Symmetry-breaking instabilities of generalized elliptical solitons

Elliptical solitons in 2D nonlinear Sch?dinger equations are studied numerically with a more-generalized formulation. New families of solitons, vortices, and soliton rings with elliptical symmetry are found and investigated. With a suitable symmetry-breaking parameter, we show that perturbed elliptical solitons tend to move transversely owing to the existences of dipole excitation modes, which are totally suppressed in circularly symmetric solitons. Furthermore, by numerical evolutions we demonstrate that elliptical vortices and soliton rings collapse into a pair of stripes and clusters, respectively, revealing the experimental observations in the literature.     

Transverse instability of strongly coupled dark-bright Manakov vector solitons

We show, by performing linear stability analysis and direct numerical simulations, that dark-soliton transverse instability is significantly reduced in Kerr media by strong coupling to a bright soliton. High instability suppression can be achieved by use of large-amplitude bright solitons.     

Transverse instability of vector solitons and generation of dipole arrays

We develop a theory of modulational instability of multiparameter solitary waves and analyze the transverse instability of composite (or vector) optical solitons in a saturable nonlinear medium. We demonstrate theoretically and experimentally that a soliton stripe breaks up into an array of ( 2+1)-dimensional dipole-mode vector solitons, thus confirming the robust nature of those solitons as fundamental composite structures of incoherently coupled fields.     

Observation of two-dimensional multimode solitons

We present the first experimental observation of (2+1) -dimensional multimode (composite) solitons. A single-hump component and a double-hump (dipole-type) component are jointly self-trapped as a composite soliton in a biased photorefractive crystal.     

Polarization locked vector solitons and axis instability in optical fiber

We experimentally observe polarization-locked vector solitons in optical fiber. Polarization locked-vector solitons use nonlinearity to preserve their polarization state despite the presence of birefringence. To achieve conditions where the delicate balance between nonlinearity and birefringence can survive, we studied the polarization evolution of the pulses circulating in a laser constructed entirely of optical fiber. We observe two distinct states with fixed polarization. This first state occurs for very small values birefringence and is elliptically polarized. We measure the relative phase between orthogonal components along the two principal axes to be +/-pi/2. The relative amplitude varies linearly with the magnitude of the birefringence. This state is a polarization locked vector soliton. The second, linearly polarized, state occurs for larger values of birefringence. The second state is due to the fast axis instability. We provide complete characterization of these states, and present a physical explanation of both of these states and the stability of the polarization locked vector solitons. (c) 2000 American Institute of Physics.     

Symmetry-breaking dynamics of the modulational instability spectrum

We demonstrate in an optical fiber that third-order dispersion yields an unexpected symmetry-breaking dynamics of the modulational instability spectrum. It is found in particular that this spectral asymmetry does not smoothly and monotonically increase when approaching the zero-dispersion wavelength. Instead, it exhibits several local extrema and it can even be reversed at a particular dispersion value. We interpret this behavior as resulting from interactions between dispersive waves and solitons generated from modulation instability.     

Symmetry-breaking vacuum and state vector reduction

It is argued by means of analogy with certain irreversible processes that a symmetry-violating vacuum need not necessarily be explained by a special cosmic initial condition.     

Dipole-mode vector solitons

We find a new type of optical vector soliton that originates from trapping of a dipole mode by the soliton-induced waveguides. These solitons, which appear as a consequence of the vector nature of the two-component system, are more stable than the previously found optical vortex solitons and represent a new type of extremely robust nonlinear vector structure.     

Internal oscillation of vector solitons and necklace solitons

Internal modes and internal oscillation of vector solitons associated with photoisomerization and necklace solitons in Bessel lattices are researched. While white noise gives rise to the unsmoothness of the vector solitons, the perturbation of internal modes results in the long-distance quasi-periodic oscillation of soliton shape. Internal modes of two-dimensional necklace solitons in Bessel lattices have both real and imaginary parts, which is different with the internal modes of one-dimensional solitons which have only real part.     

