Vector solitons in the dynamics of anharmonic monatomic lattices

It is shown that three types of solitary acoustic waves can develop in anharmonic crystal lattices corresponding to the three branches of acoustic phonons. A system of three nonlinear Schrödinger equations is derived to describe this situation. For greatly different group velocities, the interaction between solitons reduces collisions between them. When the group velocities of the different acoustic modes in a lattice are close to one another, bound states of the corresponding types of solitary waves occur. Bound states of this sort are vector solitons, whose polarization varies along the pulse. If the transverse acoustic modes are degenerate in velocity, the situation is extremely similar to the propagation of pulses in optical fibers.     

Soliton generation via continuous stokes acoustic self-scattering of hypersonic waves in a paramagnetic crystal

A new mechanism is proposed for continuous frequency down-conversion of acoustic waves propagating in a paramagnetic crystal at a low temperature in an applied magnetic field. A transverse hypersonic pulse generating a carrier-free longitudinal strain pulse via nonlinear effects is scattered by the generated pulse. This leads to a Stokes shift in the transverse hypersonic wave proportional to its intensity, and both pulses continue to propagate in the form of a mode-locked soliton. As the transverse-pulse frequency is Stokes shifted, its spectrum becomes narrower. This process can be effectively implemented only if the linear group velocity of the transverse hypersonic pulse equals the phase velocity of the longitudinal strain wave. These velocities are renormalized by spin-phonon coupling and can be made equal by adjusting the magnitude of the applied magnetic field. The transverse structure of the soliton depends on the sign of the group velocity dispersion of the transverse component. When the dispersion is positive, planar solitons can develop whose transverse component has a topological defect of dark vortex type and longitudinal component has a hole. In the opposite case, the formation of two-component acoustic “bullets” or vortices localized in all directions is possible.     

Generation of phase nuclei by solitons of the new “undulator” type in martensitic phase transitions of crystalline materials

The microdynamics of large-amplitude nonlinear lattice vibrations of plutonium and uranium materials has been investigated at high reactor temperatures in the ranges of martensitic phase transitions. Topologically new large-amplitude solitons of the “undulator” type have been revealed. Transverse and longitudinal “undulator” solitons in crystals with hexagonal and cubic symmetry, depending on the direction of motion, have different kinematic and amplitude characteristics, which differ from the characteristics of the previously known solitons. The transverse “undulator” solitons, like electrons in undulators, are observed with periodic atomic displacements orthogonal to the direction of soliton propagation. The longitudinal “undulator” solitons with displacements of atoms in the direction of soliton propagation are characterized by periodic delays with two-step velocities on the trajectory in a certain analogy with two-period engineering undulator devices. It has been shown that, at high energies, such “undulator” solitons of two types generate nuclei of a new phase in early stages of structural phase transitions.     

Molecular dynamics investigation of soliton propagation in a two-dimensional Yukawa liquid

We investigate via molecular dynamics simulations the propagation of solitons in a two-dimensional many-body system characterized by Yukawa interaction potential. The solitons are created in an equilibrated system by the application of electric field pulses. Such pulses generate pairs of solitons, which are characterized by a positive and negative density peak, respectively, and which propagate into opposite directions. At small perturbation, the features propagate with the longitudinal sound speed, from which an increasing deviation is found at higher density perturbations. An external magnetic field is found to block the propagation of the solitons, which can, however, be released upon the termination of the magnetic field and can propagate further into directions that depend on the time of trapping and the magnetic field strength.     

Two types of ground-state bright solitons in a coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate

We study two types of bright solitons in an attractive Bose-Einstein condensate with a spin-orbit interaction. By solving the coupled nonlinear Schr odinger equations with the variational method and the imaginary time evolution method,fundamental properties of solitons are carefully investigated in different parameter regimes. It is shown that the detuning between the Raman beam and energy states of the atoms dominates the ground state type and spin polarization strength.The soliton dynamics is also studied for various moving velocities for zero and nonzero detuning cases. We find that the shape of individual component solitons can be maintained when the moving speed of solitons is low and the detuning is small in the coupled harmonically trapped pseudo-spin polarization Bose-Einstein condensate.     

Quasi-solitonic propagation modes of two-component acoustic video pulses in a paramagnetic crystal

Nonlinear propagation of longitudinal-transverse acoustic pulses down to a length of one cycle (video pulses) in a low-temperature paramagnetic crystal in the direction parallel to an external magnetic field is investigated theoretically. The case of a crystal with paramagnetic impurity ions with effective S=1/2 spin is considered. It is shown that, due to spin-phonon interaction, two-component acoustic pulses can propagate in the form of high-power quasi-solitons. Conditions are determined for the formation of exponentially localized subsonic rational solitons which propagate with a velocity higher than the velocity of transverse sound and which have a transverse component with a rotating plane of polarization.     

