Decay Of Solitons Research Articles

Design optimisation for obtaining flat, high power supercontinuum source over C + L band

We propose an optimised fiber design for obtaining spectrally flat, high power supercontinuum (SC) source covering C+L band of optical communication. The design is based on the principle of controlled expansion of SC bandwidth, in the absence of soliton decay, so that a high output power along with smooth spectral profile can be achieved. A detailed optimisation has been carried out with respect to fiber dispersion profile, pulse width and fiber length, and the physical mechanism for each case has been emphasised. Numerical simulations show that single mode output with > 30 dBm (+/- 0.5 dB) optical power is attainable over 90-nm bandwidth with approximately 16 pJ of input pulse energy.

Propagation of matter-wave solitons in periodic and random nonlinear potentials

We study the motion of bright matter wave solitons in nonlinear potentials, produced by periodic or random spatial variations of the atomic scattering length. We obtain analytical results for the soliton motion, the radiation of matter wave, and the radiative soliton decay in such configurations of the Bose-Einstein condensate. The stable regimes of propagation are analyzed. The results are in remarkable agreement with the numerical simulations of the Gross-Pitaevskii equation with periodic or random spatial variations of the mean field interactions.

Oscillations of dark solitons in trapped Bose-Einstein condensates

We consider a one-dimensional defocusing Gross-Pitaevskii equation with a parabolic potential. Dark solitons oscillate near a center of the potential trap and their amplitude decays due to radiative losses (sound emission). We develop a systematic asymptotic multiscale expansion method in the limit when the potential trap is flat. The first-order approximation predicts a uniform frequency of oscillations for the dark soliton of arbitrary amplitude. The second-order approximation predicts the nonlinear growth rate of the oscillation amplitude, which results in decay of the dark soliton. The results are compared with previous publications and numerical computations.

On conservative and dissipative solitons in media with a periodic spatial modulation

A comparative theoretical analysis of properties of conservative and dissipative optical solitons in media with a periodic spatial modulation of optical characteristics is performed. It is shown that, in the case of modulation in the longitudinal (with respect to the axis of predominant propagation) direction, the mechanism of decay of conservative solitons because of the delocalization of their Fourier harmonics takes place, whereas, for dissipative solitons, this mechanism is absent. In the case of modulation in the transverse direction, the presence of discrete dissipative solitons in a set of optical fibers with nonlinear (saturable) amplification and absorption is shown, which, to a considerable extent, are similar to conservative discrete solitons.

Femtosecond second-order solitons in optical fiber transmission

A propagation of the femtosecond second-order solitons in an optical fiber is studied. We show that a generalized nonlinear Schrödinger equation well describes the propagation of the second-order soliton even containing only a few optical cycles. The propagations of a 50 fs and a 10 fs second-order soliton in an optical fiber are numerically simulated. It is found that, for the case of 10 fs second-order soliton, the soliton decay is dominated by the third-order dispersion, in contrast to the case of 50 fs second-order solitons, where the soliton decay is dominated by the delayed Raman response. It is also found that the exact delayed Raman response form must be used for the propagation of the 50 fs or less than 50 fs second-order soliton.

Optical pulse propagation in fibers with random dispersion

The propagation of optical pulses in two types of fibers with randomly varying dispersion is investigated. The first type refers to a uniform fiber dispersion superimposed by random modulations with a zero mean. The second type is the dispersion-managed fiber line with fluctuating parameters of the dispersion map. Application of the mean field method leads to the nonlinear Schrödinger equation (NLSE) with a dissipation term, expressed by a fourth-order derivative of the wave envelope. The prediction of the mean field approach regarding the decay rate of a soliton is compared with that of the perturbation theory based on the inverse scattering transform (IST). A good agreement between these two approaches is found. Possible ways of compensation of the radiative decay of solitons using the linear and nonlinear amplification are explored. The corresponding mean field equation coincides with the complex Swift–Hohenberg equation. The condition for the autosolitonic regime in propagation of optical pulses along a fiber line with fluctuating dispersion is derived and the existence of autosoliton (dissipative soliton) is confirmed by direct numerical simulation of the stochastic NLSE. The dynamics of solitons in optical communication systems with random dispersion-management is further studied applying the variational principle to the mean field NLSE, which results in a system of ODEs for soliton parameters. Extensive numerical simulations of the stochastic NLSE, mean field equation and corresponding set of ODEs are performed to verify the predictions of the developed theory.

