Dispersion-managed Systems Research Articles

(Invited) high speed densely dispersion-managed soliton and four-wave-mixing in dense periodical fibers and conventional dispersion-managed systems

I briefly reviewed the interesting densely dispersion-managed soliton (DDMS), and single channel high speed (40–160 Gbit/s) DDMS can transmit record distance at that time. I briefly reviewed the four-wave-mixing (FWM) of continous wave (CW) lasers in DPF when the EDFAs are located in the middle of dispersion section (z2 section), and our relative FWM efficiency formula was the first formula even for conventional dispersion-managed system (CDM) as well. We reached much lower FWM efficiency over a broad wavelength range in the well designed DPF than that in CDM and constant dispersion systems. We first found the FWM resonant condition for our dense periodical fiber (DPF) and CDM system. FWM strongly relates to the location of EDFAs. In this paper, I first report the analytical formula of relative FWM of CW lasers in DPF when the EDFAs are located right after the z1 section with dispersion D1, and our results are also suitable for CDM systems.

Study on increasing the capacity of RoF systems for long distance optical communication using solitons

In order to enable long distance communication, the light signal in Radio-over-fiber (RoF) technique is modulated by a radio signal. WDM (wavelength division multiplexing) technology is an effective way which can be used in the optical fiber feeder network to increase the capacity of RoF systems. In spite of the advantages RoF has nonlinear effects such as dispersion which can be mitigated by selecting appropriate dispersion management techniques. One of the challenges of WDM is the proper wavelength spacing. It must be properly designed so that signal interference does not occur. In this paper we try to review which dispersion management technique provides greater efficiency for long haul optical networks. The performance efficiency of different modulation techniques and different orders of modulation is also reviewed. So, by this work we try to propose a model which will provide better output power and low dispersion level which is the primary concern of any optical transmission system. The proposed model incorporates a WDM RoF system with soliton dispersion management system and the modulation technique employed is 64 QAM/DPSK and the results are analyzed in terms of Q-factor and Bit Error Rate (BER).

Effect of Fourth-Order Dispersion on Solitonic Interactions

Solitons became important in optical communication systems thanks to their robust nature. However, the interaction of solitons is considered as a bad effect. To avoid interactions, the obvious solution is to respect the temporal separation between two adjacent solitons determined as a bit rate. Nevertheless, many better solutions exist to decrease the bit rate error. In this context, the aim of our work is to study the possibility to delete the interaction of adjacent solitons, by using a special dispersion management system, precisely by introducing both of the third- and fourth-order dispersions in the presence of a group velocity dispersion. To study the influence of the fourth- and third-order dispersions, we use the famous non-linear Schr¨odinger equation solved with the Fast Fourier Transform method. The originality of this work is to bring together the dispersion of the fourth, third, and second orders to separate two solitons close enough to create the Kerr-induced interaction and consequently to improve the propagation by decreasing the bit rate error. This study illustrates the influence of the fourth-order dispersion on one single soliton and two co-propagative solitons with different values of the temporal separation. Then the third order dispersion is introduced in the presence of the fourth-order dispersion in the propagation of one and two solitons in order to study its influence on the interaction. Finally, we show the existence of a precise dispersion management system that allows one to avoid the interaction of solitons.

SRS generation of femtosecond pulses in a methane-filled revolver hollow-core optical fibre

The influence of the width of pump pulses (with λp = 1.026 μm) on the SRS generation of femtosecond pulses in a methane-filled hollow-core fibre is investigated. The width of pump pulses is controlled by transmitting them through an optical dispersion-managed system and thus making them linear frequency-modulated (chirped). Regimes of both the preferred SRS generation of femtosecond pulses at the Stokes wavelength (λst = 1.464 μm) and the generation of a multiband supercontinuum are experimentally demonstrated. A quantum efficiency of 41 % and a pulse width of 590 fs at the Stokes wavelength are obtained for the 1.026 → 1.464 nm Raman generation.

Dark soliton control based on dispersion and nonlinearity for third-order nonlinear Schrödinger equation

Nonlinear control is widely used in optical communications, ultrafast optics and other fields. In this paper, nonlinear control based on the dark soliton is investigated in the dispersion management system. Dark soliton solutions for the third-order nonlinear Schrödinger equation are derived. Through changing the group velocity dispersion and nonlinear parameters, the propagation characteristics of dark solitons are discussed, and the influences of corresponding parameters on dark solitons are analyzed. Some nonlinear control methods based on specific parameters are suggested. Results are beneficial to the study of the dark soliton transmission.