T(2) selectivity: comparison between different kinds of RF pulses

Techniques allowing characterization of specific T(2) species are used to perform MR imaging of structures whose signal intensity is poor on conventional methodologies. T(2)-selective pulses can be used to discriminate signals from tissues with different T(2) values. In case of soliton pulses, the magnetization from all the T(2) species is inverted, with the exception of specific T(2) structures which have both the longitudinal and the transverse magnetization nulled on resonance. Solitons have the drawback of being very long even if the selected T(2) value is in the order of tens of milliseconds. The aim of this paper is to examine whether it is possible to use pulses shorter then solitons keeping their T(2) selectivity, that is keeping null longitudinal magnetization, while accepting some residual transverse magnetization for structures with the selected T(2). Different kinds of inversion pulses were generated, all to select the same T(2) species. Pulses performance was analyzed by studying the dependence of the residual transverse magnetization on resonance from the length of the pulse. An exponential relationship between transverse magnetization and pulse length was found, which was not dependent on the pulse type.     

Diffraction effects on soliton propagation

An averaged-Lagrangian method is used to analyze diffraction effects on propagation of solitons of various types in homogeneous media. It is shown that diffraction can counteract the self-focusing of dark and gray envelope solitons described by the nonlinear Schrödinger equation and solitons described by the Korteweg-de Vries equation when the soliton intensities do not exceed certain values. Conversely, diffraction enhances the self-focusing of dark and gray envelope solitons described by the modified Korteweg-de Vries equation, kinks described by the sine-Gordon equation, and domain walls in the u 4 model, which is explained by mutual correlation between transverse and longitudinal soliton dynamics. Critical parameters that determine soliton stability with respect to self-focusing are found for several models.     

Dispersion and nonlinear management for femtosecond optical solitons

We consider the concept of femtosecond propagation for optical solitons in a dispersion management fiber and study the optimal amplification of optical solitons through dispersion wells and barriers and also for the dispersion tailored profile case. For the former, we observed periodic soliton trapping for the in-phase injection case when their respective velocities were equal and opposite with their amplitudes being unequal and no soliton trapping for the off-phase injection case when the two pulses are having a phase difference of π. For the latter, we observed an enormous amplification of the soliton pulses which is one of our main results in this Letter.     

Ion-focused propagation of a relativistic electron beam in the self-generated plasma in atmosphere

It is known that ion-focused regime (IFR) can effectively suppress expansion of a relativistic electron beam (REB). Using the particle-in-cell Monte Carlo collision (PIC-MCC) method, we numerically investigate the propagation of an REB in neutral gas. The results demonstrate that the beam body is charge neutralization and a stable IFR can be established. As a result, the beam transverse dimensions and longitudinal velocities keep close to the initial parameters. We also calculate the charge and current neutralization factors of the REB. Combined with envelope equations, we obtain the variations of beam envelopes, which agree well with the PIC simulations. However, both the energy loss and instabilities of the REB may lead to a low transport efficiency during long-range propagation. It is proved that decreasing the initial pulse length of the REB can avoid the influence of electron avalanche. Using parts of REB pulses to build a long-distance IFR in advance can improve the beam quality of subsequent pulses. Further, a long-distance IFR may contribute to the implementation of long-range propagation of the REB in space environment.     

Nonlinear focusing of picosecond baseband pulses in paraelectric crystals

The nonlinear baseband electromagnetic pulses of a wide spectrum that lies in terahertz (THz) range are investigated theoretically in the paraelectric crystals like SrTiO₃ at the temperatures ~ 77 K. The frequency dispersion is important in THz range there. The dominating nonlinearity of the crystal is cubic. The frequency dispersion and nonlinearity correspond to existence of envelope solitons and the modulation instability of long input envelope pulses, whereas in the transverse direction the modulation instability is absent. When the nonlinear wave is uniform in the transverse direction, the existence of soliton-like baseband pulses without a carrier frequency has been demonstrated. There exists a possibility to generate the regular sequences of short baseband pulses due to the nonlinearity in the paraelectric crystals. The nonlinear focusing of input long baseband pulses by the exciting antenna results in the formation of extremely short baseband pulses localized both in the longitudinal and transverse directions.     

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.     

Bilinear Forms and Dark-Dark Solitons for the Coupled Cubic-Quintic Nonlinear SchrÕdinger Equations with Variable Coefficients in a Twin-Core Optical Fiber or Non-Kerr Medium*

Twin-core optical fibers are applied in such fields as the optical sensing and optical communication,and propagation of the pulses,Gauss beams and laser beams in the non-Kerr media is reported.Studied in this paper are the coupled cubic-quintic nonlinear Schrodinger equations with variable coefficients,which describe the effects of quintic nonlinearity for the ultrashort optical pulse propagation in a twin-core optical fiber or non-Kerr medium.Based on the integrable conditions,bilinear forms are derived,and dark-dark soliton solutions can be constructed in terms of the Gramian via the Kadomtsev-Petviashvili hierarchy reduction.Propagation and interaction of the dark-dark solitons are presented and discussed through the graphic analysis.With different values of the delayed nonlinear response effect b(z),where z represents direction of the propagation,the linear-and parabolic-shaped one dark-dark soltions can be derived.Interactions between the parabolic-and periodic-shaped two dark-dark solitons are presented with b(z) as the linear and periodic functions,respectively.Directions of velocities of the two dark-dark solitons vary with z and the amplitudes of the solitons remain unchanged can be observed.Interactions between the two dark-dark solitons of different types are displayed,and we observe that the velocity of one soliton is zero and direction of the velocity of the other soliton vary with z.We find that those interactions are elastic.     

