109 research outputs found
Surface modes and breathers in finite arrays of nonlinear waveguides
We present the complete set of symmetric and antisymmetric (edge and corner)
surface modes in finite one-- and two--dimensional arrays of waveguides. We
provide classification of the modes based on the anti-continuum limit, study
their stability and bifurcations, and discuss relation between surface and bulk
modes. We put forward existence of surface breathers, which represent
two-frequency modes localized about the array edges.Comment: Accepted for publication in Physical Review
Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays
We discuss the formation of self-trapped localized states near the edge of a
semi-infinite array of nonlinear waveguides. We study a crossover from
nonlinear surface states to discrete solitons by analyzing the families of odd
and even modes centered at different distances from the surface, and reveal the
physical mechanism of the nonlinearity-induced stabilization of surface modes.Comment: 4 double-column pages, 5 figures, submitted to Optics Letter
Nonlinear localized modes at phase-slip defects in waveguide arrays
We study light localization at a phase-slip defect created by two
semi-infinite mismatched identical arrays of coupled optical waveguides. We
demonstrate that the nonlinear defect modes possess the specific properties of
both nonlinear surface modes and discrete solitons. We analyze stability of the
localized modes and their generation in both linear and nonlinear regimes.Comment: 3 pages, 6 figures, submitted to Opt. Let
Spatial optical solitons in nonlinear photonic crystals
We study spatial optical solitons in a one-dimensional nonlinear photonic
crystal created by an array of thin-film nonlinear waveguides, the so-called
Dirac-comb nonlinear lattice. We analyze modulational instability of the
extended Bloch-wave modes and also investigate the existence and stability of
bright, dark, and ``twisted'' spatially localized modes in such periodic
structures. Additionally, we discuss both similarities and differences of our
general results with the simplified models of nonlinear periodic media
described by the discrete nonlinear Schrodinger equation, derived in the
tight-binding approximation, and the coupled-mode theory, valid for shallow
periodic modulations of the optical refractive index.Comment: 15 pages, 21 figure
Nonlinear excitations in arrays of Bose-Einstein condensates
The dynamics of localized excitations in array of Bose-Einstein condensates
is investigated in the framework of the nonlinear lattice theory. The existence
of temporarily stable ground states displaying an atomic population
distributions localized on very few lattice sites (intrinsic localized modes),
as well as, of atomic population distributions involving many lattice sites
(envelope solitons), is studied both numerically and analytically. The origin
and properties of these modes are shown to be inherently connected with the
interplay between macroscopic quantum tunnelling and nonlinearity induced
self-trapping of atoms in coupled BECs. The phenomenon of Bloch oscillations of
these excitations is studied both for zero and non zero backgrounds. We find
that in a definite range of parameters, homogeneous distributions can become
modulationally unstable. We also show that bright solitons and excitations of
shock wave type can exist in BEC arrays even in the case of positive scattering
length. Finally, we argue that BEC array with negative scattering length in
presence of linear potentials can display collapse.Comment: Submitted to Phys. Rev.
Nonlinear guided waves and spatial solitons in a periodic layered medium
We overview the properties of nonlinear guided waves and (bright and dark)
spatial optical solitons in a periodic medium created by a sequence of linear
and nonlinear layers. First, we consider a single layer with a cubic nonlinear
response (a nonlinear waveguide) embedded into a periodic layered linear
medium, and describe nonlinear localized modes (guided waves and Bragg-like
localized gap modes) and their stability. Then, we study modulational
instability as well as the existence and stability of discrete spatial solitons
in a periodic array of identical nonlinear layers, a one-dimensional nonlinear
photonic crystal. Both similarities and differences with the models described
by the discrete nonlinear Schrodinger equation (derived in the tight-binding
approximation) and coupled-mode theory (valid for the shallow periodic
modulations) are emphasized.Comment: 10 pages, 14 figure
Three-wave interaction in two-component quadratic nonlinear lattices
We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale
technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill
resonance conditions. We demonstrate that energy conversion and pulse propagation known from three-wave
interaction is reproduced in the lattice and that exact phase matching of parametric processes can be obtained
in non-phase-matched lattices by tilting the interacting plane waves with respect to each other.info:eu-repo/semantics/publishedVersio
Parametric localized modes in quadratic nonlinear photonic structures
We analyze two-color spatially localized modes formed by parametrically
coupled fundamental and second-harmonic fields excited at quadratic (or chi-2)
nonlinear interfaces embedded into a linear layered structure --- a
quasi-one-dimensional quadratic nonlinear photonic crystal. For a periodic
lattice of nonlinear interfaces, we derive an effective discrete model for the
amplitudes of the fundamental and second-harmonic waves at the interfaces (the
so-called discrete chi-2 equations), and find, numerically and analytically,
the spatially localized solutions --- discrete gap solitons. For a single
nonlinear interface in a linear superlattice, we study the properties of
two-color localized modes, and describe both similarities and differences with
quadratic solitons in homogeneous media.Comment: 9 pages, 8 figure
Dark-in-Bright Solitons in Bose-Einstein Condensates with Attractive Interactions
We demonstrate a possibility to generate localized states in effectively
one-dimensional Bose-Einstein condensates with a negative scattering length in
the form of a dark soliton in the presence of an optical lattice (OL) and/or a
parabolic magnetic trap. We connect such structures with twisted localized
modes (TLMs) that were previously found in the discrete nonlinear
Schr{\"o}dinger equation. Families of these structures are found as functions
of the OL strength, tightness of the magnetic trap, and chemical potential, and
their stability regions are identified. Stable bound states of two TLMs are
also found. In the case when the TLMs are unstable, their evolution is
investigated by means of direct simulations, demonstrating that they transform
into large-amplitude fundamental solitons. An analytical approach is also
developed, showing that two or several fundamental solitons, with the phase
shift between adjacent ones, may form stable bound states, with
parameters quite close to those of the TLMs revealed by simulations. TLM
structures are found numerically and explained analytically also in the case
when the OL is absent, the condensate being confined only by the magnetic trap.Comment: 13 pages, 7 figures, New Journal of Physics (in press
Solitons in Triangular and Honeycomb Dynamical Lattices with the Cubic Nonlinearity
We study the existence and stability of localized states in the discrete
nonlinear Schr{\"o}dinger equation (DNLS) on two-dimensional non-square
lattices. The model includes both the nearest-neighbor and long-range
interactions. For the fundamental strongly localized soliton, the results
depend on the coordination number, i.e., on the particular type of the lattice.
The long-range interactions additionally destabilize the discrete soliton, or
make it more stable, if the sign of the interaction is, respectively, the same
as or opposite to the sign of the short-range interaction. We also explore more
complicated solutions, such as twisted localized modes (TLM's) and solutions
carrying multiple topological charge (vortices) that are specific to the
triangular and honeycomb lattices. In the cases when such vortices are
unstable, direct simulations demonstrate that they turn into zero-vorticity
fundamental solitons.Comment: 17 pages, 13 figures, Phys. Rev.
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