This paper presents experimental evidence that orthogonally crossed dark soliton stripes form quasi-two-dimensional spatial
solitons with a soliton constant equal to that of singly charged optical vortices. Besides the pairs of oppositely charged
optical vortex solitons, the snake instability of the dark formation at moderate saturation is found to lead to generation
of steering mixed edge–screw phase dislocations with zero total topological charges.
Received: 26 October 1998 / Revised version: 19 January 1999 / Published online: 12 May 1999 相似文献
The principal of passively mode-locked fiber soliton ring lasers is summarized, including its three output operation states: normal soliton, bound–solitons and noise-like pulse. The experimental results of the passively mode-locked fiber soliton ring lasers developed by us are given. Bound–solitons with different discrete separations and three-bound–solitons state have been observed in our fiber laser for the first time. The relationship among three operation states in fiber soliton laser is analyzed. 相似文献
We report on the experimental observation of passive harmonic mode locking of bunches of single-pulse solitons or twin-pulse
solitons in an Erbium-doped fiber ring laser. Experimental investigations on the phenomenon revealed that, although the soliton
interaction between the adjacent single-/twin-pulse solitons in a bunch is weaker than that of the pulse interaction in the
twin-pulse solitons, a soliton bunch could also function as a unit and form the state of passively harmonic mode-locking.
Harmonic mode-locking is one of the intrinsic characteristics of soliton emission in passively mode-locked fiber ring lasers.
It can be formed based on the single-pulse soliton, twin-pulse soliton, or bunch of solitons. 相似文献
We analyze the effects of additional terms in the nonlinear Schr?dinger equation for spatial solitons, directly derived from the Maxwell's equations with the Kerr nonlinearity, on the shapes of bright and dark solitons with a fixed polarization. Combining analytical and numerical methods, we find that the additional terms always render the solitons broader. The most essential result is a fundamental limitation on the width of the subwavelength soliton: The ratio of the FWHM of the bright soliton to the wavelength cannot be smaller than 1/2, and the same ratio for the FWHM of the dark soliton cannot be smaller than 1/4. 相似文献
We present experimental results on one-dimensional (1-D) spatial solitons in AlGaAs waveguides. Three distinct types of spatial solitons have been observed: namely the fundamental soliton, the Manakov soliton, and the vector soliton. The fundamental soliton is the simplest form of 1-D soliton which consists of a single polarization. The properties of waveguiding and ‘robustness’ are experimentally studied. Vector solitons which result from the complex interplay between the two orthogonally polarized beams due to self-phase modulation, cross-phase modulation, and four-wave mixing effects are studied. The complex beam dynamics and polarization behaviour of the vector solitons are experimentally studied. Manakov solitons which are a special case of the vector soliton exist when the ratio between the self-to-cross-phase modulation is one and the four-wave mixing effects becomes zero are demonstrated experimentally and the basic properties discussed. Finally, some soliton interactions such as trapping and dragging are reported and possible applications of soliton interactions are discussed. 相似文献
A relativistic electromagnetic soliton solution in the model of a one-dimensional, unbounded, cold, collisionless plasma is
obtained without using the envelope approximation. The breaking of solitons with over-critical amplitudes is observed. The
stability of undercritical solitons and the breaking of overcritical solitons are demonstrated by a particle-in-cell computer
simulation.
Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 33–38 (10 July 1998)
Published in English in the original Russian journal. Edited by Steve Torstveit. 相似文献
For the propagation of the ultrashort pulses in an inhomogeneousmulti-component nonlinear medium, a system of coupled equations isanalytically studied in this paper. Painlevé analysis shows thatthis system admits the Painlevé property under some constraints.By means of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pairof this system is derived, and the Darboux transformation (DT) isconstructed with the help of the obtained Lax pair. With symboliccomputation, the soliton solutions are obtained by virtue of the DTalgorithm. Figures are plotted to illustrate the dynamical featuresof the soliton solutions. Characteristics of the solitonspropagating in an inhomogeneous multi-component nonlinear medium arediscussed: (i) Propagation of one soliton and two-peak soliton; (ii) Elastic interactions of the parabolic two solitons; (iii) Overlapphenomenon between two solitons; (iv) Collision of two head-onsolitons and two head-on two-peak solitons; (v) Two different typesof interactions of the three solitons; (vi) Decomposition phenomenonof one soliton into two solitons. The results might be useful in thestudy on the ultrashort-pulse propagation in the inhomogeneousmulti-component nonlinear media. 相似文献
We present a review of our recent theoretical and experimental results on the interaction of incoherent two-dimensional solitary
beams in PR SBN crystals. We show that the inherent anisotropy of PR nonlinearity strongly affects the interaction between
solitons. Theoretical and experimental results reveal that solitons interacting in a plane perpendicular to the direction
of external biasing field always attract, whereas those colliding in a plane of the field exhibit anomalous behaviour. They
may experience both attractive and repulsive forces, depending on their mutual separation. We also show that this anisotropy
results in the complicated topology of soliton trajectories, featuring periodic collisions, prolonged mutual spiraling and
collapse, depending on the initial conditions.
