Multicomponent two-dimensional solitons carrying topological charges

We propose multihump N-component two-dimensional vector solitons for which each constituent carries a different topological charge. These new structures exhibit a unique triple-point phase diagram that is completely absent in the two-component limit.     

From topological charge information to sets of solitons in quadratic non-linear media

We describe the principle of operation of a new class of optical devices operating in quadratic non-linear media that mix wave front topological charge dislocations nested in focused light beams and produce certain patterns of bright spatial solitons. Central to the device behaviour is the orbital angular momentum of the light beams.     

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.     

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.     

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.     

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.     

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.     

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.     

Dynamic topological solitons in a two-dimensional ferromagnet

It is shown that stable, skyrmion-type, dynamic solitons can be constructed for a wide class of two-dimensional models of anisotropic ferromagnets. These solitons are stabilized as a result of the conservation of various integrals of motion: the z projection of the total spin S _z or the orbital angular momentum L _z of the magnetization field. A class of two-parameter solitons with quite complicated (almost periodic) magnetization-field dynamics exists for a purely uniaxial model (in the sense of both spin and spatial rotations) with maximum symmetry. Stable solitons with periodic magnetization dynamics exist for ferromagnets with lower symmetry (only S _z or L _z or the total angular momentum J _z =L _z +S _z is conserved). Zh. éksp. Teor. Fiz. 115, 1511–1530 (April 1999)     

Large-radius dynamic topological solitons in uniaxial ferromagnets

In thin ferromagnetic films with perpendicular anisotropy, there exist stable large-radius dynamic topological solitons, which are stabilized owing to conservation of the orbital angular momentum of the magnetization field. The solitons can also exist if the projection of the total spin moment of the magnet onto the easy axis is not conserved, i.e., in the absence of pure uniaxial symmetry of the model. Even in the pure uniaxial case, the magnetization distribution in a soliton with a sufficiently large radius differs significantly from centrosymmetric.     

Dynamics of topological solitons in two-dimensional ferromagnets

Dynamical topological solitons are studied in classical two-dimensional Heisenberg easy-axis ferromagnets. The properties of such solitons are treated both analytically in the continuum limit and numerically by spin dynamics simulations of the discrete system. Excitation of internal mode causes orbital motion. This is confirmed by simulations.     

Energy flow of moving dissipative topological solitons

We study the energy flow due to the motion of topological solitons in nonlinear extended systems in the presence of damping and driving. The total field momentum contribution to the energy flux, which reduces the soliton motion to that of a point particle, is insufficient. We identify an additional exchange energy flux channel mediated by the spatial and temporal inhomogeneity of the system state. In the well-known case of a dc external force the corresponding exchange current is shown to be small but nonzero. For the case of ac driving forces, which lead to a soliton ratchet, the exchange energy flux mediates the complete energy flow of the system. We also consider the case of combination of ac and dc external forces, as well as spatial discretization effects.     

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.     

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.     

Irrational charge from topological order

Topological or deconfined phases of matter exhibit emergent gauge fields and quasiparticles that carry a corresponding gauge charge. In systems with an intrinsic conserved U(1) charge, such as all electronic systems where the Coulombic charge plays this role, these quasiparticles are also characterized by their intrinsic charge. We show that one can take advantage of the topological order fairly generally to produce periodic Hamiltonians which endow the quasiparticles with continuously variable, generically irrational, intrinsic charges. Examples include various topologically ordered lattice models, the three-dimensional resonating valence bond liquid on bipartite lattices as well as water and spin ice. By contrast, the gauge charges of the quasiparticles retain their quantized values.     

On three-dimensional dissipative optical solitons: Collisions of laser bullets and topological solitons

Results of numerical simulation of collisions of two fundamental laser bullets—three-dimensional solitons formed in a medium with saturable amplification and absorption and frequency dispersion—are presented. A new collision regime resulting in the formation and the propagation of a switching wave is revealed. The existence of a metastable topological (with a wave front dislocation and an annular intensity distribution) three-dimensional dissipative optical soliton is demonstrated.     

Instantons with fractional topological charge

We introduce and discuss the properties of multivalent gauges for Yang-Mills fields, and demonstrate the existence of instantons with fractional topological charges in such gauges.     

Stable topological spatial solitons in optical parametric oscillators

We predict that nearly resonant optical parametric oscillators support stable topological spatial solitons as a result of the interplay between diffraction and parametric amplification due to chi((2)) nonlinearities. Robust soliton stripes are observed in two transverse dimensions. Their stability is ensured by the phase-sensitive nature of the underlying parametric process.