Simulation of optical fibre communication systems influenced by stimulated brillouin scattering

Boyd's SBS model which includes distributed thermal acoustic noise (DTAN) has been enhanced to enable the Stokes-spontaneous density depletion noise (SSDDN) component of the transmitted optical field to be simulated, probably for the first time, as well as the full transmitted field. SSDDN would not be generated from previous SBS models in which a Stokes seed replaces DTAN. SSDDN becomes the dominant form of transmitted SBS noise as model fibre length (MFL) is increased but its optical power spectrum remains independent of MFL. Simulations of the full transmitted field and SSDDN for different MFLs allow prediction of the optical power spectrum, or system performance parameters which depend on this, for typical communication link lengths which are too long for direct simulation. The SBS model has also been innovatively improved by allowing the Brillouin Shift Frequency (BS) to vary over the model fibre length, for the nonuniform fibre model (NFM) mode, or to remain constant, for the uniform fibre model (UFM) mode. The assumption of a Gaussian probability density function (pdf) for the BSF in the NFM has been confirmed by means of an analysis of reported Brillouin amplified power spectral measurements for the simple case of a nominally step-index single-mode pure silica core fibre. The BSF pdf could be modified to match the Brillouin gain spectra of other fibre types if required. For both models, simulated backscattered and output powers as functions of input power agree well with those from a reported experiment for fitting Brillouin gain coefficients close to theoretical. The NFM and UFM Brillouin gain spectra are then very similar from half to full maximum but diverge at lower values. Consequently, NFM and UFM transmitted SBS noise powers inferred for long MFLs differ by 1-2 dB over the input power range of 0.15 dBm. This difference could be significant for AM-VSB CATV links at some channel frequencies. The modelled characteristic of Carrier-to-Noise Ratio (CNR) as a function of input power for a single intensity modulated subcarrier is in good agreement with the characteristic reported for an experiment when either the UFM or NFM is used. The difference between the two modelled characteristics would have been more noticeable for a higher fibre length or a lower subcarrier frequency.

Analysis and optimisation of the performance of nonlinear optical communication systems

We investigate the feasibility of simultaneous suppressing of the amplification noise and nonlinearity, representing the most fundamental limiting factors in modern optical communication. To accomplish this task we developed a general design optimisation technique, based on concepts of noise and nonlinearity management. We demonstrate the immense efficiency of the novel approach by applying it to a design optimisation of transmission lines with periodic dispersion compensation using Raman and hybrid Raman-EDFA amplification. Moreover, we showed, using nonlinearity management considerations, that the optimal performance in high bit-rate dispersion managed fibre systems with hybrid amplification is achieved for a certain amplifier spacing – which is different from commonly known optimal noise performance corresponding to fully distributed amplification. Required for an accurate estimation of the bit error rate, the complete knowledge of signal statistics is crucial for modern transmission links with strong inherent nonlinearity. Therefore, we implemented the advanced multicanonical Monte Carlo (MMC) method, acknowledged for its efficiency in estimating distribution tails. We have accurately computed acknowledged for its efficiency in estimating distribution tails. We have accurately computed marginal probability density functions for soliton parameters, by numerical modelling of Fokker-Plank equation applying the MMC simulation technique. Moreover, applying a powerful MMC method we have studied the BER penalty caused by deviations from the optimal decision level in systems employing in-line 2R optical regeneration. We have demonstrated that in such systems the analytical linear approximation that makes a better fit in the central part of the regenerator nonlinear transfer function produces more accurate approximation of the BER and BER penalty. We present a statistical analysis of RZ-DPSK optical signal at direct detection receiver with Mach-Zehnder interferometer demodulation

Numerical and statistical analysis of long-haul undersea optical communication systems

