211 research outputs found
Multi-channel pulse dynamics in a stabilized Ginzburg-Landau system
We study the stability and interactions of chirped solitary pulses in a
system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a
group-velocity mismatch between them, where each CGL equation is stabilized by
linearly coupling it to an additional linear dissipative equation. In the
context of nonlinear fiber optics, the model describes transmission and
collisions of pulses at different wavelengths in a dual-core fiber, in which
the active core is furnished with bandwidth-limited gain, while the other,
passive (lossy) one is necessary for stabilization of the solitary pulses.
Complete and incomplete collisions of pulses in two channels in the cases of
anomalous and normal dispersion in the active core are analyzed by means of
perturbation theory and direct numerical simulations. It is demonstrated that
the model may readily support fully stable pulses whose collisions are
quasi-elastic, provided that the group-velocity difference between the two
channels exceeds a critical value. In the case of quasi-elastic collisions, the
temporal shift of pulses, predicted by the analytical approach, is in
semi-quantitative agrement with direct numerical results in the case of
anomalous dispersion (in the opposite case, the perturbation theory does not
apply). We also consider a simultaneous collision between pulses in three
channels, concluding that this collision remains quasi-elastic, and the pulses
remain completely stable. Thus, the model may be a starting point for the
design of a stabilized wavelength-division-multiplexed (WDM) transmission
system.Comment: a text file in the revtex4 format, and 16 pdf files with figures.
Physical Review E, in pres
Three-Dimensional Vortex Solitons in Self-Defocusing Media
We demonstrate that families of vortex solitons are possible in a bidispersive three-dimensional nonlinear Schro\ua8dinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity. Such vortex solitons can be observed in optical media with normal dispersion,
normal diffraction, and defocusing nonlinearity
Soliton control in modulated optically-induced photonic lattices
We discuss soliton control in reconfigurable optically-induced photonic
lattices created by three interfering beams. We reveal novel dynamical regimes
for strongly localized solitons, including binary switching and soliton
revivals through resonant wave mixing.Comment: 7 pages, 5 figures. Content modifie
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
We develop a complete mathematical theory for the symmetrical solutions of
the generalized nonlinear Schr\"odinger equation based on the new concept of
angular pseudomomentum. We consider the symmetric solitons of a generalized
nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus
of the field. We provide a rigorous proof of a set of mathematical results
justifying that these solitons can be classified according to the irreducible
representations of a discrete group. Then we extend this theory to
non-stationary solutions and study the relationship between angular momentum
and pseudomomentum. We illustrate these theoretical results with numerical
examples. Finally, we explore the possibilities of the generalization of the
previous framework to the quantum limit.Comment: 18 pages; submitted to Physica
Sine-Gordon Soliton on a Cnoidal Wave Background
The method of Darboux transformation, which is applied on cnoidal wave
solutions of the sine-Gordon equation, gives solitons moving on a cnoidal wave
background. Interesting characteristics of the solution, i.e., the velocity of
solitons and the shift of crests of cnoidal waves along a soliton, are
calculated. Solutions are classified into three types (Type-1A, Type-1B,
Type-2) according to their apparent distinct properties.Comment: 11 pages, 5 figures, Contents change
Demonstration of all-optical beam steering in modulated photonic lattices
We demonstrate experimentally all-optical beam steering in modulated photonic
lattices induced optically by three beam interference in a biased
photorefractive crystal. We identify and characterize the key physical
parameters governing the beam steering, and show that the spatial resolution
can be enhanced by the additional effect of nonlinear beam self-localization.Comment: 3 pages, 3 figure
Shaping soliton properties in optical Mathieu lattices
We address basic properties and stability of two-dimensional solitons in
photonic lattices induced by the nondiffracting Mathieu beams. Such lattices
allow for smooth topological transformation of radially symmetric Bessel
lattices into quasi-one-dimensional periodic ones. The transformation of
lattice topology drastically affects properties of ground-state and dipole-mode
solitons, including their shape, stability and transverse mobility.Comment: 14 pages, 4 figures, to appear in Optics Letter
Soliton control in chirped photonic lattices
We study optical solitons in chirped periodic optical lattices whose
amplitude or frequency changes in the transverse direction. We discover that
soliton propagation in such lattices can be accompanied by the progressive
self-bending of the soliton trajectory, and we show that the soliton bending
rate and output position can be controlled by varying the lattice depth, as
well as the chirp amplitude and frequency modulation rate. This effect has
potential applications for controllable soliton steering and routing.Comment: 13 pages, 3 figures, submitted to Journal of the Optical Society of
America
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