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.     

White-light solitons

Optical spatial solitons made from incoherent white light were experimentally observed in 1997 by Mitchell and Segev [Nature (London) 387, 880 (1997)]. We present what is believed to be the first theory describing these solitons and find the characteristic features of their spatiotemporal coherence properties and their temporal power spectrum.     

Talbot solitons

We propose a new type of scalar wave-mixing optical solitons, Talbot solitons. The soliton consists of sinusoidal and uniform components that are mutually coherent and jointly trapped in one direction. The intensity structure of the soliton oscillates in the propagation direction as a result of the linear Talbot effect and periodic nonlinear energy exchange between the components. Talbot solitons induce a 1D waveguide and a 2D photonic lattice within the waveguide that may be used for quasi-phase matching of frequency conversion and as a tunable waveguide filter.     

Einstein-Yang-Mills-Higgs solitons

The classical theory of the gravitational field coupled to an SO(3) gauge field and to a ghost Higgs field in (3+1) dimensions is found to admit regular localized solutions of the electric or magnetic type. These solutions, which generalize solutions previously found for the Abelian case, are characterized by a non-Euclidean spatial topology, with two points at infinity.     

Non-anticommutative solitons

Certain supersymmetric sigma models in 2+1$2+1$ dimensions feature multi-soliton solutions, with and without scattering. We subject these systems to a non-anticommutative deformation by replacing the Grassmann algebra of the odd superspace coordinates with a Clifford algebra. Static CP¹$\mathbb{C}{P}^1$ and scattering U(2) solitons are constructed and carry an additional spin-1/2 degree of freedom due to the deformation. Abelian BPS solutions exist as well but have infinite action, in contrast to the Moyal case.     

Topological solitons

These are notes of the first part of the lectures on topological solitons, presented on Baikal Summer School on Physics of Elementary Particles and Astrophysics (July 2011). I review some of the basic properties of topological solitons on a simple model example of simple one-dimensional kink solution of the nonintegrable scalar ?⁴ model. I discuss both perturbative and non-perturbative sectors of the model, oscillon solution and resonance structures in the soliton collision.     

Supersymmetric solitons

The generalization of the two-dimensional soliton to four space-time dimensions is a magnetic monopole. If the Higgs field lies in the adjoint representation electric and magnetic chargesq andg can be defined. If further the Higgs self-interaction vanishes all the particle states obey the universal, dual symmetric mass formulaM=a (q ²+g ²).There is evidence that this is exact in quantum mechanics if the theory is madeSO(2) supersymmetric.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.     

Gas-induced solitons

The self-guiding of femtosecond laser pulses in air is investigated. For powers close to the threshold for self-focusing, we show that the balance between the nonlinear focusing of the beam and its defocusing by multiphoton sources produces a new kind of solitonlike structure. Over considerably long distances, the radial profile of the pulse relaxes to a steady-state shape, whereas its temporal profile shrinks along propagation. The influence of the normal group-velocity dispersion is finally discussed.     

Holographic solitons

We propose a new kind of an optical spatial soliton: the holographic soliton. This soliton consists of two mutually coherent field components that interfere, induce a periodic change in the refractive index, and simultaneously are Bragg diffracted from the grating. Holographic solitons are formed when the broadening tendency of diffraction is balanced by phase modulation that is due to Bragg diffraction from the induced grating. Holographic solitons are solely supported by cross-phase modulation arising from the induced grating, not involving self-phase modulation at all.     

Parametric solitons

We develop a general framework for understanding the characteristics of multi-frequency (multi-colour) parametric solitons. We identify two special classes of such solitons: cascaded parametric solitons, where the optical energy is shared between several harmonically-related frequency bands; and isolated-bandwidth solitons, where all of the optical energy is localized within a single frequency band. As an example, we consider the case of a five-colour isolated-bandwidth parametric soliton in a Kerr medium.     

Thresholdless surface solitons

We report on the existence of nonlinear surface waves that, on the one hand, do not require the threshold energy flow for their excitation, and, on the other hand, extend into media at both sides of the interface at low powers, i.e., cannot be reduced to the conventional Tamm states. Such waves can be excited if the refractive index in at least one of the materials forming the interface is periodically modulated, with properly selected modulation depth and frequency. Thresholdless surface solitons can be stable in the entire existence domain.     

Spatial resonator solitons

Spatial solitons can exist in various kinds of nonlinear optical resonators with and without amplification. In the past years different types of these localized structures such as vortices, bright, dark solitons, and phase solitons have been experimentally shown to exist. Many links appear to exist to fields different from optics, such as fluids, phase transitions, or particle physics. These spatial resonator solitons are bistable and due to their mobility suggest schemes of information processing not possible with the fixed bistable elements forming the basic ingredient of traditional electronic processing. The recent demonstration of existence and manipulation of spatial solitons in semiconductor microresonators represents a step in the direction of such optical parallel processing applications. We review some proof of principle soliton experiments on slow systems, and describe in more detail the experiments on semiconductor resonator solitons which are aimed at applications.