Firstly, we numerically model a practical 20 Gb/s undersea configuration employing the Return-to-Zero Differential Phase Shift Keying data format. The modelling is completed using the Split-Step Fourier Method to solve the Generalised Nonlinear Schrdinger Equation. We optimise the dispersion map and per-channel launch power of these channels and investigate how the choice of pre/post compensation can influence the performance. After obtaining these optimal configurations, we investigate the Bit Error Rate estimation of these systems and we see that estimation based on Gaussian electrical current systems is appropriate for systems of this type, indicating quasi-linear behaviour. The introduction of narrower pulses due to the deployment of quasi-linear transmission decreases the tolerance to chromatic dispersion and intra-channel nonlinearity. We used tools from Mathematical Statistics to study the behaviour of these channels in order to develop new methods to estimate Bit Error Rate. In the final section, we consider the estimation of Eye Closure Penalty, a popular measure of signal distortion. Using a numerical example and assuming the symmetry of eye closure, we see that we can simply estimate Eye Closure Penalty using Gaussian statistics. We also see that the statistics of the logical ones dominates the statistics of the logical ones dominates the statistics of signal distortion in the case of Return-to-Zero On-Off Keying configurations.

Adaptive electrical signal post-processing in optical communications systems

Improving bit error rates in optical communication systems is a difficult and important problem. The error correction must take place at high speed and be extremely accurate. We show the feasibility of using hardware implementable machine learning techniques. This may enable some error correction at the speed required.

Nonlinear spectral shaping and optical rogue events in fiber-based systems

We provide an overview of our recent work on the shaping and stability of optical continua in the long pulse regime. Fibers with normal group-velocity dispersion at all-wavelengths are shown to allow for highly coherent continua that can be nonlinearly shaped using appropriate initial conditions. In contrast, supercontinua generated in the anomalous dispersion regime are shown to exhibit large fluctuations in the temporal and spectral domains that can be controlled using a carefully chosen seed. A particular example of this is the first experimental observation of the Peregrine soliton which constitutes a prototype of optical rogue-waves.

Dissipative nonlinear structures in optical fiber systems I : dissipative dispersion managed solitons in mode-locked lasers

In this first talk on dissipative structures in fiber applications, we extend theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fibre lasers. Dissipative structures exist at high map strengths leading to the generation of stable, short pulses with high energy. Two types of intra-map pulse evolutions are observed depending on the net cavity dispersion. These are characterized by a reduced model and semi-analytical solutions are obtained.

Dissipative nonlinear structures in optical fiber systems II : self-similar parabolic pulses in active fibers

In this second talk on dissipative structures in fiber applications, we overview theoretical aspects of the generation, evolution and characterization of self-similar parabolic-shaped pulses in fiber amplifier media. In particular, we present a perturbation analysis that describes the structural changes induced by third-order fiber dispersion on the parabolic pulse solution of the nonlinear Schrödinger equation with gain. Promising applications of parabolic pulses in optical signal post-processing and regeneration in communication systems are also discussed.

Dissipative nonlinear structures in optical fiber systems III : dissipative solitons via nonlinear mapping

In the third and final talk on dissipative structures in fiber applications, we discuss mathematical techniques that can be used to characterize modern laser systems that consist of several discrete elements. In particular, we use a nonlinear mapping technique to evaluate high power laser systems where significant changes in the pulse evolution per cavity round trip is observed. We demonstrate that dissipative soliton solutions might be effectively described using this Poincaré mapping approach.

Electronic dispersion compensation using full optical-field reconstruction in 10Gbit/s OOK based systems

We investigate the design of electronic dispersion compensation (EDC) using full optical-field reconstruction in 10Gbit/s on-off keyed transmission systems limited by optical signal-to-noise ratio (OSNR). By effectively suppressing the impairment due to low- frequency component amplification in phase reconstruction, properly designing the transmission system configuration to combat fiber nonlinearity, and successfully reducing the vulnerability to thermal noise, a 4.8dB OSNR margin can be achieved for 2160km single-mode fiber transmission without any optical dispersion compensation. We also investigate the performance sensitivity of the scheme to various system parameters, and propose a novel method to greatly enhance the tolerance to differential phase misalignment of the asymmetric Mach-Zehnder interferometer. This numerical study provides important design guidelines which will enable full optical-field EDC to become a cost-effective dispersion compensation solution for future transparent optical networks.

