Dark Soliton Trains Research Articles

Wave Tunneling and Hysteresis in Nonlinear Junctions

We consider the nonlinear tunneling of a plane wave through a small barrier potential in a medium with self-defocusing, or repulsive, interactions. We show that nonlinearity can either suppress or enhance transmission rates, determined by whether the initial kinetic energy is above or below the barrier height. Associated with this threshold is the appearance of two distinct hysteresis loops, going clockwise or counterclockwise, respectively. Spatial dynamics upon reflection and transmission reveals the formation of dispersive shock waves (dark soliton trains) due to phase jumps at the interfaces and wave steepening during propagation. The results are demonstrated experimentally for optical wave tunneling through a refractive index defect but will hold for any Schrödinger system that contains a nonlinear junction.

Continuum generation by dark solitons

We demonstrate that the dark soliton trains in optical fibers with a zero of the group-velocity dispersion can generate broad spectral distribution (continuum) associated with the resonant dispersive radiation emitted by solitons. This radiation is either enhanced or suppressed by the Raman scattering depending on the sign of the third-order dispersion.

Magnetic hole formation from the perspective of inverse scattering theory

[1] The dynamics of oblique, weakly dispersive nonlinear Alfven waves in the presence of weak resistive damping are investigated numerically through an extension of the derivative nonlinear Schrodinger (DNLS) equation. It is observed numerically that the nonlinear dynamics are organized around the dynamics and allowed interactions of the underlying DNLS soliton families. There are three types of oblique Alfven solitons: the compressive two-parameter soliton and one-parameter bright soliton along with the rarefactive one-parameter dark soliton. The damping of either of these compressive solitons is accompanied by the formation of one or more dark solitons. The implication of these processes is that any initial wave profile containing solitons in its Inverse Scattering Transformation representation, in the presence of weak resistive damping, will result in a leading train of dark solitons. These dark solitons have been identified with magnetic holes, and the results described above are discussed in the context of magnetic hole observations and theory.

On some classes of two-dimensional local models in discrete two-dimensional monatomic FPU lattice with cubic and quartic potential

This paper discusses the two-dimensional discrete monatomic Fermi–Pasta–Ulam lattice, by using the method of multiple-scale and the quasi-discreteness approach. By taking into account the interaction between the atoms in the lattice and their nearest neighbours, it obtains some classes of two-dimensional local models as follows: two-dimensional bright and dark discrete soliton trains, two-dimensional bright and dark line discrete breathers, and two-dimensional bright and dark discrete breather.

Interaction between parabolic pulses in a dispersion-decreasing fiber

The properties of the self-similar parabolic pulses interaction in a dispersion-decreasing optical fiber with normal group-velocity dispersion are firstly investigated in our paper. We find that two parabolic pulses separated by a time-delay create oscillation with a sinusoidal fit at the beginning of their overlap, and then further evolve into a train of asymptotic dark solitons. Additionally, outside the overlap regime, the evolution is equal to a single pulse’ propagating behavior. The chirp after interaction in the parabolic pulses still allows for efficient and high-quality pulse compression.

Trains of envelope solitons in nonlinear left-handed transmission line media

We report the experimental observation of the self-generated stationary trains of envelope solitons in the left-handed nonlinear transmission line metamaterials. The trains of both bright or dark solitons, as well as switching between them, have been experimentally demonstrated in short transmission lines exhibiting strong and fast nonlinearity and strong anomalous dispersion, when pumped with a continuous wave signal.

Generation of dark solitons by interaction between similaritons in Raman fiber amplifiers

We present a new method to generate dark soliton trains by exploiting the interaction between two time-delayed optical similaritons with the same wavelength. The temporal overlap of two similariton pulses creates a sinusoidal beating which subsequently evolves into an ultrahigh repetition-rate train of dark solitons through the combined effects of normal dispersion, nonlinearity, and adiabatic Raman gain. The experimental results are in good agreement with numerical predictions. We also investigate how the the repetition rate of the dark soliton train depends on the time separation between the initial pulses, the initial pulse energy, and the Raman gain. Finally, we numerically study the interaction between three similaritons of the same wavelength.

GENERATION AND EVOLUTION OF DARK-SOLITON TRAINS IN ONE-DIMENSIONAL BOSE–EINSTEIN CONDENSATES

Generation and evolution of dark-soliton trains are studied. We focus on the dynamics resulting from large initial excitations in one-dimensional Bose–Einstein condensates trapped by a harmonic potential numerically. We consider three different techniques of controllable creation of multisolition structures (soliton trains). Multisoliton effects are discussed.

Management of matter waves in optical lattices by means of the Feshbach resonance

The mean-field dynamics of Bose-Einstein condensates loaded in an optical lattice, confined by a parabolic potential, and subjected to a change of scattering length by means of the Feshbach resonance is considered. The system is described by the Gross-Pitaevskii (GP) equation with varying nonlinearity, which in a number of cases is reduced to one-dimensional (1D) perturbed nonlinear Schr\"odinger (NLS) equations, the particular form of which depends on the relation among the parameters of the problem. We analytically describe the adiabatic dynamics of periodic solutions of the respective NLS equations, provide a numerical study of 1D models confined by a parabolic trap, and carry out numerical simulations of the matter-wave dynamics within the framework of the radially symmetric 3D GP equation. Special attention is paid to processes of generation of trains of bright and dark matter solitons from initially periodic waves. The results of the 1D approximation are compared with direct numerical simulation of the original 3D GP eqation, showing remarkable coincidence for definite regions of parameters.

Interaction between optical parabolic pulses in a Raman fiber amplifier

We investigate the interaction between optical parabolic pulses in a Raman fiber amplifier. Self-similar amplification of two identical time-delayed pulses creates an oscillation which further evolves into a train of dark solitons through the combined effects of non-linearity, normal dispersion and adiabatic Raman gain. Theoretical predictions are in good agreement with experimental results.

