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Yuri S. Kivshar

Publications and source records attributed to Yuri S. Kivshar.

At least 343 records · Page 19Linked to original sources
arXiv2000

Multi-component optical solitary waves

We discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for high performance computer networks, multi-colour parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons due to quasi-phase-matching in Fibonacci optical superlattices.

nlin.PS↗
arXiv2000

Long-range interaction and nonlinear localized modes in photonic crystal waveguides

We develop the theory of nonlinear localised modes (intrinsic localised modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear dielectric rods in an otherwise perfect linear 2D photonic crystal, and demonstrate that the effective interaction in such waveguides is nonlocal, being described by a new type of nonlinear lattice models with long-range coupling and nonlocal nonlinearity. We reveal the existence of different types of nonlinear guided modes which are also localised in the waveguide direction, and describe their unique properties including bistability.

cond-mat↗
arXiv2000

Two-color multistep cascading and parametric soliton-induced waveguides

We introduce the concept of two-color multistep cascading for vectorial parametric wave mixing in optical media with quadratic (second-order or chi-2) nonlinear response. We demonstrate that the multistep cascading allows light-guiding-light effects with quadratic spatial solitons. With the help of the so-called `almost exact' analytical solutions, we describe the properties of parametric waveguides created by two-wave quadratic solitons.

patt-sol↗
arXiv1999

Dipole-Mode Vector Solitons

We find a new type of optical vector soliton that originates from trapping of a dipole mode by a soliton-induced waveguide. 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-mode solitons and represent a new type of extremely robust nonlinear vector structure.

patt-sol↗
arXiv1999

Vector solitons in (2+1) dimensions

We address the problem of existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of (2+1)-dimensional two-mode self-trapped beams, with and without a topological charge, and describe their properties analytically and numerically.

patt-sol↗
arXiv1999

Origin of Multikinks in Dispersive Nonlinear Systems

We develop {\em the first analytical theory of multikinks} for strongly {\em dispersive nonlinear systems}, considering the examples of the weakly discrete sine-Gordon model and the generalized Frenkel-Kontorova model with a piecewise parabolic potential. We reveal that there are no $2π$-kinks for this model, but there exist {\em discrete sets} of $2πN$-kinks for all N>1. We also show their bifurcation structure in driven damped systems.

patt-sol↗
arXiv1999

Stability criterion for attractive Bose-Einstein condensates

A general stability criterion is derived for the D-dimensional ground states of the Gross-Pitaevskii equation, which describes attractive Bose-Einstein condensates confined in a magnetic trap. These ground states are shown to avoid the collapse in finite time and are proven to be stable in two and three spatial dimensions.

cond-mat↗
arXiv1999

Coupled-mode theory for Bose-Einstein condensates

We apply the concepts of nonlinear guided-wave optics to a Bose-Einstein condensate (BEC) trapped in an external potential. As an example, we consider a parabolic double-well potential and derive coupled-mode equations for the complex amplitudes of the BEC macroscopic collective modes. Our equations describe different regimes of the condensate dynamics, including the nonlinear Josephson effect for any separation between the wells. We demonstrate macroscopic self-trapping for both repulsive and attractive interactions, and confirm our results by numerical simulations.

cond-mat↗
arXiv1999

Nonlinear Modes of a Macroscopic Quantum Oscillator

We consider the Bose-Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes - a nonlinear generalisation of the (symmetric and antisymmetric) Hermite-Gauss eigenmodes of a harmonic quantum oscillator.

cond-mat↗
arXiv1999

Quasiperiodic Envelope Solitons

We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially localized self-trapping of a quasiperiodic wave. We point out a link between the quasiperiodic soliton and partially incoherent spatial solitary waves recently generated experimentally.

patt-sol↗
arXiv1999

Two-color nonlinear localized photonic modes

We analyze second-harmonic generation (SHG) at a thin effectively quadratic nonlinear interface between two linear optical media. We predict multistability of SHG for both plane and localized waves, and also describe two-color localized photonic modes composed of a fundamental wave and its second harmonic coupled together by parametric interaction at the interface.

patt-sol↗
arXiv1999

Optical Vortex Solitons in Parametric Wave Mixing

We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localised waves, namely, parametric vortex solitons due to phase-matched second-harmonic generation in an optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a `halo-vortex', consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a `ring-vortex' soliton which is a vortex in a harmonic field that guides a ring-like localized mode of the fundamental-frequency field.

patt-sol↗
arXiv1999

Stability of multi-hump optical solitons

We demonstrate that, in contrast with what was previously believed, multi-hump solitary waves can be stable. By means of linear stability analysis and numerical simulations, we investigate the stability of two- and three-hump solitary waves governed by incoherent beam interaction in a saturable medium, providing a theoretical background for the experimental results reported by M. Mitchell, M. Segev, and D. Christodoulides [Phys. Rev. Lett. v. 80, p. 4657 (1998)].

patt-sol↗
arXiv1999

Trapped Bose-Einstein Condensates: Role of Dimensionality

We analyse systematically, from the viewpoint of the nonlinear physics of solitary waves, the effect of the spatial dimension (D = 1,2,3) on the structure and stability of the Bose-Einstein condensates (BECs) trapped in an external anisotropic parabolic potential. While for the positive scattering length the stationary ground-state solutions of the Gross-Pitaevskii equation are shown to be always stable independently of the spatial dimension, for the negative scattering length the ground-state condensate is stable only in the 1D and 2D cases, whereas in the 3D case it becomes unstable. A direct link between nonlinear modes of BECs and (bright and dark) solitary waves of the nonlinear Schrodinger equation is demonstrated for all the dimensions.

cond-mat↗
arXiv1999

Spatial Optical Solitons due to Multistep Cascading

We introduce a novel class of parametric optical solitons supported simultaneously by two second-order nonlinear cascading processes, second-harmonic generation and sum-frequency mixing. We obtain, analytically and numerically, the solutions for three-wave spatial solitons and show that the presence of an additional cascading mechanism can change dramatically the properties and stability of two-wave quadratic solitary waves.

patt-sol↗
arXiv1998

Induced Coherence and Stable Soliton Spiraling

We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states. Our theory not only explains earlier observations, but provides a number of predictions which are also verified experimentally. Finally, we show theoretically and experimentally that soliton spiraling can be controled by the degree of mutual initial coherence.

patt-sol↗
arXiv1998

Discreteness-Induced Oscillatory Instabilities of Dark Solitons

We reveal that even weak inherent discreteness of a nonlinear model can lead to instabilities of the localized modes it supports. We present the first example of an oscillatory instability of dark solitons, and analyse how it may occur for dark solitons of the discrete nonlinear Schrodinger and generalized Ablowitz-Ladik equations.

patt-sol↗