Nonlinearity compensation in multi-rate 28 Gbaud WDM systems employing optical and digital techniques under diverse link configurations

Digital back-propagation (DBP) has recently been proposed for the comprehensive compensation of channel nonlinearities in optical communication systems. While DBP is attractive for its flexibility and performance, it poses significant challenges in terms of computational complexity. Alternatively, phase conjugation or spectral inversion has previously been employed to mitigate nonlinear fibre impairments. Though spectral inversion is relatively straightforward to implement in optical or electrical domain, it requires precise positioning and symmetrised link power profile in order to avail the full benefit. In this paper, we directly compare ideal and low-precision single-channel DBP with single-channel spectral-inversion both with and without symmetry correction via dispersive chirping. We demonstrate that for all the dispersion maps studied, spectral inversion approaches the performance of ideal DBP with 40 steps per span and exceeds the performance of electronic dispersion compensation by ~3.5 dB in Q-factor, enabling up to 96% reduction in complexity in terms of required DBP stages, relative to low precision one step per span based DBP. For maps where quasi-phase matching is a significant issue, spectral inversion significantly outperforms ideal DBP by ~3 dB.

All-optical phase and amplitude regenerator for next-generation telecommunications systems

Fibre-optic communications systems have traditionally carried data using binary (on-off) encoding of the light amplitude. However, next-generation systems will use both the amplitude and phase of the optical carrier to achieve higher spectral efficiencies and thus higher overall data capacities(1,2). Although this approach requires highly complex transmitters and receivers, the increased capacity and many further practical benefits that accrue from a full knowledge of the amplitude and phase of the optical field(3) more than outweigh this additional hardware complexity and can greatly simplify optical network design. However, use of the complex optical field gives rise to a new dominant limitation to system performance-nonlinear phase noise(4,5). Developing a device to remove this noise is therefore of great technical importance. Here, we report the development of the first practical ('black-box') all-optical regenerator capable of removing both phase and amplitude noise from binary phase-encoded optical communications signals.

Channel estimation and compensation in chromatic dispersion limited optical fast OFDM systems

We experimentally investigate the channel estimation and compensation in a chromatic dispersion (CD) limited 20Gbit/s optical fast orthogonal frequency division multiplexing (F-OFDM) system with up to 840km transmission. It is shown that symmetric extension based guard interval (GI) is required to enable CD compensation using one-tap equalizers. As few as one optical F-OFDM symbol with four and six pilot tones per symbol can achieve near-optimal channel estimation and compensation performance for 600km and 840km respectively.

All-optical passive quasi-regeneration in transoceanic 40 Gbit/s return-to-zero transmission systems with strong dispersion management

A method of all-optical passive quasi-regeneration in transoceanic 40 Gbit/s return-to-zero transmission systems with strong dispersion management was described. The use of in-line nonlinear optical loop mirrors (NOLM) by the method was demonstrated. The quasi-regeneration of signals performed by NOLMs was found to improve the systems's performance.

Auto-solitons guided by in-line nonlinear optical loop mirrors in dispersion-managed communication systems

Summary form only given. Both dispersion management and the use of a nonlinear optical loop mirror (NOLM) as a saturable absorber can improve the performance of a soliton-based communication system. Dispersion management gives the benefits of low average dispersion while allowing pulses with higher powers to propagate, which helps to suppress Gordon-Haus timing jitter without sacrificing the signal-to-noise ratio. The NOLM suppresses the buildup of amplifier spontaneous emission noise and background dispersive radiation which, if allowed to interact with the soliton, can lead to its breakup. We examine optical pulse propagation in dispersion-managed (DM) transmission system with periodically inserted in-line NOLMs. To describe basic features of the signal transmission in such lines, we develop a simple theory based on a variational approach involving Gaussian trial functions. It, has already been proved that the variational method is an extremely effective tool for description of DM solitons. In the work we manage to include in the variational description the point action of the NOLM on pulse parameters, assuming that the Gaussian pulse shape is inherently preserved by propagation through the NOLM. The obtained results are verified by direct numerical simulations