61 research outputs found
Numerical instability of the Akhmediev breather and a finite-gap model of it
In this paper we study the numerical instabilities of the NLS Akhmediev
breather, the simplest space periodic, one-mode perturbation of the unstable
background, limiting our considerations to the simplest case of one unstable
mode. In agreement with recent theoretical findings of the authors, in the
situation in which the round-off errors are negligible with respect to the
perturbations due to the discrete scheme used in the numerical experiments, the
split-step Fourier method (SSFM), the numerical output is well-described by a
suitable genus 2 finite-gap solution of NLS. This solution can be written in
terms of different elementary functions in different time regions and,
ultimately, it shows an exact recurrence of rogue waves described, at each
appearance, by the Akhmediev breather. We discover a remarkable empirical
formula connecting the recurrence time with the number of time steps used in
the SSFM and, via our recent theoretical findings, we establish that the SSFM
opens up a vertical unstable gap whose length can be computed with high
accuracy, and is proportional to the inverse of the square of the number of
time steps used in the SSFM. This neat picture essentially changes when the
round-off error is sufficiently large. Indeed experiments in standard double
precision show serious instabilities in both the periods and phases of the
recurrence. In contrast with it, as predicted by the theory, replacing the
exact Akhmediev Cauchy datum by its first harmonic approximation, we only
slightly modify the numerical output. Let us also remark, that the first rogue
wave appearance is completely stable in all experiments and is in perfect
agreement with the Akhmediev formula and with the theoretical prediction in
terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv
admin note: text overlap with arXiv:1707.0565
Vectorial dissipative solitons in vertical-cavity surface-emitting Lasers with delays
We show that the nonlinear polarization dynamics of a vertical-cavity
surface-emitting laser placed into an external cavity leads to the formation of
temporal vectorial dissipative solitons. These solitons arise as cycles in the
polarization orientation, leaving the total intensity constant. When the cavity
round-trip is much longer than their duration, several independent solitons as
well as bound states (molecules) may be hosted in the cavity. All these
solutions coexist together and with the background solution, i.e. the solution
with zero soliton. The theoretical proof of localization is given by the
analysis of the Floquet exponents. Finally, we reduce the dynamics to a single
delayed equation for the polarization orientation allowing interpreting the
vectorial solitons as polarization kinks.Comment: quasi final resubmission version, 12 pages, 9 figure
Polarisation dynamics of vector soliton molecules in mode locked fibre laser
Two fundamental laser physics phenomena - dissipative soliton and polarisation of light are recently merged to the concept of vector dissipative soliton (VDS), viz. train of short pulses with specific state of polarisation (SOP) and shape defined by an interplay between anisotropy, gain/loss, dispersion, and nonlinearity. Emergence of VDSs is both of the fundamental scientific interest and is also a promising technique for control of dynamic SOPs important for numerous applications from nano-optics to high capacity fibre optic communications. Using specially designed and developed fast polarimeter, we present here the first experimental results on SOP evolution of vector soliton molecules with periodic polarisation switching between two and three SOPs and superposition of polarisation switching with SOP precessing. The underlying physics presents an interplay between linear and circular birefringence of a laser cavity along with light induced anisotropy caused by polarisation hole burning
Observation of bright polariton solitons in a semiconductor microcavity
Microcavity polaritons are composite half-light half-matter quasi-particles,
which have recently been demonstrated to exhibit rich physical properties, such
as non-equilibrium Bose-Einstein condensation, parametric scattering and
superfluidity. At the same time, polaritons have some important advantages over
photons for information processing applications, since their excitonic
component leads to weaker diffraction and stronger inter-particle interactions,
implying, respectively, tighter localization and lower powers for nonlinear
functionality. Here we present the first experimental observations of bright
polariton solitons in a strongly coupled semiconductor microcavity. The
