Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations. © 2005 Springer Science+Business Media, Inc.

Design of Raman-based nonlinear loop mirror for all-optical 2R regeneration of differential phase-shift-keying transmission

We present a concept for all-optical regeneration of signals modulated in phase-sensitive modulation formats, which is based on a new design of Raman amplified nonlinear optical loop mirror (RA-NOLM). We demonstrate simultaneous amplitude-shape regeneration and phase-noise reduction in high-speed differential phase-shift-keying transmission systems by use of the RA-NOLM combined with spectral filtering. © 2006 IEEE.

Multiwavelength fiber laser based on nonlinear polarization rotation

Multiwavelength fiber laser is a perfect light source for future wavelength-division-multiplexing optical communication systems. A multiwavelength fiber laser based on nonlinear polarization rotation with up to 18 wavelengths has been proposed and demonstrated. The intensity- and wavelength-dependent loss induced by nonlinear polarization rotation effect is used to alleviate the mode competition in the homogeneous broadening gain medium of erbium-doped fiber. Instead of traditional filters, a polarization-maintaining fiber is inserted into the laser cavity, with which the polarization-dependent isolator composes an equivalent Lyot birefringent fiber filter. The in-line birefringence fiber filter is used to simplify the laser configuration, which benefits systematic integration. The effect of the 980 nm pump power on the multiwavelength generation is investigated. It is shown that the pump power contributes a lot to the evenness of the multiwavelength spectra due to the intensity dependence of nonlinear polarization rotation effect.

Dissipative nonlinear structures in fiber optics

Optical fiber materials exhibit a nonlinear response to strong electric fields, such as those of optical signals confined within the small fiber core. Fiber nonlinearity is an essential component in the design of the next generation of advanced optical communication systems, but its use is often avoided by engineers because of its intractability. The application of nonlinear technologies in fiber optics offers new opportunities for the design of photonic systems and devices. In this chapter, we make an overview of recent progress in mathematical theory and practical applications of temporal dissipative solitons and self-similar nonlinear structures in optical fiber systems. The design of all-optical high-speed signal processing devices, based on nonlinear dissipative structures, is discussed.

Evolution of timing jitter in nonlinearly-guided, dispersion managed transmission systems

Timing jitter is a major factor limiting the performance of any high-speed, long-haul data transmission system. It arises from a number of reasons, such as interaction with accumulated spontaneous emission, inter-symbol interference (ISI), electrostriction etc. Some effects causing timing jitter can be reduced by means of non-linear filtering, using, for example, a nonlinear optical loop mirror (NOLM) [1]. The NOLM has been shown to reduce the timing jitter by suppressing the ASE and by stabilising the pulse duration [2, 3]. In this paper, we investigate the dynamics of timing jitter in a 2R regenerated system, nonlinearly guided by NOLMs at bit rates of 10, 20, 40, and 80- Gbit/s. Transmission performance of an equivalent non-regenerated (generic) system is taken as a reference.

Advanced perturbation technique for digital backward propagation in WDM systems

An improved digital backward propagation (DBP) is proposed to compensate inter-nonlinear effects and dispersion jointly in WDM systems based on an advanced perturbation technique (APT). A non-iterative weighted concept is presented to replace the iterative in analytical recursion expression, which can dramatically simplify the complexity and improve accuracy compared to the traditional perturbation technique (TPT). Furthermore, an analytical recursion expression of the output after backward propagation is obtained initially. Numerical simulations are executed for various parameters of the transmission system. The results indicate that the advanced perturbation technique will relax the step size requirements and reduce the oversampling factor when launch power is higher than -2 dBm. We estimate this technique will reduce computational complexity by a factor of around seven with respect to the conventional DBP. © 2013 Optical Society of America.

