Search results for " Nonlinear"
showing 10 items of 1224 documents
Modulational instability processes in optical isotropic fibers under dual- frequency circular polarization pumping
2002
Experiments are presented showing that, under dual-frequency, circular polarization pumping, host modulational instability processes can be generated in a single-mode isotropic fiber by careful tuning of the frequency spacing between the pumps.
Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems
2001
We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverg…
Stochastic Response Of Fractionally Damped Beams
2014
Abstract This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system. Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional de…
COMPUTER SIMULATION OF PROFILES OF INTERFACES BETWEEN COEXISTING PHASES: DO WE UNDERSTAND THEIR FINITE SIZE EFFECTS?
2000
Interfaces between coexisting phases are very common in condensed matter physics, and thus many simulations attempt to characterize their properties, in particular, the interfacial tension and the interfacial profile. However, while theory usually deals with the "intrinsic profile", the latter is not a straightforward output of a simulation: The actual profile (observed in simulations and/or experiments!) is broadened by lateral fluctuations. Therefore, in the usual simulation geometry of L × L × L (in three dimensions), where one chooses suitable boundary conditions to stabilize one or two interfaces of (minimal) area L × L, the profile (and in particular the interfacial width) depends on…
Self-dressing and radiation reaction in classical electrodynamics
2002
A canonical approach to self-dressing in classical electrodynamics is presented. A slowly moving, rigid charge distribution is assumed to be completely deprived of the transverse electric E⊥ at an initial time t1' and the development of this component of the field is studied for t > t1' by solving the coupled charge-field Hamilton equations of motion. The theory is specialized to charge distributions of spherical symmetry, and in particular the point-charge, the spherical shell of charge and the spherical volume of charge are considered. As for the dynamics of the charge, the radiation-reaction force during self-dressing is obtained and it is shown to be substantially different at short tim…
Universal description of pattern formation in optical oscillators under bichromatic injection
2018
We study pattern formation in a complex Swift–Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems submitted to a bichromatic injection when the instability is toward long (transverse) wavelengths. Applications include two-level lasers and photorefractive oscillators. Under such an injection, the original continuous phase symmetry of the system is replaced by a discrete one and phase bistability emerges. This leads to the spontaneous formation of phase-locked spatial structures, such as phase domains and dark-ring (phase) cavity solitons. The stability o…
Inelastic scattering and interactions of three-wave parametric solitons.
2006
We study the interactions of velocity-locked three-wave parametric solitons in a medium with quadratic nonlinearity and dispersion. We reveal that the inelastic scattering between three-wave solitons and linear waves may be described in terms of analytical solutions with dynamically varying group velocity, or boomerons. Moreover, we demonstrate the elastic nature of three-wave soliton-soliton collisions and interactions.
Line of polarization attraction in highly birefringent optical fibers
2014
We investigate the phenomenon of polarization attraction in a highly birefringent fiber. This polarization process originates from the nonlinear interaction of two counter-propagating beams. We show that all polarization states of the forward (signal) beam are attracted toward a specific line of polarization states on the surface of the Poincare sphere, whose characteristics are determined by the polarization state of the injected backward (pump) beam. This phenomenon of polarization attraction takes place without any loss of energy for the signal beam. The stability of different stationary solutions is also discussed through intensive numerical simulations. On the basis of mathematical tec…
Electro-optic time lens with an extended time aperture
2010
We propose what we believe to be a new approach to correct the residual aberrations of time lenses implemented through electro-optic sinusoidal phase modulation. The method is based on a single modulator driven with various harmonic channels coming from the same clock signal. Proper weighting of the amplitude and phase of the channels allows us to achieve nearly perfect parabolic phase modulation over a fraction of the clock period. We show numerically that our proposal only requires three harmonics of the clock frequency to achieve truly parabolic modulation over a time window that extends across 70% of the period. We illustrate the benefits of this aberration-free scheme in a pulse compre…
Monte-Carlo Study of Pure-Phase Cumulants of 2D q-State Potts Models
1997
We performed Monte Carlo simulations of the two-dimensional q-state Potts model with q=10, 15, and 20 to study the energy and magnetization cumulants in the ordered and disordered phase at the first-order transition point $\beta_t$. By using very large systems of size 300 x 300, 120 x 120, and 80 x 80 for q=10, 15, and 20, respectively, our numerical estimates provide practically (up to unavoidable, but very small statistical errors) exact results which can serve as a useful test of recent resummed large-q expansions for the energy cumulants by Bhattacharya `et al.' [J. Phys. I (France) 7 (1997) 81]. Up to the third order cumulant and down to q=10 we obtain very good agreement, and also the…