed optical fiber links

The interaction between random birefringence and the Kerr effect is investigated numerically with dispersion-managed (DM) soli- tons. In zero-averaged-path DM optical fiber links, because linear disper- sion is fully compensated, the Kerr effect becomes a detrimental residual factor to the transmission of DM soliton and results in a narrower optical pulse. However, under the proper conditions, an optical pulse can propa- gate better through the balance between random birefringence and the Kerr effect. After optimally mapping the optical pulse power and birefrin- gence parameter of an optical fiber, the polarization-mode dispersion resulting from random birefringence can essentially be balanced by the Kerr effect. In addition, considering polarization-dependent losses, we find that the pulse width's fluctuation and broadening are very large even with little loss difference in the two polarization components. © 2002 So-

Raman-Induced timing jitter in dispersion-managed optical communication systems

The moment method is used to calculate the Raman-induced timing jitter generated by amplifier-induced fluctuations in the energy, frequency, and position of optical pulses propagating inside dispersion-managed fiber links. Using a Gaussian form for chirped optical pulses in combination with the variational analysis, we obtain an analytic expression for the timing jitter whose predictions agree well with the numerical results obtained by solving the nonlinear Schrodinger equation directly. The effects of third-order dispersion are also included in the analysis. We also apply the moment method to standard solitons propagating inside dispersion-decreasing fiber as well as to chirped return-to-zero (CRZ) lightwave systems. We apply our results to a specific 160-Gb/s system and find that the Raman jitter resulting from intrapulse Raman scattering limits the transmission distance in all three cases.

Collective variable theory for optical solitons in fibers

We present a projection-operator method to express the generalized nonlinear Schrödinger equation for pulse propagation in optical fibers, in terms of the pulse parameters, called collective variables, such as the pulse width, amplitude, chirp, and frequency. The collective variable (CV) equations of motion are derived by imposing a set of constraints on the CVs to minimize the soliton dressing during its propagation. The lowest-order approximation of this CV approach is shown to be equivalent to the variational Lagrangian method. Finally, we demonstrate the application of this CV theory for pulse propagation in dispersion-managed optical fiber links.

Experimental quantification of soliton robustness to polarization-mode dispersion in dispersion-managed systems

We have, for the first time, observed and experimentally quantified the soliton robustness to polarization-mode dispersion (PMD) in a dispersion-managed (DM) fiber link. Long-term measurements were performed in a system where the PMD-characteristics were varying randomly over time. The results show that DM solitons are very robust, at least for low map strengths (0<S<10).

Pulse interactions and collisions in asymmetric higher-order dispersion managed fiber link

Intra-channel pulse interactions and inter-channel collisions may substantially limit the transmission performance in dispersion managed fiber optics links. We discuss how the theory of dispersion-managed solitons may be applied to optimize the dispersion map, as to reduce both pulse interactions and cross-phase modulation induced timing jitter at the system output.

Stable propagation of solitons in strongly dispersion-managed unequal-length optical fiber link with loss

Using average approximation, we obtained a phase plane evolution picture of soliton propagated in strongly dispersion-managed optical fiber link with loss. After analyzed this picture, we proposed a new picture to keep soliton propagation stably in this system. Stable propagation parameters are given and twenty points we are interested in are selected. Using these parameters, we can construct any type of optical fiber link. Considering the length of article, we give two types of link with peak power 2 and 8 mW. With an input pulse train consisting of 32 bits in return-to-zero (RZ) format, numerical simulation has been done. We find that soliton can stably propagate through these optical fiber link constructed by ten unequal-length unit with a data rate of 13.33 Gb/s.

Influence of transmission distance on XPM-inducedintensitydistortion in dispersion-managed, amplified fibre links

The variation of cross-phase modulation (XPM) induced distortion with transmission distance is investigated for dispersion-managed fibre links using a recirculating loop. New results are reported showing the distance dependence of the XPM-induced distortion in an IM-DD system on channel spacing and dispersion. It is demonstrated that the acquired XPM distortion can be effectively reduced by use of additional dispersive fibre at the receiver.

