3,139 research outputs found
Optical pulse propagation in fibers with random dispersion
The propagation of optical pulses in two types of fibers with randomly
varying dispersion is investigated. The first type refers to a uniform fiber
dispersion superimposed by random modulations with a zero mean. The second type
is the dispersion-managed fiber line with fluctuating parameters of the
dispersion map. Application of the mean field method leads to the nonlinear
Schr\"odinger equation (NLSE) with a dissipation term, expressed by a 4th order
derivative of the wave envelope. The prediction of the mean field approach
regarding the decay rate of a soliton is compared with that of the perturbation
theory based on the Inverse Scattering Transform (IST). A good agreement
between these two approaches is found. Possible ways of compensation of the
radiative decay of solitons using the linear and nonlinear amplification are
explored. Corresponding mean field equation coincides with the complex
Swift-Hohenberg equation. The condition for the autosolitonic regime in
propagation of optical pulses along a fiber line with fluctuating dispersion is
derived and the existence of autosoliton (dissipative soliton) is confirmed by
direct numerical simulation of the stochastic NLSE. The dynamics of solitons in
optical communication systems with random dispersion-management is further
studied applying the variational principle to the mean field NLSE, which
results in a system of ODE's for soliton parameters. Extensive numerical
simulations of the stochastic NLSE, mean field equation and corresponding set
of ODE's are performed to verify the predictions of the developed theory.Comment: 17 pages, 7 eps figure
Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices
Properties of localized states on array of BEC confined to a potential,
representing superposition of linear and nonlinear optical lattices are
investigated. For a shallow lattice case the coupled mode system has been
derived. The modulational instability of nonlinear plane waves is analyzed. We
revealed new types of gap solitons and studied their stability. For the first
time a moving soliton solution has been found. Analytical predictions are
confirmed by numerical simulations of the Gross-Pitaevskii equation with
jointly acting linear and nonlinear periodic potentials.Comment: 9 pages, 14 figure
Dynamical localization of matter wave solitons in managed barrier potentials
The bright matter wave soliton propagation through a barrier with a rapidly
oscillating position is investigated. The averaged over rapid oscillations
Gross-Pitaevskii (GP) equation is derived. It is shown that the soliton is
dynamically trapped by the effective double-barrier.
The analytical predictions for the soliton effective dynamics is confirmed by
the numerical simulations of the full GP equation.Comment: 10 pages, 6 figure
Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length
Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate
under periodic variation in time of the atomic scattering length have been
studied analytically and numerically. The time-dependent variational approach
is used for the analysis of the characteristics of nonlinear resonances in the
oscillations of the condensate. The bistability in oscillations of the BEC
width is invistigated. The dependence of the BEC collapse threshold on the
drive amplitude and parameters of the condensate and trap is found. Predictions
of the theory are confirmed by numerical simulations of the full
Gross-Pitaevski equation.Comment: 17 pages, 10 figures, submitted to Journal of Physics
Tunable Modulational Instability Sidebands via Parametric Resonance in Periodically Tapered Optical Fibers
We analyze the modulation instability induced by periodic variations of group
velocity dispersion and nonlinearity in optical fibers, which may be
interpreted as an analogue of the well-known parametric resonance in mechanics.
We derive accurate analytical estimates of resonant detuning, maximum gain and
instability margins, significantly improving on previous literature on the
subject. We also design a periodically tapered photonic crystal fiber, in order
to achieve narrow instability sidebands at a detuning of 35 THz, above the
Raman maximum gain peak of fused silica. The wide tunability of the resonant
peaks by variations of the tapering period and depth will allow to implement
sources of correlated photon pairs which are far-detuned from the input pump
wavelength, with important applications in quantum optics.Comment: 15 pages, 7 figure
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