Interactions between M-typed solitons based on nonlinear optimization in dispersion management systems

Investigations on soliton interactions in dispersion management systems are beneficial to improving the communication capacity. In this paper, the variable-coefficient fifth-order nonlinear Schrödinger equation, which can be used to describe the soliton interactions in dispersion management systems, is studied analytically. M-typed soliton interactions are presented based on the obtained soliton solutions. Influences of nonlinear effects on M-typed soliton interactions are analyzed. Results indicate that we can effectively control soliton interactions by means of nonlinear optimization of dispersion management systems.

Nonlinear control of M-typed solitons in dispersion management systems

As the optical transmission system is developing in the direction of ultra-high speed and ultra-long distance, the dispersion and nonlinearity of optical fibers has an increasing influence on signal transmission. In this paper, the variable-coefficient higher-order nonlinear Schrödinger equation is studied to investigate the effect of nonlinearity on soliton transmission in dispersion management systems. Analytic soliton solution is derived, and M-typed solitons are observed. The improvement of system performance is analyzed. In addition, a nonlinear control method is proposed based on the analysis of corresponding parameters.

Black and gray soliton interactions and cascade compression in the variable coefficient nonlinear Schrödinger equation

We present the theoretical study of dark soliton dynamics in inhomogeneous fiber system by means of a variable coefficient nonlinear Schrödinger equation (Vc-NLSE). The dark soliton interaction in the dispersion-managed system with gain/loss and cascade compression of solitons by the nonlinear tunneling phenomena are studied in detail. Numerically, we study the dark soliton propagation in the continuous wave background, and the obtained soliton solution is found to be robust against perturbations. The elastic collision behavior of the dark solitons are observed by means of asymptotic analysis. For better insight, we study the impact of the blackness factor in the phase profile and also on the interaction dynamics of the different dark soliton settings, such as black and gray soliton. Additionally, we extend the study to the investigation of tunneling of the dark soliton across the barrier/well with a particular emphasize on the role of blackness parameter in the nonlinear tunneling phenomena, and demonstrated a cascaded compression of soliton in the inhomogeneous system.

Nonautonomous multi-peak solitons and modulation instability for a variable-coefficient nonlinear Schrödinger equation with higher-order effects

In this paper, we study a variable-coefficient nonlinear Schrodinger (vc-NLS) equation with fourth-order effects describing an inhomogeneous one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain or alpha helical protein. The first-order nonautonomous breather solution of the fourth-order vc-NLS equation is derived. The state transition between nonautonomous breather and nonautonomous multi-peak soliton can be realized when group velocity dispersion (GVD) coefficient is proportional to the fourth-order dispersion (FOD) coefficient. We also display how the higher-order effects influence the nonautonomous multi-peak solitons. Our results show that the velocity and localization of the nonautonomous multi-peak soliton are affected by the FOD coefficient, and the peak number is controlled by the GVD coefficient. Further, we also show the compression effect and motion with variable velocity of nonautonomous multi-peak soliton in two kinds of dispersion management systems. Finally, we reveal the relation between the state transition and the modulation instability (MI) analysis.

Tailored dispersion profile in controlling optical solitons in a tapered parabolic index fiber

We investigate the soliton dynamics in tapered parabolic index fibers via symbolic computation for a variety of dispersion profiles to inspect how a specific dispersion profile controls the optical soliton. By means of AKNS procedure, Lax pair is constructed for nonlinear Schrödinger equation with variable coefficients. Using obtained Lax pair, multi-soliton solutions are generated via Darboux transformation technique. Using multi-soliton solutions, soliton dynamics in tapered parabolic index fiber with the hyperbolic, Gaussian, exponential, and linear profiles are discussed. Results obtained in this study will be of certain potential application on construction of the nonlinear optical devices by soliton control. Results obtained in this study will be of certain value to the studies on the propagation and application of the soliton in the tapered parabolic index fiber and dispersion-managed fiber system.

Controllable Nonautonomous Rogue Waves in the Modified Nonlinear Schrödinger Equation with Distributed Coefficients in Inhomogeneous Fibers

Abstract Under investigation in this paper is an inhomogeneous modified nonlinear Schrödinger (MNLS) equation describing the ultrashort pulse dynamics with the distributed dispersion, self-phase modulation, self-steepening, and linear gain/loss. Nonautonomous rogue waves for the inhomogeneous MNLS equation are constructed via the modified Darboux transformation with the inhomogeneous parameters. The dynamical behaviours and main characteristics of the nonautonomous rogue waves in inhomogeneous fibers are discussed by analysing certain physical quantities. The inhomogeneous effects on the evolution of rogue waves are considered by virtue of the presented rational solutions with distributed coefficients. It is found that the group velocity dispersion (GVD) and linear gain/loss coefficients have effects on the trajectories and amplitudes of the rogue waves, respectively. Additionally, an intriguing composite rogue wave of the inhomogeneous MNLS equation is revealed, owing to the proper choice of the GVD coefficient. Our results could be useful for controlling the rogue waves in the dispersion-managed fiber system.

