1,439 research outputs found
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.Comment: 12 pages, 11 figures; To be published in: Proceedings of the Dynamics
Days Asia-Pacific: First International Conference on Nonlinear Science
(Hong-Kong, 13-16 July, 1999), Editor: Bambi Hu (Elsevier Publishers, 2000
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.Comment: Submitted to PRL. 4 pages with 5 figure
Small noise asymptotic of the timing jitter in soliton transmission
We consider the problem of the error in soliton transmission in long-haul
optical fibers caused by the spontaneous emission of noise inherent to
amplification. We study two types of noises driving the stochastic focusing
cubic one dimensional nonlinear Schr\"{o}dinger equation which appears in
physics in that context. We focus on the fluctuations of the mass and arrival
time or timing jitter. We give the small noise asymptotic of the tails of these
two quantities for the two types of noises. We are then able to prove several
results from physics among which the Gordon--Haus effect which states that the
fluctuation of the arrival time is a much more limiting factor than the
fluctuation of the mass. The physical results had been obtained with arguments
difficult to fully justify mathematically.Comment: Published in at http://dx.doi.org/10.1214/07-AAP449 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Vector-soliton collision dynamics in nonlinear optical fibers
We consider the interactions of two identical, orthogonally polarized vector
solitons in a nonlinear optical fiber with two polarization directions,
described by a coupled pair of nonlinear Schroedinger equations. We study a
low-dimensional model system of Hamiltonian ODE derived by Ueda and Kath and
also studied by Tan and Yang. We derive a further simplified model which has
similar dynamics but is more amenable to analysis. Sufficiently fast solitons
move by each other without much interaction, but below a critical velocity the
solitons may be captured. In certain bands of initial velocities the solitons
are initially captured, but separate after passing each other twice, a
phenomenon known as the two-bounce or two-pass resonance. We derive an analytic
formula for the critical velocity. Using matched asymptotic expansions for
separatrix crossing, we determine the location of these "resonance windows."
Numerical simulations of the ODE models show they compare quite well with the
asymptotic theory.Comment: 32 pages, submitted to Physical Review
A nonpolynomial Schroedinger equation for resonantly absorbing gratings
We derive a nonlinear Schroedinger equation with a radical term, in the form
of the square root of (1-|V|^2), as an asymptotic model of the optical medium
built as a periodic set of thin layers of two-level atoms, resonantly
interacting with the electromagnetic field and inducing the Bragg reflection. A
family of bright solitons is found, which splits into stable and unstable
parts, exactly obeying the Vakhitov-Kolokolov criterion. The soliton with the
largest amplitude, which is |V| = 1, is found in an explicit analytical form.
It is a "quasi-peakon", with a discontinuity of the third derivative at the
center. Families of exact cnoidal waves, built as periodic chains of
quasi-peakons, are found too. The ultimate solution belonging to the family of
dark solitons, with the background level |V| = 1, is a dark compacton, also
obtained in an explicit analytical form. Those bright solitons which are
unstable destroy themselves (if perturbed) attaining the critical amplitude,
|V| = 1. The dynamics of the wave field around this critical point is studied
analytically, revealing a switch of the system into an unstable phase.
Collisions between bright solitons are investigated too. The collisions between
fast solitons are quasi-elastic, while slowly moving ones merge into breathers,
which may persist or perish (in the latter case, also by attaining |V| = 1).Comment: Physical Review A, in pres
The Discrete Nonlinear Schr\"odinger equation - 20 Years on
We review work on the Discrete Nonlinear Schr\"odinger (DNLS) equation over
the last two decades.Comment: 24 pages, 1 figure, Proceedings of the conference on "Localization
and Energy Transfer in Nonlinear Systems", June 17-21, 2002, San Lorenzo de
El Escorial, Madrid, Spain; to be published by World Scientifi
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