Generation of Dark and Bright Spin Wave Envelope Soliton Trains through Self-Modulational Instability in Magnetic Films

The generation of dark spin wave envelope soliton trains from a continuous wave input signal due to spontaneous modulational instability has been observed for the first time. The dark soliton trains were formed from high dispersion dipole-exchange spin waves propagated in a thin yttrium iron garnet film with pinned surface spins at frequencies situated near the dipole gaps in the dipole-exchange spin wave spectrum. Dark and bright soliton trains were generated for one and the same film through placement of the input carrier frequency in regions of negative and positive dispersion, respectively. Two unreported effects in soliton dynamics, hysteresis and period doubling, were also observed.

Dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms

We consider formation of dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms. It is shown that big enough initial inhomogeneity of density leads to wave breaking phenomenon followed by generation of a train of dark solitons. Analytical theory is confirmed by numerical simulations.

Creation and evolution of trains of dark solitons in a trapped one-dimensional Bose-Einstein condensate

The generation of dark solitons from large initial excitations and their evolution in a one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. We consider three different techniques of controllable creation of multisoliton structures (soliton trains) from large initial excitations and calculate their initial parameters (depths and velocities) with the use of a generalized Bohr-Sommerfeld quantization rule. Multisoliton effects are discussed.

Modulational Instability and Stimulated Raman Scattering in Normally Dispersive Highly Birefringent Fibers

The nonlinear interaction of two laser beams in normally dispersive highly birefringent optical fibers leads to a large set of fascinating physical effects such as modulational instability (MI) and stimulated Raman scattering (SRS). These two nonlinear phenomena have a positive role as a mechanism for the generation of short optical pulses and represent a drawback in fiber-optics transmissions. Indeed, we will show that an induced process of modulational instability may be exploited for the generation of THz train of vector dark solitons. The technique of frequency-resolved optical gating is used to completely characterize the intensity and phase of the dark soliton trains. On the other hand, we shall discuss control processes for MI and SRS in birefringent optical fibers. In particular, we analyze experiments showing that with dual-frequency, orthogonal polarization pumping one may achieve the simultaneous suppression of modulational instability and substantial reduction of stimulated Raman scattering.

Generation of bright and dark soliton trains from continuous-wave light using cross-phase modulation in a nonlinear-optical loop mirror

A simple technique for the simultaneous generation of bright and dark soliton trains from continuous-wave (CW) light is proposed and demonstrated theoretically. It is based on the optical switching characteristics of a nonlinear-optical loop mirror (NOLM) through which the CW signal is switched by a pump pulse train at another wavelength by the creation of cross-phase modulation-induced phase bias between the counter-propagating CW components. The transmitted and reflected signals exiting from the NOLM can then evolve, respectively, into bright and dark soliton trains in fibers with the appropriate group-velocity dispersion at the signal wavelength. Numerical simulations indicate that the generated solitons can be narrower than the pump pulses and that the scheme permits the conversion of nearly all of the CW energy into the soliton train energy without generating pulse pedestals.

Complete characterization of terahertz pulse trains generated from nonlinear processes in optical fibers

The measurement technique of frequency-resolved optical gating (FROG) is used to characterize the intensity and phase of terahertz pulse trains generated from nonlinear and dispersive interactions in optical fibers. We show that existing FROG retrieval algorithms are easily adapted to allow the retrieval of periodic pulse characteristics and, using synthetic pulse trains generated from numerical simulations, we demonstrate how FROG can differentiate between periodic pulse trains with fundamentally different intensity and phase characteristics, yet qualitatively similar autocorrelation functions and spectra. Experimental results are presented for the FROG characterization of a 0.3-THz sinusoidal beat signal from a dual wavelength laser source, a 2.5-THz train of dark solitons generated in a high-birefringence fiber, and a 0.6-THz bright polarization domain wall soliton train generated in an ultra-low birefringence fiber. These results are shown to be in good agreement with nonlinear Schrodinger equation simulations.

Stationary solutions of the one-dimensional nonlinear Schrödinger equation. I. Case of repulsive nonlinearity

All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the attractive case. Our solutions take the form of stationary trains of dark or grey density-notch solitons. Real stationary states are in one-to-one correspondence with those of the linear Schr\"odinger equation. Complex stationary states are uniquely nonlinear, nodeless, and symmetry-breaking. Our solutions apply to many physical contexts, including the Bose-Einstein condensate and optical pulses in fibers.

Complete intensity and phase characterisation ofoptical pulse trains at terahertz repetition rates

Complete intensity and phase characterisation of optical pulse trains at terahertz repetition rates is carried out using an adapted frequency-resolved optical gating technique. The experimental characterisation of a 2.5 THz train of dark solitons in an optical fibre is in good agreement with numerical simulations.

Generation of vector dark-soliton trains by induced modulational instability in a highly birefringent fiber

We present a set of experimental observations that demonstrate the generation of vector trains of dark-soliton pulses in the orthogonal axes of a highly birefringent optical fiber. We generated dark-soliton trains with terahertz repetition rate in the normal group-velocity dispersion regime by inducing a polarization modulational instability by mixing two intense, orthogonal continuous laser beams. Numerical solutions of the propagation equations were used to optimize the emission of vector dark pulses at the fiber output.

Buildup of terahertz vector dark-soliton trains from induced modulation instability in highly birefringent optical fiber

We present the experimental observation of generation of vector dark-soliton pulse trains with terahertz repetition rates in the normal dispersion regime of an optical fiber. The polarization solitons build up from induced cross-phase modulation instability of two orthogonal pumps in a highly birefringent fiber.