polariton solitons are shown to be non-diffracting high density wavepackets,
that are strongly localised in real space with a corresponding broad spectrum
in momentum space. Unlike solitons known in other matter-wave systems such as
Bose condensed ultracold atomic gases, they are non-equilibrium and rely on a
balance between losses and external pumping. Microcavity polariton solitons are
excited on picosecond timescales, and thus have significant benefits for
ultrafast switching and transfer of information over their light only
counterparts, semiconductor cavity lasers (VCSELs), which have only nanosecond
response time
A generic travelling wave solution in dissipative laser cavity
A large family of cosh-Gaussian travelling wave solution of a complex Ginzburg–Landau equation (CGLE), that describes dissipative semiconductor laser cavity is derived. Using perturbation method, the stability region is identified. Bifurcation analysis is done by smoothly varying the cavity loss coefficient to provide insight of the system dynamics. He’s variational method is adopted to obtain the standard sech-type and the notso-explored but promising cosh-Gaussian type, travelling wave solutions. For a given set of system parameters, only one sech solution is obtained, whereas several distinct solution points are derived for cosh-Gaussian case. These solutions yield a wide variety of travelling wave profiles, namely Gaussian, near-sech, flat-top and a cosh-Gaussianwith variable central dip. A split-step Fourier method and pseudospectral method have been used for direct numerical solution of the CGLE and travelling wave profiles identical to the analytical profiles have been obtained. We also identified the parametric zone that promises an extremely large family of cosh-Gaussian travelling wave solutions with tunable shape. This suggests that the cosh-Gaussian profile is quite generic and would be helpful for further theoretical as well as experimental investigation on pattern formation, pulse dynamics andlocalization in semiconductor laser cavity
Double-Wall Carbon Nanotube Hybrid Mode-Locker in Tm-doped Fibre Laser: A Novel Mechanism for Robust Bound-State Solitons Generation
The complex nonlinear dynamics of mode-locked fibre lasers, including a broad variety of dissipative structures and self-organization effects, have drawn significant research interest. Around the 2 μm band, conventional saturable absorbers (SAs) possess small modulation depth and slow relaxation time and, therefore, are incapable of ensuring complex inter-pulse dynamics and bound-state soliton generation. We present observation of multi-soliton complex generation in mode-locked thulium (Tm)-doped fibre laser, using double-wall carbon nanotubes (DWNT-SA) and nonlinear polarisation evolution (NPE). The rigid structure of DWNTs ensures high modulation depth (64%), fast relaxation (1.25 ps) and high thermal damage threshold. This enables formation of 560-fs soliton pulses; two-soliton bound-state with 560 fs pulse duration and 1.37 ps separation; and singlet+doublet soliton structures with 1.8 ps duration and 6 ps separation. Numerical simulations based on the vectorial nonlinear Schr¨odinger equation demonstrate a transition from single-pulse to two-soliton bound-states generation. The results imply that DWNTs are an excellent SA for the formation of steady single- and multi-soliton structures around 2 μm region, which could not be supported by single-wall carbon nanotubes (SWNTs). The combination of the potential bandwidth resource around 2 μm with the soliton molecule concept for encoding two bits of data per clock period opens exciting opportunities for data-carrying capacity enhancement.M.C. acknowledges the support of EU Horizon2020 Marie S.-Curie IF MINDFLY project. A.E.B. acknowledges the support of Russian Science Foundation (grant 14-21-00110). M.A.A. acknowledges the support of Ministry of Higher Education Sultanate of Oman. T.H. acknowledges the support of Royal Academy of Engineering Fellowship (Graphlex). The support by the Marie-Curie Inter-national Research Staff Exchange Scheme “TelaSens” project, Research Executive Agency Grant No. 269271, Programme: FP7-PEOPLE-2010-IRSES and European Research Council through the FP7-IDEAS-ERC grant ULTRALASER are gratefully acknowledged
Temporal cavity solitons buffering optical data
Packets of light persisting in a continuously driven nonlinear resonator in the time domain offer new possibilities not only for applications in all-optical storage, pulse reshaping and wavelength conversion, but also for fundamental experiments in nonlinear science
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