Analytical soliton solutions for the cubic–quintic nonlinear Schrödinger equation with Raman effect in the nonuniform management systems

Based on the Kundu–Eckhaus equation with variable coefficients, the exact one-soliton and two-soliton solutions have been explicitly given by an appropriate similarity transformation method. As an example, an exponential distributed fiber control system, nonlinearity management system and dispersion management system have been considered, and the propagation characteristics of the exact soliton solutions in the three nonuniform management systems have been investigated in detail. Especially, the dynamic properties of the amplitude, pulse width and the central position of the soliton with transmission distance have been studied. The results have some guiding significance for soliton amplification, compression and control management, and can provide some theoretical analysis for carrying out optical soliton communication experiment.

Digital compensation of cross-phase modulation distortions using perturbation technique for dispersion-managed fiber-optic systems

A digital compensation scheme based on a perturbation theory for mitigation of cross-phase modulation (XPM) distortions is developed for dispersion-managed fiber-optic communication systems. It is a receiver-side scheme that uses a hard-decision unit to estimate data for the calculation of XPM fields using the perturbation technique. The intra-channel nonlinear distortions are removed by intra-channel digital backward propagation (DBP) based on split-step Fourier scheme before the hard-decision unit. The perturbation technique is shown to be effective in mitigating XPM distortions. However, wrong estimations in the hard-decision unit result in performance degradation. A hard-decision correction method is proposed to correct the wrong estimations. Numerical simulations show that the hybrid compensation scheme with DBP for dispersion and intra-channel nonlinear impairments compensation and the perturbation technique for XPM compensation brings up to 3.7 dBQ and 1.7 dBQ improvements as compared with the schemes of linear compensation only and intra-channel DBP, respectively. The perturbation technique for XPM compensation requires only one-stage (or two-stage when hard-decision correction is applied) compensation and symbol-rate signal processing.

Analytical modeling of XPM in dispersion-managed coherent fiber-optic systems.

An analytical model for the cross-phase modulation (XPM) variance in dispersion-managed coherent fiber-optic systems is developed based on the first order perturbation theory. The XPM variance is analytically calculated for arbitrary pulse shapes. For a non-Gaussian pulse, the summation of time-shifted Gaussian pulses is used to fit the target pulse shape, which not only provides a good approximation of the non-Gaussian pulse but also allows explicit derivation of the XPM variance. The analytically estimated XPM variance is found to be in good agreement with numerical simulations.

Experimental study of cross-phase modulation reduction in hybrid systems with co-propagating 100G PM-QPSK and 10G OOK

We experimentally investigate various methods for reducing cross-phase modulation in hybrid networks with mixed 100G and 10G traffic. The experimental results over standard single-mode and non-zero dispersion-shifted fiber types demonstrate the effectiveness of several different XPM reduction techniques as well as the interplay between them. Nonlinear transmission performance is quantified using the Nonlinear Threshold metric as a function of key system features, including DCM type, dispersion map, spectral guard bands, and carrier phase estimation window size. Fiber Bragg grating-based DCMs are shown to offer a distinct advantage over fiber-based DCMs under certain conditions, particularly in dispersion-managed systems with very strong XPM. The average walk-off per span is introduced as a simple yet effective metric to compare different methods of XPM mitigation.

Transmission of mixed 260-Gb/s PDM-16QAM and 130-Gb/s PDM-QPSK over 960-km and 4160-km dispersion-managed SSMF spans

We transmit a mix of 260-Gb/s polarization-division-multiplexed 16-ary quadrature-amplitude modulation (PDM-16QAM) and 130-Gb/s polarization-division-multiplexed quadrature-phase-shift-keying (PDM-QPSK) channels at a 50-GHz channel spacing in a dispersion-managed (DM) system with standard single-mode-fiber (SSMF) spans. We study the impact of pulse shaping, time interleaving of polarizations and maximum likelihood (ML) detection techniques on the performance of the system. We show that the pulse shaping and ML detection can increase the transmission distances of the PDM-16QAM channels and PDM-QPSK channels by 50% and 10%, respectively. With 20% overhead hard-decision forward-error-correction (FEC) coding, we successfully transmit the 260-Gb/s PDM-16QAM and 130-Gb/s PDM-QPSK channels over 960-km and 4,160-km, respectively, in the DM system.