Parametric Resonance and Radiative Decay of Dispersion-Managed Solitons

We study propagation of dispersion-managed solitons in optical fibers which are modeled by the nonlinear Schrodinger equation with a periodic dispersion coefficient. When the dispersion variations are weak compared to the average dispersion, we develop perturbation series expansions and construct asymptotic solutions at the first and second orders of approximation. Due to a parametric resonance between the dispersion map and the dispersion-managed soliton, the soliton generates continuous-wave radiation leading to its radiative decay. The nonlinear Fermi golden rule for radiative decay of dispersion-managed solitons is derived from the solvability condition for the perturbation series expansions. Analytical results are compared to direct numerical simulations, and good agreement is obtained.

Soliton Collisions and Ghost Particle Radiation

This paper investigates the nature of particle collisions for three-soliton solutions of the Korteweg-de Vries (KdV) equation by describing mathematically the interaction of soliton particles and generation of ghost particle radiation. In particular, it is proven that a collision between any two soliton particles results in an exchange of particle identities and an emission of a ghost particle pair. Moreover, collisions between any two ghost particles results in their fusion and is accompanied by fission of the corresponding anti-ghost particle. Mass and momentum are conserved for both soliton particle decay and ghost particle interaction at all times.

Transition radiation by matter-wave solitons in optical lattices.

We demonstrate that matter-wave solitary pulses formed from Bose condensed atoms moving inside optical lattices continuously radiate dispersive matter waves with prescribed momentum. Our analytical results for the radiation parameters and the soliton decay rate are found to be in excellent agreement with numerical modeling performed for experimentally relevant parameters.

Formation of a standing-light pulse through collision of gap solitons.

Results of a systematic theoretical study of collisions between moving solitons in a fiber grating are presented. Various outcomes of the collision are identified, the most interesting one being merger of the solitons into a single zero-velocity pulse, which suggests a way to create pulses of "standing light." The merger occurs with the solitons whose energy takes values between 0.15 and 0.35 of the limit value, while their velocity is limited by approximately 0.2 of the limit light velocity in the fiber. If the energy is larger, another noteworthy outcome is acceleration of the solitons as a result of the collision. In the case of mutual passage of the solitons, inelasticity of the collision is quantified by the energy-loss share. Past the soliton's stability limit, the collision results in strong deformation and subsequent destruction of the solitons. Simulations of multiple collisions of two solitons in a fiber-loop configuration are performed too. In this case, the maximum velocity admitting the merger increases to approximately 0.4 of the limit velocity. The influence of an attractive local defect on the collision is also studied, with the conclusion that the defect does not alter the overall picture, although it traps a small-amplitude pulse. Related effects in single-soliton dynamics are considered too, the most important one being the possibility of slowing down the soliton (reducing its velocity to the above-mentioned values that admit fusion of colliding solitons) by passing it through an apodized fiber grating, i.e., one with a gradually increasing Bragg reflectivity. Additionally, transformation of an input sech signal into a gap soliton (which is quantified by the share of lost energy), and the rate of decay of a quiescent gap soliton in a finite fiber grating, due to energy leakage through loose edges, are also studied.

Discrete solitons in inhomogeneous waveguide arrays.

The existence and dynamical properties of discrete solitons in inhomogeneous waveguide arrays with a Kerr nonlinearity are studied in two different configurations. First we investigate the effect of a longitudinal periodic modulation of the coupling strength on the dynamics of discrete solitons. It is shown that resonances of internal modes of the soliton with the longitudinal structure may lead to soliton oscillations and decay. Second we study the existence and stability of discrete solitons in arrays exhibiting a linear variation of the waveguide effective index in the transverse direction. We find that resonant coupling between conventional discrete solitons and linear Wannier-Stark states leads to the formation of so-called hybrid discrete solitons.

The Decay of Unstable Noncommutative Solitons

We study the classical decay of unstable scalar solitons in noncommutative field theory in 2+1 dimensions. This can, but does not have to, be viewed as a toy model for the decay of D-branes in string theory. In the limit that the noncommutativity parameter \theta is infinite, the gradient term is absent, there are no propagating modes and the soliton does not decay at all. If \theta is large, but finite, the rotationally symmetric decay channel can be described as a highly excited nonlinear oscillator weakly coupled to a continuum of linear modes. This system is closely akin to those studied in the context of discrete breathers. We here diagonalize the linear problem and compute the decay rate to first order using a version of Fermi's Golden Rule, leaving a more rigorous treatment for future work.

Shedding and interaction of solitons in weakly disordered optical fibers.