Generalized root-mean-square momentum method to describe chirped return-to-zero signal propagation in dispersion-managed fiber links

We present a generalized momentum method to describe evolution of the root-mean-square (rms) (averaged over time) optical pulse characteristics in dispersion-managed fiber lines. A closed system of the ordinary differential equations is derived for the rms pulse power, width, and chirp. The developed method can be useful for massive numerical simulations required to optimize wavelength-division-multiplexing dispersion-managed transmission using chirped return-to-zero format.

Generalized momentum method to describe high-frequency solitary wave propagation in systems with varying dispersion

We present a generalized momentum method to describe the evolution of the averaged (integral) pulse characteristics in nonlinear systems with periodically modulated dispersion and nonlinearity. A closed system of the ordinary differential equations is derived for averaged pulse power, width, and chirp. As a particular example, the developed theory is applied to the practical problem of the optical soliton transmission in dispersion-managed fiber links.

Dispersion-Managed Solitons and Optimization of the Dispersion Management

We overview recent progress in dispersion-managed (DM) fiber optic communications. Wavelength-division-multiplexing transmission of a DM soliton (or more general return-to-zero (RZ) formatted data) is an attractive way to realize middle- and long-distance ultra-high-capacity fiber communication systems. We present a theory of the DM optical soliton and a simple basic theory of the general DM RZ transmission. Two ordinary differential equations for the root-mean-square pulse width and chirp (momentum equations) describe the fast (during compensation period) evolution of the DM pulse. Applying chirped Gauss–Hermite orthogonal functions we derive a path-averaged propagation equation governing both the shape of the DM soliton and the slow (average) evolution of any chirped DM pulse. We describe the breathing dynamics of the self-similar core and oscillating tails of the DM optical pulse propagating in a fiber line with an arbitrary dispersion map. Based on the developed theory we describe the basic system principles, the design, and the optimization rules for DM fiber links. We demonstrate how to determine the energy enhancement of the DM soliton and optimal (chirp-free) points for launching of the signal, and how to evaluate the characteristics of a carrier signal for specific system parameters. DM solitons in systems with in-line filtering and Bragg gratings are also studied. Analytical results are illustrated by numerical simulations for a number of specific dispersion maps actively used in practice.

Strong time jitter reduction using solitons in “1/ z” dispersion managed fiber links

We propose and study a novel dispersion management method that permits the propagation of soliton pulses with a very low time jitter. The scheme assumes a chromatic dispersion that on average decreases with a 1/ z law, where z is the propagation distance. The advantage of this method consists in the fact that at the end of the link the mean chromatic dispersion is very small and as a consequence the jitter can be deeply reduced, while at the beginning of the link the chromatic dispersion is high, hence the system can operate with a large input power that permits a good signal to noise ratio. The scheme is simply implemented by periodically compensating the chromatic dispersion with fiber pieces having different lengths.

Optimization of soliton transmissions in dispersion-managed fiber links

We propose a simple optimization criterion (including the best launch point position in-between amplifiers) for the design of soliton transmission lines. The present approach is shown to minimize energy scattering from the solitons into the continuum.

Input pulse optimization in wavelength-division-multiplexed soliton transmissions

Amplitudes of input pulses in different channels of wavelength-division-multiplexed soliton transmissions should be adjusted according to their wavelength shift. The optimal distribution of input amplitudes maintains the initial time width and minimizes the radiations. Numerical simulations indicate that using this simple method, WDM transmission capacities of 80 Gbit/s over transoceanic distances may be possible in dispersion-managed fiber links without introducing any in-line soliton controls.

Quasi-stable soliton transmission in dispersion managed fiber links with lumped amplifiers

We study quasi-stable solitons in a cascaded fiber line with alternating positive and negative dispersions, with and without fiber loss. Although more energy is required for forming the quasi-stable solitons than the regular solitons in a uniform fiber system with the same average dispersion, the required soliton energy decreases as the energy loss in one amplification period increases, eventually approaching the same value as in a uniform fiber system. Thus, the predicted advantage of higher soliton energy in dispersion-managed system is diminished in the presence of loss.