Generation Of Dark Solitons Research Articles

Optical realization of Newton-cotes-based integrators for dark soliton generation

An optical integrator is an analog optical signal processor that performs the time integral of an input optical signal. This paper presents a theory of Newton-Cotes optical integrators for high-speed optical signal processing. The Newton-Cotes optical integrators are designed using the cascade of a finite impulse response (FIR) optical waveguide filter with an infinite impulse response (IIR) optical waveguide filter. To demonstrate the effectiveness of the proposed optical integrators, the authors show, by means of computer simulations, that a trapezoidal optical integrator can generate a fundamental dark-soliton pulse that can propagate stably over a large distance of single-mode optical fiber. Although the analysis is directed at optical integrators implemented using waveguide technology, the theory, design method, and results are applicable to other physical systems such as optical systems based on free-space optics, fiber optics, and fiber gratings.

Transmission of digital images consisting of white-light dark solitons

A distortion-free digital image is transmitted through parallel propagation of white-light photovoltaic dark solitons. The waveguide channels induced by white-light dark solitons can guide both the laser beam and the white-light beam well. We determine experimentally the critical separations of the dark solitons in the directions parallel and perpendicular to the crystalline c axis for the given crystal thickness.

Dynamics of Spatial Dark Solitons Trapped in the Media withGain and TPA

The propagation of dark solitons in nonlinear media that include gainand loss described by a nonlinear Schrödinger equation isinvestigated. Based on the direct approach of perturbation theory,the width, height and other related quantities of dark solitonsare obtained. It is shown that stationary propagationof dark solitons is found to be possible in the presence of bothgain and absorption. The results obtained by means of our analyticmethod are in excellent agreement with numerical simulations. Ourresults are helpful for the research into the optical solitontransmission system.

Dark soliton propagation in a dispersion-managed system with periodically inhomogeneous perturbations

Periodically inhomogeneous perturbations are considered in a dispersion-managed dark soliton system, and their effects on the dark soliton propagation and interaction are investigated. The perturbations lead to the soliton submergence, and enhance the soliton interaction. The distances of the soliton submergence and interaction relate to the period length, the strength of every perturbation, and the pulse width. There are the worst period length and the resonance between the two perturbations in the system. Finally, the avoidance and the control of the effects are introduced.

Evolution of Dark Spatial Soliton in Quasi-phase-matched Quadratic Media

We theoretically investigate the evolvement of dark spatial soliton withcascading quadratic nonlinearity in quasi-phase-matched second harmonicgeneration. It is shown that the dark solitary wave can propagate stablywhen background intensity is large enough, in which diffraction of beam canbe balanced by the cascading quadratic nonlinearity. We also analyze theinfluence of phase-mismatch on the stability of dark soliton propagation.

Generation of spin-wave dark solitons with phase engineering

We generate experimentally spin-wave envelope dark solitons from rectangular high-frequency dark input pulses with externally introduced phase shifts in yttrium-iron garnet magnetic fims. We observe the generation of both odd and even numbers of magnetic dark solitons when the external phase shift varies. The experimental results are in a good qualitative agreement with the theory of the dark-soliton generation in magnetic films developed earlier [Phys. Rev. Lett. 82, 2583 (1999)].

Generation of dark solitons in oscillating Bose–Einstein condensates

We propose an experimentally tractable setting for observing an “instability” of a repulsive oscillating Bose–Einstein condensate that leads to the generation of dark solitons. We illustrate that when the trap of the condensate (which incorporates a localized impurity) is displaced so that the condensate flow is characterized by an atomic velocity larger than the local speed of sound, dark solitons are generated. The subcritical, near critical and supercritical are analyzed in detail.

Magnetostatic spin solitons in ferromagnetic nanotubes

We study the linear and nonlinear evolution of a magnetostatic spin wave (MSW) in a charge free, isotropic ferromagnetic hollow nanotube. By analyzing the dispersion relation we observe that elliptically polarized forms of wave can propagate through the ferromagnetic nanotube. Using the multiple scale analysis we find that the dynamics of magnetization of the medium is governed by the cubic nonlinear Schr\"odinger equation. The stability of the continuous wave, related to the propagation of either bright or dark (MS) solitons in the nanotube, is governed by the direction of the external magnetic field relative to the magnetized nanotube.

Effects of correlated perturbations on dark soliton propagation and interaction

Correlated perturbations are considered in a dark soliton system and their effects on soliton propagation and interaction are investigated numerically. These perturbations result in large sidebands, lead to submergence of dark soliton and enhance the interaction. The correlation amplifies these effects and shortens the distance until submergence. The comparison of the distinction is made between the degradations of these effects on dark soliton and the corresponding bright soliton. It is found that these effects on dark soliton are less than those on bright soliton. Finally the nonlinear gain is introduced to suppress efficiently these effects.