The propagation of the soliton pattern through optical fiber with weakly disordered dispersion coefficient is considered. Solitons perturbed by this disorder radiate and, as a consequence, decay. The average radiation profile is found. Emergence of a long-range intrachannel interaction between the solitons (mediated by this radiation) is reported. We show that soliton in a multisoliton pattern experiences a random jitter: intersoliton separation is zero mean Gaussian random field. Fluctuations of this separation are estimated by deltay approximately Dz(2)square root mu, where D measures the disorder strength, z is the propagation distance, and mu stands for the transmission rate (number of solitons per unit length of the fiber). Direct numerical simulations are used to validate theoretical predictions for single soliton decay and two-soliton interaction. Relevance of these results to fiber optics communication technology is discussed.

Wavelength conversion through higher-order soliton splitting initiated by localized channel perturbations

The decay of higher-order solitons in optical fiber, initiated by a step change in dispersion or by a localized loss element or filter, is explored theoretically as a means of generating pairs of pulses with wavelengths that are upshifted and downshifted from the input wavelength. One can tune the wavelengths by varying the magnitude of the perturbation. Pulse parameter requirements for achieving useful wavelength shifts while avoiding unwanted nonlinear effects are presented. Additionally, conditions are described under which the separated pulses can be recombined at a distant location to restore the higher-order soliton at the original wavelength.

Soliton dynamics in a random Toda chain

This paper addresses the soliton dynamics in a Toda lattice with a randomly distributed chain of masses. Applying the inverse scattering transform, we derive effective equations for the decay of the soliton amplitude that take into account radiative losses. It is shown that the soliton energy decays as approximately N(-3/2) for small-amplitude solitons and approximately exp(-N) for large-amplitude solitons. The decay rate does not depend on the incoming energy for large-amplitude soliton. An important feature is the generation of a soliton gas consisting of a large collection of small solitons (a number of the order of epsilon (-2) of solitons with momenta of the order of epsilon (2), where epsilon is the strength of fluctuations). The soliton gas plays an important role in that the changes in the conservation equations cannot be correctly understood if the soliton production is neglected. The role of the correlation length of fluctuations on the soliton decay is discussed. It is shown that in the presence of long-range correlation the Toda soliton is not backscattered, but progressively converted into forward-going radiation. The analytical predictions are confirmed by full numerical simulations.

Nonlinear propagation of a-few-optical-cycle pulses in a photonic crystal fiber-experimental and theoretical studies beyond the slowly varying-envelope approximation

The evolution of spectral and temporal profiles of 4.5 optical-cycle pulses propagating near zero-dispersion wavelength (ZDW) in a photonic crystal fiber is investigated experimentally and theoretically beyond the slowly varying-envelope approximation. The excellent agreement between the experimental an theoretical results suggests that the observed gap in the spectral profile, the most distinctive feature, originates from the self-steepening effect. This effect intensifies the spectral component shorter than the ZDW with the decay of higher order solitons and consequently induces the intrapulse four-wave mixing (FWM). As a result, the anti-Stokes and Stokes components produced by the FWM enables us to generate a supercontinuum from 480 to 1020 nm.

Hybrid discrete solitons.

The existence and stability of discrete solitons in waveguide arrays exhibiting a linear variation of the effective index and a Kerr nonlinearity is studied. We find that the resonant coupling of the conventional discrete soliton to a linear Wannier-Stark state does not entail soliton decay. We rather observe the formation of a bound state where the Wannier-Stark state gets nonlinearly modified. This results in an infinite number of isolated branches of hybrid discrete solitons.

Soliton decay in a coupled system of scalar fields

A system of coupled scalar fields is introduced which possesses a spectrum of massive single-soliton solutions. Some of these solutions are unstable and decay into lower mass stable solitons. Some properties of the solutions are obtained using general principles including conservations of energy and topological charges. Rest energies are calculated via a variational scheme, and the dynamics of the coupled fields are obtained by solving the field equations numerically.

Dynamics of dark solitons in elongated Bose-Einstein condensates.

We find two types of moving dark soliton textures in elongated condensates: nonstationary kinks and proper dark solitons. The latter have a flat notch region and we obtain the diagram of their dynamical stability. At finite temperatures the dynamically stable solitons decay due to the thermodynamic instability. We develop a theory of their dissipative dynamics and explain experimental data.

Two- and three-dimensional oscillons in nonlinear faraday resonance.

We study 2D and 3D localized oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton's phase, coupled to the driver, to its amplitude and width.