Multi-soliton solutions to the modified nonlinear Schrödinger equation with variable coefficients in inhomogeneous fibers

Multi-soliton solutions to the modified nonlinear Schrödinger equation (MNLSE) with variable coefficients (VCs) in inhomogeneous fibers are obtained with the help of mapping transformation, which reduces the VC MNLSE into a constant-coefficient MNLSE. Based on the analytical solutions, one- and two-soliton transmissions in the proper dispersion management systems are discussed. The sustainment of solitons and the disappearance of breathers for the VC MNLSE are first reported here.

Modeling nonlinearity in coherent transmissions with dominant intrachannel-four-wave-mixing

By extending a well-established time-domain perturbation approach to dual-polarization propagation, we provide an analytical framework to predict the nonlinear interference (NLI) variance, i.e., the variance induced by nonlinearity on the sampled field, and the nonlinear threshold (NLT) in coherent transmissions with dominant intrachannel-four-wave-mixing (IFWM). Such a framework applies to non dispersion managed (NDM) very long-haul coherent optical systems at nowadays typical baudrates of tens of Gigabaud, as well as to dispersion-managed (DM) systems at even higher baudrates, whenever IFWM is not removed by nonlinear equalization and is thus the dominant nonlinearity. The NLI variance formula has two fitting parameters which can be calibrated from simulations. From the NLI variance formula, analytical expressions of the NLT for both DM and NDM systems are derived and checked against recent NLT Monte-Carlo simulations.

Impact of nonlinear and polarization effects in coherent systems

Coherent detection with digital signal processing (DSP) significantly changes the ways impairments are managed in optical communication systems. In this paper, we review the recent advances in understanding the impact of fiber nonlinearities, polarization-mode dispersion (PMD), and polarization-dependent loss (PDL) in coherent optical communication systems. We first discuss nonlinear transmission performance of three coherent optical communication systems, homogeneous polarization-division-multiplexed (PDM) quadrature-phase-shift-keying (QPSK), hybrid PDM-QPSK and on/off keying (OOK), and PDM 16-ary quadrature-amplitude modulation (QAM) systems. We show that while the dominant nonlinear effects in coherent optical communication systems without optical dispersion compensators (ODCs) are intra-channel nonlinearities, the dominant nonlinear effects in dispersion-managed (DM) systems with inline dispersion compensation fiber (DCF) are different when different modulation formats are used. In DM coherent optical communication systems using modulation formats of constant amplitude, the dominant nonlinear effect is nonlinear polarization scattering induced by cross-polarization modulation (XPolM), whereas when modulation formats of non-constant amplitude are used, the impact of inter-channel cross-phase modulation (XPM) is much larger than XPolM. We then describe the effects of PMD and PDL in coherent systems. We show that although in principle PMD can be completely compensated in a coherent optical receiver, a real coherent receiver has limited tolerance to PMD due to hardware limitations. Two PDL models used to evaluate PDL impairments are discussed. We find that a simple lumped model significantly over-estimates PDL impairments and show that a distributed model has to be used in order to accurately evaluate PDL impairments. Finally, we apply system outage considerations to coherent systems, taking into account the statistics of polarization effects in fiber.

Impact of Channel Count and PMD on Polarization-Multiplexed QPSK Transmission

Through graphics-processing-unit-based simulations with different numbers of copropagating channels (1--81), the dependence of the nonlinear threshold on channel count, as well as on the fiber polarization mode dispersion (PMD) coefficient, is investigated for both dispersion-managed and DCM-free 40 and 100 Gb/s coherent-detected polarization-multiplexed quadrature phase-shift keying (CP-QPSK) transmission systems. Different fiber types including standard single-mode fiber (SSMF), large effective area fiber (LEAF), and truewave classic fiber (TWC) are considered and compared. Our investigations show that the required number of simulated copropagating channels to correctly simulate the nonlinear penalty caused by interchannel nonlinearities on CP-QSPK modulation is strongly dependent on the fiber type. The generally used assumption of around ten channels for simulating interchannel nonlinearities is only valid for the SSMF with relative low channel input power. For transmission links consisting of fiber types with low dispersion or high nonlinear coefficients, such as the LEAF or TWC, ten copropagating channels are clearly not sufficient. In dispersion-managed systems with DCMs, the required number of simulated copropagating channels is not only dependent on fiber types and data rates but also strongly on PMD present in the links. Our investigations have indicated that for transmission over fibers with very low PMD (this is the case of most new fibers), ten copropagating channels are not sufficient to correctly characterize the interchannel nonlinearities even for high-dispersion fiber types, such as the SSMF, and hence causes a clear underestimation of the nonlinearity penalty. Finally, synchronized and interleaved CP-QPSK is compared. We show that despite the depolarization effect of PMD, there are still some benefits of using interleaved RZ-CP-QPSK systems.