Solitons: permanent waves

Communications engineers are learning to create an electromagnet wave at will, to transmit information. This wave, the optical soliton, is the subject of astounding recent developments in nonlinear optics and lasers. The author describes the principles behind the use of solitons in optical communications and shows that in the context of such communications the most important property of solitons is that they are extremely stable. Not only do they not disperse, but an encounter with a perturbation (e.g. a joint in optical fibre) will usually leave the soliton unaltered.

Optimising transmission capacity: long distance and terrestrial applications

This paper identifies the important limiting processes in transmission capacity for amplified soliton systems. Some novel control techniques are described for optimizing this capacity. In particular, dispersion compensation and phase conjugation are identified as offering good control of jitter without the need for many new components in the system. An advanced average soliton model is described and demonstrated to permit large amplifier spacing. The potential for solitons in high-dispersion land-based systems is discussed and results are presented showing 10 Gbit s$^{-1}$ transmission over 1000 km with significant amplifier spacing.

A perturbative analysis of dispersion-managed solitons

We study soliton solutions of the path-averaged propagation equation governing the transmission of dispersion-managed (DM) optical pulses in the (practical) limit when residual dispersion and nonlinearity only slightly affect the pulse dynamics over one compensation period. In the case of small dispersion map strengths, the averaged pulse dynamics is governed by a perturbed form of the nonlinear Schrödinger equation; applying a perturbation theory – elsewhere developed – based on inverse scattering theory, we derive an analytic expression for the envelope of the DM soliton. This expression correctly predicts the power enhancement arising from the dispersion management. Theoretical results are verified by direct numerical simulations.

Statistics of three interacting optical solitons

We examine the statistics of three interacting optical solitons under the effects of amplifier noise and filtering. We derive rigorously the Fokker-Planck equation that governs the probability distribution of soliton parameters.

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

Dispersion-managed solitons: a new paradigm for high data rate

The WDM properties of dispersion managed (DM) solitons and the reduction in Gordon-Haus jitter means that it is possible to contemplate multiple channels each at 10 Gbit/s for transoceanic distances without the need for elaborate soliton control. This paper will concentrate on fundamental principles of DM solitons, but will use these principles to indicate optimum maps for future high-speed soliton systems.

An interpretation of the energy variations of dispersion managed solitons in terms of effective average dispersion

We show that the variation in dispersion managed soliton energy that occurs as the amplifier position varies within the dispersion map, for a fixed map strength, can be interpreted using the concept of effective average dispersion. Using this concept we physically explain why the location of the amplifier can produce a greater or lesser energy enhancement factor than the lossless model. © 2001 Elsevier Science B.V. All rights reserved.

Nonlinear pulse shaping and polarization dynamics in mode-locked fiber lasers

We review our recent progress on the study of new nonlinear mechanisms of pulse shaping in passively mode-locked fiber lasers. These include a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on our recent experimental studies unveiling new types of vector solitons with processing states of polarization for multi-pulse and tightly bound-state soliton (soliton molecule) operations in a carbon nanotube (CNT) mode-locked fiber laser with anomalous dispersion cavity. © 2014 World Scientific Publishing Company.

Conversion of a chirped Gaussian pulse to a soliton or a bound multisoliton state in quasi-lossless and lossy optical fiber spans

The formation of single-soliton or bound-multisoliton states from a single linearly chirped Gaussian pulse in quasi-lossless and lossy fiber spans is examined. The conversion of an input-chirped pulse into soliton states is carried out by virtue of the so-called direct Zakharov-Shabat spectral problem, the solution of which allows one to single out the radiative (dispersive) and soliton constituents of the beam and determine the parameters of the emerging bound state(s). We describe here how the emerging pulse characteristics (the number of bound solitons, the relative soliton power) depend on the input pulse chirp and amplitude. © 2007 Optical Society of America.

Multiple-period dispersion-managed solitons

We present a class of solutions with a period multiple to that one of the standard dispersion-managed soliton in the nonlinear Schrödinger equation with periodic variations of dispersion. © 2007 The American Physical Society.

Calculation of non-Gaussian statistics and bit error rate degradation due to pulse-to-pulse interaction

We develop a theoretical method to calculate jitter statistics of interacting solitons. Applying this approach, we have derived the non-Gaussian probability density function and calculated the bit-error rate as a function of noise level, initial separation and phase difference between solitons.

Stochasticity and coherent structures in ultra-long mode-locked lasers

Ultra-long mode-locked lasers are known to be strongly influenced by nonlinear interactions in long cavities that results in noise-like stochastic pulses. Here, by using an advanced technique of real-time measurements of both temporal and spatial (over round-trips) intensity evolution, we reveal an existence of wide range of generation regimes. Different kinds of coherent structures including dark and grey solitons and rogue-like bright coherent structures are observed as well as interaction between them are revealed.

Dissipative Raman solitons

A new type of dissipative solitons - dissipative Raman solitons - are revealed on the basis of numerical study of the generalized complex nonlinear Ginzburg-Landau equation. The stimulated Raman scattering significantly affects the energy scalability of the dissipative solitons, causing splitting to multiple pulses. We show, that an appropriate increase of the group-delay dispersion can suppress the multipulsing instability due to formation of the dissipative Raman soliton, which is chirped, has a Stokes-shifted spectrum, and chaotic modulation on its trailing edge. The strong perturbation of a soliton envelope caused by the stimulated Raman scattering confines the energy scalability, preventing the so-called dissipative soliton resonance. We show that in practical implementations, a spectral filter can extend the stability regions of high-energy pulses.