Search results for "Nonlinear system"
showing 10 items of 1446 documents
Modulational instability and critical regime in a highly birefringent fiber
1996
We report experimental observations of modulational instability of copropagating waves in a highly birefringent fiber for the normal dispersion regime. We first investigate carefully the system behavior by means of nonlinear Schr\"odinger equations and phase-matching conditions, and then, experimentally, we use two distinct techniques for observing MI (modulational instability) in the fiber; namely, the single-frequency copropagation, where two pump waves of identical frequency copropagate with orthogonal polarizations parallel to the two birefringence axes of the fiber, and the two-frequency copropagation, where the two polarized waves copropagate with different frequencies. In both cases …
Nonlinear plasmonic amplification via dissipative soliton-plasmon resonances
2017
In this contribution we introduce a new strategy for the compensation of plasmonic losses based on a recently proposed nonlinear mechanism: the resonant interaction between surface plasmon polaritons and spatial solitons propagating in parallel along a metal/dielectric/Kerr structure. This mechanism naturally leads to the generation of a quasi-particle excitation, the so-called soliplasmon resonance. We analyze the role played by the effective nonlinear coupling inherent to this system and how this can be used to provide a new mechanism of quasi-resonant nonlinear excitation of surface plasmon polaritons. We will pay particular attention to the introduction of asymmetric linear gain in the …
Numerical study of the stability of the Peregrine solution
2017
International audience; The Peregrine solution to the nonlinear Schrödinger equations is widely discussed as a model for rogue waves in deep water. We present here a detailed fully nonlinear numerical study of high accuracy of perturbations of the Peregrine solution as a solution to the nonlinear Schrödinger (NLS) equations.We study localized and nonlocalized perturbations of the Peregrine solution in the linear and fully nonlinear setting. It is shown that the solution is unstable against all considered perturbations.
Light self-confinement via second harmonic generation in a 2D nonlinear photonic crystal waveguide
2007
Spatial solitary waves induced by quadratic nonlinearities have been the subject of many theoretical and experimental investigations in the last decade, with extensive studies being devoted to soliton formation in 1D nonlinear photonic crystals (NPC) such as PPLN (periodically poled LiNbO3). Here we present results on a new class of (1 + 1)D spatial solitary waves, the first examples of quadratic self-confinement in a 2D NPC.
Existence and orbital stability of standing waves to nonlinear Schr��dinger system with partial confinement
2018
We are concerned with the existence of solutions to the following nonlinear Schr\"odinger system in $\mathbb{R}^3$: \begin{equation*} \left\{ \begin{aligned} -\Delta u_1 + (x_1^2+x_2^2)u_1&= \lambda_1 u_1 + \mu_1 |u_1|^{p_1 -2}u_1 + \beta r_1|u_1|^{r_1-2}u_1|u_2|^{r_2}, \\ -\Delta u_2 + (x_1^2+x_2^2)u_2&= \lambda_2 u_2 + \mu_2 |u_2|^{p_2 -2}u_2 +\beta r_2 |u_1|^{r_1}|u_2|^{r_2 -2}u_2, \end{aligned} \right. \end{equation*} under the constraint \begin{align*} \int_{\mathbb{R}^3}|u_1|^2 \, dx = a_1>0,\quad \int_{\mathbb{R}^3}|u_2|^2 \, dx = a_2>0, \end{align*} where $\mu_1, \mu_2, \beta >0, 2 1, r_1 + r_2 < \frac{10}{3}$. In the system, the parameters $\lambda_1, \lambda_2 \in \R$ are unknown …
A numerical study of postshock oscillations in slowly moving shock waves
2003
Abstract Godunov-type methods and other shock capturing schemes can display pathological behavior in certain flow situations. This paper discusses the numerical anomaly associated to slowly moving shocks. We present a series of numerical experiments that illustrate the formation and propagation of this pathology, and allows us to establish some conclusions and question some previous conjectures for the source of the numerical noise. A simple diagnosis on an explicit Steger-Warming scheme shows that some intermediate states in the first time steps deviate from the true direction and contaminate the flow structure. A remedy is presented in the form of a new flux split method with an entropy i…
Giant collective incoherent shock waves in strongly nonlinear turbulent flows
2016
Contrary to conventional coherent shocks, we show theoretically and experimentally that nonlocal turbulent flows lead to the emergence of large-scale incoherent shock waves, which constitute a collective phenomenon of the incoherent field as a whole.
Nonlinear theory of slow light.
2011
In the framework of the nonlinear Λ model, propagation of solitons was analysed in atomic vapours and Bose–Einstein condensates. The complicated nonlinear interplay between fast and slow-light solitons in a Λ -type medium was shown to facilitate control of its optical transparency and formation of optical gates. An exact analytical description was given for the deceleration, stopping and revival of slow-light solitons in the experimentally relevant non-adiabatic regime. A stopping slow-light soliton imprints a localized immobile polarization pattern in the medium, which, as explicitly demonstrated here, can be used as a bit of readable optical memory. The whole process can be controlled wi…
Stationary and Pulsating Dissipative Optical Bullets
2006
We demonstrate the existence of stable optical light bullets in nonlinear dissipative media. Beyond the domain where stable bullets are found, unstable bullets show unusual behaviors, like "optical rockets", pulsating solutions or pattern formation.
Switching dynamics of dark-pulse Kerr frequency comb states in optical microresonators
2021
Dissipative Kerr solitons are localized structures that exist in nonlinear optical cavities. They lead to the formation of microcombs - chip-scale frequency combs that could facilitate precision frequency synthesis and metrology by capitalizing on advances in silicon photonics. Previous demonstrations have mainly focused on anomalous dispersion cavities. Notwithstanding, localized structures also exist in the normal dispersion regime in the form of circulating dark pulses, but their physical dynamics is far from being understood. Here, we explore dark-pulse Kerr combs generated in normal dispersion optical microresonators and report the discovery of reversible switching between coherent dar…