Search results for "Linear system"
showing 10 items of 1558 documents
Dissipative Solitons: present understanding, applications and new developments
2009
Dissipative solitons form a new paradigm for the investigation of phenomena involving stable structures in nonlinear systems far from equilibrium. Basic principles can be applied to a wide range of phenomena in science. Recent results involving solitons and soliton complexes of the complex cubic-quintic Ginzburg–Landau equation are presented.
Spatiotemporal optical solitons in nonlinear dissipative media: From stationary light bullets to pulsating complexes
2007
Nonlinear dissipative systems display the full (3+1) D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1) D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation. © 2007 American Institute of Physics.
Vibrating and shaking soliton pairs in dissipative systems
2007
We show that two-soliton solutions in nonlinear dissipative systems can exist in various forms. As with single solitons, they can be stationary, periodic or chaotic. In particular, we find new types of vibrating and shaking soliton pairs. Each type of pair is stable in the sense that the bound state exists in the same form indefinitely. © 2006 Elsevier B.V. All rights reserved.
Wave turbulence in integrable systems: nonlinear propagation of incoherent optical waves in single-mode fibers.
2011
International audience; We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a statistically stationary state. The evolution of the power spectrum of the field is characterized by the rapid growth of spectral tails that exhibit damped oscillations, until the whole spectrum ultima…
Regions of Existence and Transformations of (3+1)-D Dissipative Optical Solitons
2006
We demonstrate the existence of stable optical light bullets in nonlinear dissipative media featuring both normal and anomalous chromatic dispersion. Beyond the domain where stable bullets are found, unstable bullets can be transformed into "rockets".
Peregrine soliton in optical fiber-based systems
2011
International audience; We report the first observation in optics of the Peregrine soliton, a novel class of nonlinear localized structure. Two experimental configurations are explored and the impact of non-ideal initial conditions is discussed.
Numerical Maps for Fiber Lasers Mode Locked with Nonlinear Polarization Evolution: Comparison with Semi-Analytical Models
2008
We have used a fully vectorial model based on two coupled nonlinear Schrodinger equations to study mode locking and pulse generation initiated and stabilized by nonlinear polarization evolution in a stretched pulse, double-clad, Yb-doped, fiber laser. The model takes explicitly into account gain saturation, finite amplification bandwidth, Kerr-induced self- and cross-phase modulations, group velocity dispersion, polarization control, and linear birefringence. Complete maps versus the orientation of intra-cavity wave-plates have been established. They comprise a large variety of pulse regimes that can be simply obtained by turning the intracavity wave-plate: stable single pulse per round tri…
Optimal control and shortcuts to adiabaticity techniques in linear and non-linear systems : from ion cyclotron resonance to nuclear magnetic resonance
2021
The goal of our research is to develop efficient and robust control protocols for classical and quantum systems. To this end, we have applied optimal control theory (OCT) and shortcuts to adiabaticity (STA) with inverse engineering and motion planning approaches in three different examples, which are RC (Resistor Capacitor) circuits, Fourier Transform-Ion Cyclotron Resonance (FT-ICR), and Nuclear Magnetic Resonance (NMR). Some of our results are not limited to these systems but are rather general. We apply OCT and STA with an inverse engineering approach to control the time-evolution of the charge on a capacitor. We show that OCT is a member of the family of STA solutions. In order to contr…
Near-field control of optical bistability in a nanocavity
2009
Micro- and nanocavities allow for strong light confinement in very small volume [1]. They give opportunities for new experiments such as cavity quantum electrodynamics, waveguiding, light slowing or trapping…[2] The increase of the electromagnetic (EM) field in the cavity enhances the interaction between light and matter, resulting in the possible observation of nonlinear effects [3]. Several studies have recently been published on the observation and characterisation of nonlinear silicon cavities [4]. As a step further, we propose and demonstrate the feasibility of an innovative way to mechanically control the bistable operating regime of a nanovavity. Using a near-field tip, we switch the…
Nonlinear Sculpturing of Optical Pulses in Fibre Systems
2019
The interplay among the effects of dispersion, nonlinearity and gain/loss in optical fibre systems can be efficiently used to shape the pulses and manipulate and control the light dynamics and, hence, lead to different pulse-shaping regimes [1,2]. However, achieving a precise waveform with various prescribed characteristics is a complex issue that requires careful choice of the initial pulse conditions and system parameters. The general problem of optimisation towards a target operational regime in a complex multi-parameter space can be intelligently addressed by implementing machine-learning strategies. In this paper, we discuss a novel approach to the characterisation and optimisation of …