Received: 16 November 1998 / Revised version: 12 February 1999 / Published online: 12 April 1999 相似文献
Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam (FPU)-like lattices
were recently generalized to the
case of dispersive long-range interactions (LRI) of the Kac-Baker form.
The variance of the soliton position shows a stronger than linear
time-dependence (superdiffusion) as found earlier for lattice solitons on FPU chains with
nearest-neighbour interactions (NNI). Since the superdiffusion seems to be generic for nontopological solitons, we want to
illuminate the role of the soliton shape on the superdiffusive mechanism.
Therefore, we concentrate on an FPU-like lattice with a certain class of power-law long-range interactions where the solitons
have algebraic tails instead of
the exponential tails in the case of FPU-type interactions (with or without Kac-Baker LRI).Despite of structurally similar
Langevin equations which hold for the soliton position and width of the two soliton types, the
algebraic solitons reach the superdiffusive long-time limit with a
characteristic t3/2 time-dependence much faster than
exponential solitons. The soliton shape determines the diffusion constant in the long-time limit that is approximately a factor
of π smaller for algebraic
solitons. Our results appear to be generic for nonlinear excitaitons in
FPU-chains, because the same superdiffusive time-dependence was also observed in
simulations with discrete breathers. 相似文献
We present the observation of incoherent anti-dark photovoltaic solitons in LiNbO3:Fe crystal. This new class of soliton states involves bright photovoltaic solitons on a background beam meeting ?? > 1, where ?? is the ratio of background illumination photovoltaic constant to that of soliton beam. For ?? < 1, dark photovoltaic solitons are generated. Furthermore, this novel type solitons are investigated experimentally by injecting coherent light and partially coherent background of infinite extent. In case of spatial coherence of the background lower than the threshold of incoherent modulation instability, these results indicate that bright photovoltaic solitons can propagate in a stable fashion. 相似文献
We present an analytical and numerical investigation of the propagation of spatial solitons in a nonlinear waveguide with ramp linear refractive index profile (ramp waveguide). For the propagation of a single soliton beam in a ramp waveguide, the particle theory shows that the soliton beam follows a parabolic curve in the region where the linear refractive index increases and a straight line outside the waveguide. The acceleration of the soliton depends on the beam intensity: higher amplitude solitons experience higher acceleration. Numerical calculations using an implicit Crank–Nicolson scheme confirm the result of the particle theory. Combining these propagation properties with the theory about bound-N-soliton, we study the break up of such a bound-N-soliton in a ramp waveguide. In a ramp waveguide, a bound-N-soliton will always be splitted into N independent solitons with the higher amplitude soliton emitted first. The amplitude of the separated solitons after break up are calculated using the soliton theory as if the solitons are independent. Numerical simulations show that the results agree quite well with this theoretical prediction, indicating that the interaction during break up has only little influence. 相似文献
In this paper we answer the question: “what types of
spatial soliton can be formed based on two-photon-isomerisation (TPI)”. The
conclusion that anti-dark solitons are not supported by monotonic
nonlinearity should cast light on the notion of fundamental spatial
solitons. The idea to obtain a bright TPI soliton with the joining of a
background light or with the coupling of a dark soliton offers new schemes
of light-controlling-light. 相似文献
Optical solitons and quasisolitons are investigated in reference to Cherenkov radiation. It is shown that both solitons and
quasisolitons can exist, if the linear operator specifying their asymptotic behavior at infinity is sign-definite. In particular,
the application of this criterion to stationary optical solitons shifts the soliton carrier frequency at which the first derivative
of the dielectric constant with respect to the frequency vanishes. At that point the phase and group velocities coincide.
