Conventional Solitons Research Articles

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

We have experimentally quantified the soliton robustness to polarization mode dispersion (PMD) in both conventional and dispersion-managed (DM) soliton systems. Long-term measurements were performed in a computer-controlled system where the PMD characteristics varied randomly with time. Apart from the PMD itself, the performance of both systems depends on the average dispersion while the performance of the DM system also depends on the dispersion map strength. The results show that the robustness can be even more pronounced for DM systems with relatively small dispersion map strengths (0<S<10), compared with conventional systems (S=0), which is an effect of the increased power requirements. The experiments were also compared with numerical simulations.

Enhanced robustness of dispersion-managed solitons with respect to polarization mode dispersion

Polarization mode dispersion causes solitons to emit background radiation, which degrades transmission quality. It is shown theoretically and confirmed by numerical simulations that dispersion-managed solitons can trap part of that radiation into localized eigenmodes, thus yielding improvement in transmission quality compared with that of conventional solitons.

Effect of map strength on polarization mode dispersion in dispersion-managed soliton systems

Solitons in dispersion managed lines have large tolerance to polarization mode dispersion (PMD) because of the strong nonlinear trap helped by a power enhancement factor compared with conventional solitons. We present numerical results on the effect of map strength S on PMD and discuss the optimum choice of S in practical soliton systems.

Dispersion-managed soliton propagation in short-period dispersion maps

We show through detailed numerical simulations that stable dispersion-managed solitons exist in short-period dispersion maps characterized by a dispersion-management period that is less than the amplifier spacing. These pulses show regular dynamics within the amplifier span and have greater energy enhancement than the conventional dispersion-managed soliton. We also show that greater interaction is obtained in this regime as a result of this increased enhancement.

QUANTUM TOPOLOGY CHANGE IN (2+1)d

The topology of orientable (2+1) space–times can be captured by certain lumps of nontrivial topology called topological geons. They are the topological analogs of conventional solitons. We give a description of topological geons where the degrees of freedom related to topology are separated from the complete theory that contain metric (dynamical) degrees of freedom. The formalism also allows us to investigate processes of quantum topology change. They correspond to creation and annihilation of quantum geons. Selection rules for such processes are derived.

Coupled-mode envelope solitary waves in a pair of cubic Schrödinger equations with cross modulation: Analytical solution and collisions with application to Rossby waves

Coupled-Nonlinear Schrödinger equations, linked by cross modulation terms, arise in both nonlinear optics and in Rossby waves in the atmosphere and ocean. In this paper, we derive exact, analytic solutions for the “bright” coupled-mode soliton, for which the envelope in each mode asymptotes to zero at spatial infinity, and for its spatially periodic generalization. We then numerically study the collisions of the coupled-mode solitary wave both with a conventional envelope soliton, confined to a single mode, and also with a second coupled-mode solitary wave. The collisions are sensitive to both the relative speed and phase of the solitons. In some parameter ranges, the collisions are nearly elastic, but in others, one or both solitons fission.

High-speed soliton transmission in dense periodic fibers

An 80-Gbit/s soliton can be transmitted over a cross-Pacific distance in a dense periodic fiber, even in the presence of higher-order effects. Such a dense dispersion-managed soliton is generally more stable and faces fewer mutual interactions than a conventional dispersion-managed soliton.

Symmetries of a Class of Nonlinear Fourth Order Partial Differential Equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations (1) where α, β, γ, κ and µ are arbitrary constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a “Boussinesqtype” equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both “compacton” and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are not obtainable through the classical method.

Constructing D-branes from $K$-theory

A detailed review of recent developments in the topological classification of D-branes in superstring theory is presented. Beginning with a thorough, self-contained introduction to the techniques and applications of topological K-theory, the relationships between the classic constructions of K-theory and the recent realizations of D-branes as tachyonic solitons, coming from bound states of higher dimensional systems of unstable branes, are described. It is shown how the K-theory formalism naturally reproduces the known spectra of BPS and non-BPS D-branes, and how it can be systematically used to predict the existence of new states. The emphasis is placed on the new interpretations of D-branes as conventional topological solitons in other brane worldvolumes, how the mathematical formalism can be used to deduce the gauge field content on both supersymmetric and non-BPS branes, and also how K-theory predicts new relationships between the various superstring theories and their D-brane spectra. The implementations of duality symmetries as natural isomorphisms of K-groups are discussed. The relationship with the standard cohomological classification is presented and used to derive an explicit formula for D-brane charges. Some string theoretical constructions of the K-theory predictions are also briefly described.