Low-amplitude vector screening solitons

We show self-coupled and cross-coupled vector beam evolution equations in the low-amplitude regime for screening solitons,which can exhibit the analytical solutions of bright-bright and dark-dark vector solitons.Our analysis indicates that these self-coupled vector solitons are obtained irrespective of the intensities of the two optical beams,whereas these cross-coupled vector solitons can be established when the intensities of the two optical beams are equal.Relevant examples are provided where the photorefractive crystal is lithium niobate(LiNbO3).The stability properties of these vector solitons have been investigated numerically and it has been found that they are stable.     

Stabilized two-dimensional vector solitons

In this Letter, we introduce the concept of stabilized vector solitons as nonlinear waves constructed by the addition of mutually incoherent fractions of Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We analyze the stability of these new kinds of structures and describe their behavior and formation in Manakov-like interactions. Potential applications of our results in Bose-Einstein condensation and nonlinear optics are also discussed.     

Multigap discrete vector solitons

We analyze nonlinear collective effects in periodic systems with multigap transmission spectra such as light in waveguide arrays or Bose-Einstein condensates in optical lattices. We reveal that the interband interactions in nonlinear periodic structures can be efficiently managed by controlling their geometry. We predict novel types of discrete vector solitons supported by nonlinear coupling between different band gaps and study their stability.     

Multipole spatial vector solitons

We introduce the concept of multipole spatial optical vector solitons associated with higher-order guided modes trapped by a soliton-induced waveguide in a bulk medium. Such stationary localized waves include previously predicted vortex- and dipole-mode vector solitons and also describe new higher-order vector solitons and necklace-type beams. We present the theoretical and experimental results of the structure, formation, and instability development of the quadrupole vector solitons.     

Multiband vector lattice solitons

We predict multiband vector solitons in nonlinear periodic systems, using photonic lattices as a prime example. The solitons consist of two optical fields arising from different bands of the transmission spectrum, which involve both bound state and radiation mode components.     

Observation of dipole-mode vector solitons

We report on the first experimental observation of a novel type of optical vector soliton, a dipole-mode soliton, recently predicted theoretically. We show that these vector solitons can be generated in a photorefractive medium employing two different processes: a phase imprinting, and a symmetry-breaking instability of a vortex-mode vector soliton. The experimental results display remarkable agreement with the theory, and confirm the robust nature of these radially asymmetric two-component solitary waves.     

Symmetry-breaking phase transition without a Peierls instability in conducting monoatomic chains

The one-dimensional (1D) model system Au/Ge(001), consisting of linear chains of single atoms on a surface, is scrutinized for lattice instabilities predicted in the Peierls paradigm. By scanning tunneling microscopy and electron diffraction we reveal a second-order phase transition at 585 K. It leads to charge ordering with transversal and vertical displacements and complex interchain correlations. However, the structural phase transition is not accompanied by the electronic signatures of a charge density wave, thus precluding a Peierls instability as origin. Instead, this symmetry-breaking transition exhibits three-dimensional critical behavior. This reflects a dichotomy between the decoupled 1D electron system and the structural elements that interact via the substrate. Such substrate-mediated coupling between the wires thus appears to have been underestimated also in related chain systems.     

Skyrme solitons with vector mesons

We investigate the Skyrme type soliton with vector mesons (ρ, A₁ and ω), first in the massive Yang-Mills approach and then using the hidden local symmetry Lagrangian. It is demonstrated that the two schemes give identical results for the soliton properties. A comparison is made with alternative approaches in which the A₁ degrees of freedom is eliminated.     

Phase interaction of short vector solitons

An interaction of vector solitons in the frame of coupled third-order nonlinear Schrödinger equations taking into account third-order linear dispersion, nonlinear dispersion, and cross-phase modulation terms is considered. Phase nature of the solitons? interaction is shown. In particular, dependence of solitons? trajectories on initial distance between solitons is shown. Conditions of reflection and propagation of solitons through each other are obtained.     

n-body dynamics of stabilized vector solitons

In this work we study the interactions between stabilized Townes solitons. By means of effective Lagrangian methods, we have found that the interactions between these solitons are governed by central forces, in a first approximation. In our numerical simulations we describe different types of orbits, deflections, trapping, and soliton splitting. Splitting phenomena are also described by finite-dimensional reduced models. All these effects could be used for potential applications of stabilized solitons.