Searcharxiv⌕ Search

arXiv subjects

Tristram J. Alexander

Publications and source records attributed to Tristram J. Alexander.

30 records · Page 2Linked to original sources
arXiv2004

Asymmetric vortex solitons in nonlinear periodic lattices

We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices, and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance relations. We present the examples of rhomboid, rectangular, and triangular vortex solitons on a square lattice, and also describe novel coherent states where the populations of clockwise and anti-clockwise vortex modes change periodically due to a nonlinearity-induced momentum exchange through the lattice. Asymmetric vortex solitons are expected to exist in different nonlinear lattice systems including optically-induced photonic lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical lattices.

physics.optics↗
arXiv2004

Observation of discrete vortex solitons in optically-induced photonic lattices

We report on the frst experimental observation of discrete vortex solitons in two-dimensional optically-induced photonic lattices. We demonstrate strong stabilization of an optical vortex by the lattice in a self-focusing nonlinear medium and study the generation of the discrete vortices from a broad class of singular beams.

nlin.PS↗
arXiv2001

Vortices in atomic-molecular Bose-Einstein condensates

The structure and stability of vortices in hybrid atomic-molecular Bose-Einstein condensates is analyzed in the framework of a two-component Gross-Pitaevskii-type model that describes the stimulated Raman-induced photoassociation process. New types of topological vortex states are predicted to exist in the coherently coupled two-component condensates even without a trap, and their nontrivial dynamics in the presence of losses is demonstrated.

cond-mat↗
arXiv2000

Existence and stability of atomic-molecular Bose-Einstein condensates

We analyze the model of an atomic Bose-Einstein condensate (BEC) parametrically coupled to a molecular BEC via a photoassociation process. We show that an interplay of nonlinear inter- and intra-species interactions leads to the formation of mutually trapped states of a hybrid condensate, which are spatially localized even without a trap. The untrapped atomic-molecular condensates with a large number of atoms in either fraction are shown to be dynamically stable in the framework of a mean field theory.

cond-mat↗
arXiv2000

Multistep cascading and fourth-harmonic generation

We apply the concept of multistep cascading to the problem of fourth-harmonic generation in a single quadratic crystal. We analyze a new model of parametric wave mixing and describe its stationary solutions for two- and three-color plane waves and spatial solitons. Some applications to the optical frequency division as well as the realization of the double-phase-matching processes in engineered QPM structures with phase reversal sequences are also discussed.

nlin.PS↗
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↗
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

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

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

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↗