Supersonic vibron solitons and their possible existence in polypeptides.

Nonlinear interactions of vibrons with lattice solitons due to the soft cubic nonlinearity in a quasi-one-dimensional lattice yield supersonic vibron solitons. Their binding energy is larger than those of the conventional Davydov solitons and vibron solitons, and their propagation velocity is uniquely determined in contrast to the latter two. Examination of parameters in the model Hamiltonian for polypeptides leads to the result that the supersonic vibron solitons obtained here are more likely to be realizable than the Davydov solitons and the conventional vibron solitons in alpha-helical proteins.

Subwavelength spatial solitons of TE mode

The wave equation of TE subwavelength beam propagations in a nonlinear planar waveguide is derived. This equation contains more higher-order linear and nonlinear terms than the nonlinear Schrödinger equation. The analytic solution of TE subwavelength spatial soliton is found to be the same as the conventional spatial soliton in amplitude but different in phase. The numerical results show that the analytic solution is stable.

Pulsating multiplet solutions of quintic wave equations

Numerical studies are used to demonstrate that, in addition to supporting conventional solitons, the quintic Korteweg-de Vries equation, u t +( u 2) x = u xxxxx , and its regularized version, u t +( u 2) x + u txxxx = 0, support multihumped solitary waves (doublets, triplets, quadruplets, etc.), referred to collectively as multiplets. Their peaks pulsate as they travel and undergo nearly elastic conllisions with other multiplets. An N-humped multiplet can pulsate thousands of cycles before disassociating into an ( N − 1)-humped multiplet and a single-peak solitary wave (singlet). Although multiplets are easily created from an initial wide compact pulse, they rarely are formed by fusing singlets or multiplets in collisions. We describe the emergence and evolution of multiplets, their nearly elastic collision dynamics, and their eventual decomposition into singlets. To consider the effect of cubic dispersion on the solution of these, equations, we also study u t + ( u 2) x + ηu xxx = δu xxxxx . The impact of cubic dispersion critically depends on the sign of η and its amplitude. For sufficiently large η > η 1 > 0, only a train of singlets emerge from an initial pulse with compact support. If η is decreased, multiplets begin to emerge leading the train of singlets. The number of humps in the multiplet increases as η is decreased, until below a critical point η < η ∞ < 0 the initial pulse decomposes into highly oscillatory waves.

Theory of multidimensional parametric band-gap simultons

Multidimensional spatiotemporal parametric simultons (simultaneous solitary waves) are possible in a nonlinear chi((2)) medium with a Bragg grating structure, where large effective dispersion occurs near two resonant band gaps for the carrier and second-harmonic field, respectively. The enhanced dispersion allows much reduced interaction lengths, as compared to bulk medium parametric simultons. The nonlinear parametric band-gap medium permits higher-dimensional stationary waves to form. In addition, solitons can occur with lower input powers than conventional nonlinear Schrodinger equation gap solitons. In this paper, the equations for electromagnetic propagation in a grating structure with a parametric nonlinearity are derived from Maxwell's equation using a coupled mode Hamiltonian analysis in one, two, and three spatial dimensions. Simultaneous solitary wave solutions are proved to exist by reducing the equations to the coupled equations describing a nonlinear parametric waveguide, using the effective-mass approximation (EMA). Exact one-dimensional numerical solutions in agreement with the EMA solutions are also given. Direct numerical simulations show that the solutions have similar types of stability properties to the bulk case, providing the carrier waves are tuned to the two Bragg resonances, and the pulses have a width in frequency space less than the band gap. In summary, these equations describe a physically accessible localized nonlinear wave that is stable in up to 3 + 1 dimensions. Possible applications include photonic logic and switching devices. [S1063-651X(98)06109-1].

Reduction of Gordon-Haus jitter in a dispersion compensated optical transmission system: analysis

We theoretically analyze the Gordon-Haus timing jitter in an optical transmission system with dispersion compensation. The enhanced power obtained in such a system reduces the frequency shift induced by noise, and choosing an appropriate position of the receiver further reduces the timing jitter converted from the frequency shift. Based on these results, we can obtain the reduction of the Gordon-Haus timing jitter in a dispersion compensated system, compared with a conventional soliton having equal pulse width and path-average dispersion.