Dark spatial solitons in bulk azo-dye-doped polymer using photoinduced molecular reorientation

We report the generation of dark spatial solitons in bulk Disperse Red 1 doped poly(methyl methacrylate) using photoinduced reorientation of azo-dye molecules. Planar solitions are formed when illuminated with a continuous-wave laser at intensities of the order of hundreds of miliwatts per square centimeter. The width of the soliton saturates to a minimum value at high intensity; and when the width of the initial dark notch is reduced, the equilibrium minimum width is unchanged.

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.

Dynamic quantum depletion in phase-imprinted generation of dark solitons

We investigate the quantum fluctuations associated with dark-soliton generation in Bose-Einstein condensates. With the phase imprinting procedure treated as a part of the dynamical process, we present numerical solutions of time-dependent quantum depletion. Our results provide evidence of a rapid growth of noncondensate atoms at dark-soliton notches without making assumptions of final quasiparticle states.

Adiabatic dynamics of periodic waves in Bose-Einstein condensates with time dependent atomic scattering length.

Evolution of periodic matter waves in one-dimensional Bose-Einstein condensates with time-dependent scattering length is described. It is shown that variation of the effective nonlinearity is a powerful tool for controlled generation of bright and dark solitons starting with periodic waves.

Generation and interaction of solitons in Bose-Einstein condensates

Generation, interaction, and detection of dark solitons in Bose-Einstein condensates are studied. In particular, we focus on the dynamics resulting from phase imprinting and density engineering. We show that solitons slow down significantly when the trap is opened and that soliton phase shifts after binary interactions cannot be observed with present experiments. Finally, motivated by the recent experimental results of Cornish et al. [Phys. Rev Lett. 85, 1795 (2000)], we analyze the stability of dark solitons under changes of the scattering length and thereby demonstrate a new way to detect them. Our theoretical and numerical results compare well with the existing experimental ones and provide guidance for future experiments.

Propagation of dark solitons in a system of coupled higher-order nonlinear Schrödinger equations

In this paper, we consider the higher-order linear and nonlinear effects in optics and analyse a coupled system of higher-order nonlinear Schrodinger equations to identify the conditions for dark-soliton propagation through Painleve analysis, to supplement the known bright-soliton conditions. We also construct the explicit Lax pair and the Hirota bilinear form is used to generate one and two dark solitons.

Control of interactions between two dark solitons propagating in optical fiber exhibiting randomly varying birefringence

AbstractIn fiber with randomly varying birefringence, the interactions between dark solitons in the same polarization channel and in two orthogonal polarization channels are investigated by the use of numerical simulations. The results obtained show that the interaction between dark solitons in the same polarization channel is weak, whereas in the two orthogonal polarization channels it is strong and leads to the soliton splitting and soliton propagation instability. The randomly varying birefringence enhances the interaction between dark solitons in two orthogonal polarization channels. A nonlinear gain can be used to suppress the interactions and stabilize dark soliton propagation. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 49–52, 2002; DOI 10.1002/mop.10228

Dark soliton generation for the intermediate nonlinear Schrödinger equation

The generation of dark solitons due to a small change of the initial data is studied within the framework of the intermediate nonlinear Schrödinger (INLS) equation. In particular, we analyze the spectral problem associated with the INLS equation when the potential consists of a small perturbation imposed on a constant background. We derive a criterion for the perturbation to generate a pair of new discrete eigenvalues as well as their explicit expressions in terms of the perturbation. In addition, we demonstrate that the eigenvalues appear without a threshold on the magnitude of the perturbation. We also consider both the shallow- and deep-water limits of various results obtained for the INLS spectral problem. In the former case, the limiting procedure can be performed smoothly whereas in the latter case, the spectral equation exhibits a new feature of bound states, showing that the eigenvalue is exponentially small compared with the magnitude of the perturbation.

Controlled generation of dark solitons with phase imprinting.

The generation of dark solitons in Bose-Einstein condensates with phase imprinting is studied by mapping it into the classic problem of a damped driven pendulum. We provide a simple but powerful scheme, designing the phase imprint for various desired outcomes of soliton generation. For a given phase step, we derive a formula for the number of dark solitons traveling in each direction, and examine the physics behind the generation of counterpropagating dark solitons.

Propagation of dark solitons with higher-order effects in optical fibers.

In this paper, we analyze dark soliton propagation in nonlinear optical fibers with higher-order effects such as third order dispersion, self-steepening, and stimulated Raman scattering. We consider the Hirota equation and the higher-order nonlinear Schrödinger equation, and identify conditions for dark soliton propagation through Painlevé analysis. We also construct an explicit Lax pair, and Hirota bilinear form is used to generate one and two dark solitons.

Stable propagation of dark solitons in dispersionmapsof either sign of path-average dispersion

In fibres with alternating dispersion, dark solitons are shown to propagate stably as far as can be told from numerical simulation. This holds even in the case of a dispersion map with average anomalous dispersion, i.e. in the regime which for homogeneous fibres is the 'forbidden' regime for dark solitons. We have shown that the pulse shape is characteristically modified in the dispersion-managed fibre, and we see indications of a modified soliton power. These results demonstrate an appealing symmetry with earlier corresponding finding that bright solitons are modified in shape and power, and can extend their existence into their 'forbidden' regime.