Non-periodic quasi-stable nonlinear optical carrier pulses with sliding chirp-free points for transmission at 40 Gbit/s rate

In this paper, we demonstrate the possibility of reaching a quasi-stable nonlinear transmission regime with carrier pulses of 12.5 ps width in multi-channel 40 Gbit/s systems. The quasi-stable pulses that are presented in this work for the first time are not dispersion-managed solitons, and are indeed supported by a large normal span average dispersion and misbalanced optical amplification, and representing a new type of nonlinear carrier.

Nonlinearity management in hybrid amplification systems

A theory of nonlinearity management in transmission lines with periodic dispersion compensation and hybrid Raman-EDFA amplification is developed. Different transmission/compensating fiber pairs performances are compared and the optimal amplification scheme determined for each case.

Shannon capacity of nonlinear communication channels

The exponentially increasing demand on operational data rate has been met with technological advances in telecommunication systems such as advanced multilevel and multidimensional modulation formats, fast signal processing, and research into new different media for signal transmission. Since the current communication channels are essentially nonlinear, estimation of the Shannon capacity for modern nonlinear communication channels is required. This PhD research project has targeted the study of the capacity limits of different nonlinear communication channels with a view to enable a significant enhancement in the data rate of the currently deployed fiber networks. In the current study, a theoretical framework for calculating the Shannon capacity of nonlinear regenerative channels has been developed and illustrated on the example of the proposed here regenerative Fourier transform (RFT). Moreover, the maximum gain in Shannon capacity due to regeneration (that is, the Shannon capacity of a system with ideal regenerators – the upper bound on capacity for all regenerative schemes) is calculated analytically. Thus, we derived a regenerative limit to which the capacity of any regenerative system can be compared, as analogue of the seminal linear Shannon limit. A general optimization scheme (regenerative mapping) has been introduced and demonstrated on systems with different regenerative elements: phase sensitive amplifiers and the proposed here multilevel regenerative schemes: the regenerative Fourier transform and the coupled nonlinear loop mirror.

Reduction of nonlinear intrachannel effects by channel asymmetry in transmission lines with strong bit overlapping

We have examined the statistics of simulated bit-error rates in optical transmission systems with strong patterning effects and have found strong correlation between the probability of marks in a pseudorandom pattern and the error-free transmission distance. We discuss how a reduced density of marks can be achieved by preencoding optical data.

Granular superconductors:from the nonlinear σ model to the Bose-Hubbard description

We modify a nonlinear σ model (NLσM) for the description of a granular disordered system in the presence of both the Coulomb repulsion and the Cooper pairing. We show that under certain controlled approximations the action of this model is reduced to the Ambegaokar-Eckern-Schön (AES) action, which is further reduced to the Bose-Hubbard (or “dirty-boson”) model with renormalized coupling constants. We obtain an effective action which is more general than the AES one but still simpler than the full NLσM action. This action can be applied in the region of parameters where the reduction to the AES or the Bose-Hubbard model is not justified. This action may lead to a different picture of the superconductor-insulator transition in two-dimensional systems.

Probabilistic control for uncertain systems

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

A probabilistic indirect adaptive control for systems with input-dependent noise

A probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input–dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system.

Enhanced information transmission with signal-dependent noise in an array of nonlinear elements

We have investigated information transmission in an array of threshold units that have signal-dependent noise and a common input signal. We demonstrate a phenomenon similar to stochastic resonance and suprathreshold stochastic resonance with additive noise and show that information transmission can be enhanced by a nonzero level of noise. By comparing system performance to one with additive noise we also demonstrate that the information transmission of weak signals is significantly better with signal-dependent noise. Indeed, information rates are not compromised even for arbitrary small input signals. Furthermore, by an appropriate selection of parameters, we observe that the information can be made to be (almost) independent of the level of the noise, thus providing a robust method of transmitting information in the presence of noise. These result could imply that the ability of hair cells to code and transmit sensory information in biological sensory systems is not limited by the level of signal-dependent noise. © 2007 The American Physical Society.

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.