Thirring combo-solitons with cubic nonlinearity and spatio-temporal dispersion

Abstract

The vector-coupled nonlinear Schrödinger equation, which can be applied to describe the propagation of Thirring optical solitons in birefringent ?bers with Kerr law nonlinearity, detuning, intermodal dispersion and spatiotemporal dispersion, has been studied analytically. By means of the complex envelope function ansatz, exact Thirring bright-dark combosolitons are reported, and the properties of these solitons are discussed.     

Parametric wave interaction in media exhibiting quadratic and cubic nonlinearities under high-frequency pumping conditions

Specific features of parametric interaction in media exhibiting quadratic and cubic nonlinearities under conditions of high-frequency pumping and nonzero detuning from the phase matching are analyzed. It is shown that the presence of two types of nonlinearities and frequency detuning broaden the possibilities of controlling the dynamics of the forming partial pulses by changing the pump power. The possibility of the signal and idler waves’ decay into four frequency-modulated partial wave packets with different values of chirp and velocities of their envelope maximum is established. The envelope maximum velocities of the partial pulses, as well as their walk-off velocities, can reach values exceeding the speed of light in vacuum.     

Stability of weakly nonparaxial spatial optical solitons in a medium with a Kerr nonlinearity

A variant of perturbation theory is developed to determine the characteristics and stability of transversely two-dimensional spatial solitons in a Kerr medium under conditions of small deviations from paraxial. Distributions of the transverse and longitudinal components of the soliton electric and magnetic fields are obtained. It is shown that the power of a nonparaxial soliton in a Kerr medium increases as the propagation constant increases. A linear analysis is made of soliton stability. In addition to confirming stability, this analysis revealed “internal modes” of nonparaxial solitons and their characteristics were determined.     

Slow-light optical bullets in arrays of nonlinear Bragg-grating waveguides

We demonstrate that propagation direction and velocity of optical pulses can be controlled independently in the structures with multiscale modulation of the refractive index in transverse and longitudinal directions. We reveal that, in arrays of waveguides with phase-shifted Bragg gratings, the refraction angle does not depend on the speed of light, allowing for efficient spatial steering of slow light. In this system, both spatial diffraction and temporal dispersion can be designed independently, and we identify the possibility for self-collimation of slow light when spatial diffraction is suppressed for certain propagation directions. We also show that broadening of pulses in space and time can be eliminated in nonlinear media, supporting the formation of slow-light optical bullets that remain localized irrespective of propagation direction.     

超短激光脉冲在等离子体中的分裂以及类孤子结构的形成

用一维粒子模拟研究了超短脉冲在等离子体中传播时产生的光孤子结构以及由此形成的脉冲分裂现象，比较了不同峰值强度和脉冲宽度对形成光孤子以及脉冲传播方式的影响.研究表明: 脉冲宽度在若干个到十几个振荡周期的超短脉冲在等离子体中可能形成高速传播的光孤子；脉冲宽度增加和强度增大两种方式都可以使得孤子结构的传播速度减慢,且由于高阶孤子的衰变使得初始激光脉冲在等离子体中发生分裂，形成两个以不同速度向前传播的孤子结构.由孤子阶数的理论计算可较好地预言激光脉冲在等离子体中分裂的子脉冲数. 关键词： 光孤子 超短激光脉冲 等离子体 粒子模拟     

On the propagation of hypersonic solitons in a strained paramagnetic crystal

Nonlinear dynamics of a subnanosecond transverse elastic pulse in a low-temperature paramagnetic crystal placed into a magnetic field and statically strained in the same direction is investigated. Paramagnetic impurities implanted into the crystal have an effective spin of 3/2, and the pulse propagates at right angles to the magnetic field. In the general case, the structure of the pulse is such that the approximation of slowly varying envelopes, which is standard for quasi-monochromatic signals, is inapplicable. Under certain conditions, the pulse propagation in the 1D case is described by the Konno-Kameyama-Sanuki integrable wave equation for strain, which is transformed into the Hirota equation for the envelope of the given strain in the quasi-monochromatic limit. The effect of transverse perturbations on extremely short and quasi-monochromatic solitons is studied in detail. The conditions and features of self-focusing and defocusing of acoustic solitons in the form of extremely short pulses and envelope solitons are revealed. The propagation of an extremely short “half-wave” hypersonic pulse in the “acoustic bullet” regime in the medium with a quasiequilibrium population of quantum sublevels of effective spins is predicted.