Solitons and quasisolitons are absent, if the third-order dispersion is taken into account. The stability of a soliton is
proved for fourth order dispersion using the sign-definiteness of the operator and integral estimates of the Sobolev type.
This proof is based on the boundedness of the Hamiltonian for a fixed value of the pulse energy.
Zh. éksp. Teor. Fiz. 113, 1892–1914 (May 1998) 相似文献
Several issues concerning the self-dual solutions of the Chern-Simons-Higgs model are addressed. The topology of the configuration
space of the model is analysed when the space manifold is either the plane or an infinite cylinder. We study the local structure
of the moduli space of self-dual solitons in the second case by means of an index computation. It is shown how to manage the
non-integer contribution to the heat-kernel supertrace due to the non-compactness of the base space. A physical picture of
the local coordinates parametrizing the non-topological soliton moduli space arises.
Received: 9 October 1998 / Revised version: 12 December 1998 / Published online: 22 March 1999 相似文献
We present an analytical and numerical investigation of the propagation of spatial solitons in a nonlinear waveguide with
ramp linear refractive index profile (ramp waveguide). For the propagation of a single soliton beam in a ramp waveguide, the
particle theory shows that the soliton beam follows a parabolic curve in the region where the linear refractive index increases
and a straight line outside the waveguide. The acceleration of the soliton depends on the beam intensity: higher amplitude
solitons experience higher acceleration. Numerical calculations using an implicit Crank-Nicolson scheme confirm the result
of the particle theory. Combining these propagation properties with the theory about bound-N-soliton, we study the break up of such a bound-N-soliton in a ramp waveguide. In a ramp waveguide, a bound-N-soliton will always be splitted intoN independent solitons with the higher amplitude soliton emitted first. The amplitude of the separated solitons after break
up are calculated using the soliton theory as if the solitons are independent. Numerical simulations show that the results
agree quite well with this theoretical prediction, indicating that the interaction during break up has only little influence.
On Leave from Jurusan Matematika, Universitas Brawijaya, Jl. MT Haryono 167 Malang Indonesia. 相似文献
In fiber lasers, the study of the cubic‐quintic complex Ginzburg‐Landau equations (CGLE) has attracted much attention. In this paper, four families (kink solitons, gray solitons, Y‐type solitons and combined solitons) of exact soliton solutions for the variable‐coefficient cubic‐quintic CGLE are obtained via the modified Hirota method. Appropriate parameters are chosen to investigate the properties of solitons. The influences of nonlinearity and spectral filtering effect are discussed in these obtained exact soliton solutions, respectively. Methods to amplify the amplitude and compress the width of solitons are put forward. Numerical simulation with split‐step Fourier method and fourth‐order Runge‐Kutta algorithm are carried out to validate some of the analytic results. Transformation from the variable‐coefficient cubic‐quintic CGLE to the constant coefficients one is proposed. The results obtained may have certain applications in soliton control in fiber lasers, and may have guiding value in experiments in the future.
This article continues the series of the works of 1998–2007 years devoted to the Multidimensional Superposition Principle, the concept easily explaining both classical soliton and more complex wave interactions in nonlinear PDEs and allowing one, in particular, to construct the general Superposition Formulae for nonlinear wave interactions. In the present research the technique of multiexpansions with constraints is considered for finding the above SFs and investigation of the related solitons. (The simplest case of such expansions technically is analogous to the so-called invariant truncated singular expansions.) As the applications, the soliton SFs of the MKdV±, Kaup-Kupershmidt and new A± equation are obtained for the bell-shape exponential solitons of the various families, algebraic solitons, and the configuration of the two noninteracting kinks. The linearized, parameterized versions of these SFs are investigated then, and the related analysis of the interactions is presented. The obtained results allow one to consider the one soliton solutions mentioned as the strong bound states of the simpler solitons. Concerning the results for the above concrete nonlinear PDEs, the approach being developed made it possible both to obtain the new results and to reveal new moments for the already known ones. 相似文献
An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations. 相似文献
The polarization clusters observed experimentally in the high-temperature phase of ferroelectrics are interpreted as solitons
in the microscopic pseudospin formalism. These solitons are the result of modulation of the pseudospin interaction constant
by acoustic vibrations, which represents an electrostriction interaction from the phenomenological point of view. The influence
of higher-order nonlinearities present in the pseudospin subsystem and the damping of acoustic modes on a soliton is analyzed.
Fiz. Tverd. Tela (St. Petersburg) 40, 713–715 (April 1998) 相似文献