194 research outputs found
Modulational Instability in Bose-Einstein Condensates under Feshbach Resonance Management
We investigate the modulational instability of nonlinear Schr{\"o}dinger
equations with periodic variation of their coefficients. In particular, we
focus on the case of the recently proposed, experimentally realizable protocol
of Feshbach Resonance Management for Bose-Einstein condensates. We derive the
corresponding linear stability equation analytically and we show that it can be
reduced to a Kronig-Penney model, which allows the determination of the windows
of instability. The results are tested numerically in the absence, as well as
in the presence of the magnetic trapping potential
Dynamics of subpicosecond dispersion-managed soliton in a fibre: A perturbative analysis
A model is studied which describes a propagation of a subpicosecond optical
pulse in dispersion-managed fibre links. In the limit of weak chromatic
dispersion management, the model equation is reduced to a perturbed modified
NLS equation having a nonlinearity dispersion term. By means of the
Riemann--Hilbert problem, a perturbation theory for the soliton of the modified
NLS equation is developed. It is shown in the adiabatic approximation that
there exists a unique possibility to suppress the perturbation-induced shift of
the soliton centre at the cost of proper matching of the soliton width and
nonlinearity dispersion parameter. In the next-order approximation, the
spectral density of the radiation power emitted by a soliton is calculated.Comment: 16 pages, 3 figures, to appear in J. Mod. Optic
Modulation instabilities in birefringent two-core optical fibers
Previous studies of the modulation instability (MI) of continuous waves (CWs) in a two-core fibre (TCF) did not consider effects caused by co-propagation of the two polarized modes in a TCF that possesses birefringence, such as cross-phase modulation (XPM), polarization-mode dispersion (PMD) and polarization-dependent coupling (PDC) between the cores. This paper reports an analysis of these effects on the MI by considering a linear-birefringence TCF and a circular-birefringence TCF, which feature different XPM coefficients. The analysis focuses on the MI of the asymmetric CW states in the TCFs, which have no counterparts in single-core fibres. We find that the asymmetric CW state exists when its total power exceeds a threshold (minimum) value, which is sensitive to the value of the XPM coefficient. We consider, in particular, a class of asymmetric CW states that admit analytical solutions. In the anomalous dispersion regime, without taking the PMD and PDC into account, the MI gain spectra of the birefringent TCF, if scaled by the threshold power, are almost identical to those of the zero-birefringence TCF. However, in the normal dispersion regime, the power-scaled MI gain spectra of the birefringent TCFs are distinctly different from their zero-birefringence counterparts, and the difference is particularly significant for the circular-birefringence TCF, which takes a larger XPM coefficient. On the other hand, the PMD and PDC only exert weak effects on the MI gain spectra. We also simulate the nonlinear evolution of the MI of the CW inputs in the TCFs and obtain good agreement with the analytical solutions.postprin
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Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrodinger lattices
We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities. Several species of stationary solutions are constructed, and bifurcations linking their families are investigated using parameter continuation starting from the anti-continuum limit, and also with the help of a variational approximation. In particular, a species of hybrid solitons, intermediate between the site- and bond-centered types of the localized states (with no counterpart in the 1D model), is analyzed in 2D and 3D lattices. We also discuss the mobility of multi-dimensional discrete solitons that can be set in motion by lending them kinetic energy exceeding the appropriately defined Peierls–Nabarro barrier; however, they eventually come to a halt, due to radiation loss
Tunability and Robustness of Dirac Points of Photonic Nanostructures
We study the tunability and robustness of photonic Dirac points (DPs) in plasmonic nanostructures. The tunability of the DP is demonstrated in graphene-based photonic superlattices by adjusting the graphene permittivity via the optical Kerr effect or electrical doping. The robustness of DPs is demonstrated in plasmonic lattices by showing that even very high levels of disorder are unable to localize the modes located near the DP. The robustness of the DP also manifests itself in the fact that the inversely-proportional dependence of the transmission on the lattice length near the DP remains unchanged under strong disorder
Accumulation of embedded solitons in systems with quadratic nonlinearity
Previous numerical studies have revealed the existence of embedded solitons
(ESs) in a class of multi-wave systems with quadratic nonlinearity, families of
which seem to emerge from a critical point in the parameter space, where the
zero solution has a fourfold zero eigenvalue. In this paper, the existence of
such solutions is studied in a three-wave model. An appropriate rescaling casts
the system in a normal form, which is universal for models supporting ESs
through quadratic nonlinearities. The normal-form system contains a single
irreducible parameter , and is tantamount to the basic model of
type-I second-harmonic generation. An analytical approximation of WKB type
yields an asymptotic formula for the distribution of discrete values of
at which the ESs exist. Comparison with numerical results shows
that the asymptotic formula yields an exact value of the scaling index, -6/5,
and a fairly good approximation for the numerical factor in front of the
scaling term.Comment: 25 pages, 4 figure
Nonlinear vortex light beams supported and stabilized by dissipation
We describe nonlinear Bessel vortex beams as localized and stationary
solutions with embedded vorticity to the nonlinear Schr\"odinger equation with
a dissipative term that accounts for the multi-photon absorption processes
taking place at high enough powers in common optical media. In these beams,
power and orbital angular momentum are permanently transferred to matter in the
inner, nonlinear rings, at the same time that they are refueled by spiral
inward currents of energy and angular momentum coming from the outer linear
rings, acting as an intrinsic reservoir. Unlike vortex solitons and dissipative
vortex solitons, the existence of these vortex beams does not critically depend
on the precise form of the dispersive nonlinearities, as Kerr self-focusing or
self-defocusing, and do not require a balancing gain. They have been shown to
play a prominent role in "tubular" filamentation experiments with powerful,
vortex-carrying Bessel beams, where they act as attractors in the beam
propagation dynamics. Nonlinear Bessel vortex beams provide indeed a new
solution to the problem of the stable propagation of ring-shaped vortex light
beams in homogeneous self-focusing Kerr media. A stability analysis
demonstrates that there exist nonlinear Bessel vortex beams with single or
multiple vorticity that are stable against azimuthal breakup and collapse, and
that the mechanism that renders these vortexes stable is dissipation. The
stability properties of nonlinear Bessel vortex beams explain the experimental
observations in the tubular filamentation experiments.Comment: Chapter of boo
Periodic waves in fiber Bragg gratings
Author name used in this publication: P. K. A. Wai2007-2008 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe
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