4,025 research outputs found
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
Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics
Quasiparticle approach to dynamics of dark solitons is applied to the case of
ring solitons. It is shown that the energy conservation law provides the
effective equations of motion of ring dark solitons for general form of the
nonlinear term in the generalized nonlinear Schroedinger or Gross-Pitaevskii
equation. Analytical theory is illustrated by examples of dynamics of ring
solitons in light beams propagating through a photorefractive medium and in
non-uniform condensates confined in axially symmetric traps. Analytical results
agree very well with the results of our numerical simulations.Comment: 10 pages, 4 figure
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
Localization of Two-Component Bose-Einstein Condensates in Optical Lattices
We reveal underlying principles of nonlinear localization of a two-component
Bose-Einstein condensate loaded into a one-dimensional optical lattice. Our
theory shows that spin-dependent optical lattices can be used to manipulate
both the type and magnitude of nonlinear interaction between the ultracold
atomic species and to observe nontrivial two-componentnlocalized states of a
condensate in both bands and gaps of the matter-wave band-gap structure.Comment: 4 pages, 4 figure
Simple and efficient generation of gap solitons in Bose-Einstein condensates
We suggest an efficient method for generating matter-wave gap solitons in a
repulsive Bose-Einstein condensate, when the gap soliton is formed from a
condensate cloud in a harmonic trap after turning on a one-dimensional optical
lattice. We demonstrate numerically that this approach does not require
preparing the initial atomic wave packet in a specific state corresponding to
the edge of the Brillouin zone of the spectrum, and losses that occur during
the soliton generation process can be suppressed by an appropriate adiabatic
switching of the optical lattice.Comment: 7 pages, 10 figure
Engineering Fano resonances in discrete arrays
We study transmission properties of discrete arrays composed of a linear waveguide coupled to a system of N side defect states. This simple system can be used to model discrete networks of coupled defect modes in photonic crystals, complex waveguide arrays in two-dimensional nonlinear lattices, and ring-resonator structures. We demonstrate the basic principles of the resonant scattering management through engineering Fano resonances and find exact results for the wave transmission coefficient. We reveal conditions for perfect reflections and transmissions due to either destructive or constructive interferences, and associate them with Fano resonances, also demonstrating how these resonances can be tuned by nonlinear defects
Dark soliton past a finite-size obstacle
We consider the collision of a dark soliton with an obstacle in a
quasi-one-dimensional Bose condensate. We show that in many respects the
soliton behaves as an effective classical particle of mass twice the mass of a
bare particle, evolving in an effective potential which is a convolution of the
actual potential describing the obstacle. Radiative effects beyond this
approximation are also taken into account. The emitted waves are shown to form
two counterpropagating wave packets, both moving at the speed of sound. We
determine, at leading order, the total amount of radiation emitted during the
collision and compute the acceleration of the soliton due to the collisional
process. It is found that the radiative process is quenched when the velocity
of the soliton reaches the velocity of sound in the system
Matter-wave gap solitons in atomic band-gap structures
We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic crystal for light waves. We study in detail the case of a two-dimensional square optical lattice and show that this atomic band-gap structure allows nonlinear localization of atomic Bloch waves in the form of two-dimensional matter-wave gap solitons
Self-trapping and stable localized modes in nonlinear photonic crystals
We predict the existence of stable nonlinear localized modes near the band edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr nonlinearity. Employing the technique based on the Green function, we reveal a physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystal
Controlled switching of discrete solitons in waveguide arrays
We suggest an effective method for controlling nonlinear switching in arrays
of weakly coupled optical waveguides. We demonstrate the digitized switching of
a narrow input beam for up to eleven waveguides in the engineered waveguide
arrays.Comment: 15 pages, four figures. Accepted in Optics Letter
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