Conditions for stationary pulse propagation in the strong dispersion management regime

Using the variational method, we obtain analytical conditions for stationary propagation of a Gaussian pulse in a fibre with strong dispersion management. We consider both the lossless fibre and the one with losses and periodic amplification. The analytical predictions have been checked against direct numerical simulations, and a good agreement between the two has been demonstrated. In particular, we find that in a certain region of parameters, the average dispersion necessary to support the stationary propagation is negative (normal). We also show that under a certain assumption, the variance of the Gordon-Haus timing jitter for the pulse in a strongly dispersion-managed system approximately equals that for the conventional soliton, reduced by an energy enhancement factor. Using our analytical conditions, we obtain an estimate for this factor. In particular, we show that in the presence of losses and periodic amplification, this jitter suppression factor can be made to be as large as that for the lossless case, by properly choosing the segment lengths in the dispersion map.

Impact of polarisation-mode dispersion in dispersion-managed soliton systems

Since enhanced power solitons are usually applied in dispersion-managed soliton systems, it might be expected that dispersion-managed solitons have a stronger resistance to polarisation-mode dispersion than conventional solitons. However, it is shown that dispersion-managed solitons behave similarly to conventional solitons in terms of resistance to polarisation-mode dispersion.

A multilevel soliton communication system

A multilevel soliton communication system is proposed and assessed. In this system, at the transmitter end each channel transmits its data via fundamental solitons with a pre-specified amplitude (i.e., soliton width). At the receiver end we take advantage of the sensitive relationship between the amount or fundamental soliton self-wavelength shift and the width of the soliton in the subpicosecond region. We first compress the incoming soliton noises to the subpicosecond level and pass them through a short length of fiber at the end of which the pulses have become separated in the wavelength domain since each soliton, corresponding to a data channel, has experienced a different Raman self-wavelength shift. The channels are then easily separated by optical filters. We have derived the design constraint relations for such a system. We have then heuristically designed a 40 Gbs (four channels) system for a 1000 km propagation distance (total data-rate distance product of 40 Tb/km). Numerical simulations and noise analyses have verified the feasibility and practicality of the proposed system with very good design margins. The wavelength jitter is found to be much smaller than the desired filter spacing, and thus its contribution to the bit error rate is negligible. We also argue that the system is more tolerant to Gordon-Haus timing jitter than conventional TDM soliton systems. The system is all fiber and is, therefore very cost effective as it does not require sophisticated electro-optic and microwave circuits for demultiplexing. The system can potentially operate at much higher speeds than those achievable in conventional soliton systems and it can be used in parallel with WDM soliton system.

Stable chirped black solitary waves in dispersive media with intensity-dependent gain and loss

We examine the stationary propagation of a black solitary wave in a fiber laser or in a fiber transmission system with periodically distributed amplifiers and saturable absorbers that is governed by the Ginzburg-Landau equation. An analytical solution of the chirped black solitary wave to the Ginzburg-Landau equation that includes the nonlinear saturation effect is obtained for what we believe to be the first time. The stability analyses reveal that the stationary propagation of the chirped black solitary wave can be stable when the saturation effect of nonlinear gain or loss is taken into account, whereas the chirped black solitary-wave solution of the Ginzburg-Landau equation that does not include the nonlinear saturation of gain or loss is found to be unstable. The criterion for the stable or unstable propagation of the chirped black solitary wave in the presence of the nonlinear gain or loss saturation is presented. Also, it is shown that two identical chirped black solitary waves launched in parallel will attract each other and may develop into a bound state of two parallel chirped black solitary waves. This is in contrast to the behavior of conventional black solitons of an unperturbed system, in which the two black solitons launched in parallel repel each other and distance themselves during propagation.

Periodically amplified system based on loss compensating dispersion decreasing fibre

We demonstrate for the first time to our knowledge the use of loss compensating, dispersion decreasing fibre (LCDDF) in a periodically amplified transmission system. The significant limiting effects of the soliton acoustic interaction and third order dispersion are observed and discussed. The results illustrate the potential of such techniques for extending data transmission to regimes forbidden by conventional average soliton dynamics.

Stationary soliton bound states existing in resonance with linear waves.

The phenomenon of stable propagation of spatially localized solitary waves, has been investigated for various dynamical systems. If a solitonlike pulse is in resonance with linear waves, then this pulse emits radiation and, therefore, it cannot exist as a stationary wave. Nevertheless, it is shown here that two (or more) radiating (and thus nonexisting as stationary waves) single solitonlike pulses can still form a stationary bound state due to mutual trapping of their own radiation. Trapped radiation forms a standing wave which, in turn, produces local minima in an effective interaction potential of the neighboring solitons. However, in contrast to conventional solitons, soliton bound states that are formed due to trapped radiation exist only for discrete values of soliton parameters, i.e., such bound states do not form continuous families of localized solutions, and they are inherently unstable. Two physically important systems for which stationary bound states of radiating solitons can be found are considered.