Search results for "Nonlinear"
showing 10 items of 3684 documents
Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension
2011
International audience; We analyze the role of soliton solutions and Hamiltonian singularities in the dynamics of counterpropagating waves in a medium of finite spatial extension. The soliton solution can become unstable due to the finite extension of the system. We show that the spatiotemporal dynamics then relaxes toward a Hamiltonian singular state of a nature different than that of the soliton state. This phenomenon can be explained through a geometrical analysis of the singularities of the stationary Hamiltonian system.
INFLUENCE OF THE INITIAL PHASE PROFILE ON THE ASYMPTOTIC SELF-SIMILAR PARABOLIC DYNAMICS
2009
International audience; We describe the influence of the initial phase profile on the convergence towards asymptotic self-similar parabolic shape. More precisely, based on numerical simulations, we discuss the impact of an initial linear chirp and a p phase shift. If the parabolic shape has been found to describe accurately the pulse envelope, dark structures can appear and evolve also self-similarly on the parabolic background.
Dissipative soliton in a laser cavity: A novel concept in action
2006
International audience; The recent concept of a dissipative optical soliton sheds new light for understanding the stability of optical pulses that are generated in passively mode-locked lasers. Considering in these lasers the multiple pulsing regime of operation, the dissipative soliton concept is able to explain the great diversity of interaction behaviours that have been observed experimentally. Among the most spectacular behaviours are the formation of "soliton molecules" and "elastic-type" collisions. The dissipative soliton also explains the existence of complex limit cycles of pulsations within single pulse operation.
Toward a thermodynamic description of supercontinuum generation
2008
International audience; We consider the incoherent nonlinear regime of the supercontinuum generation process in optical fibers. We show that, under certain conditions, the phenomenon of spectral broadening inherent to the supercontinuum generation may be described by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the supercontinuum generation process may be regarded as a thermalization process, which is characterized by an irreversible evolution of the optical field toward a thermodynamic equilibrium state, i.e., the state of maximum nonequilibrium entropy.
Rogue waves, rational solitons and wave turbulence theory
2011
International audience; Considering a simple one dimensional nonlinear Schrödinger optical model, we study the existence of rogue wave events in the highly incoherent state of the system and compare them with the recently identified hierarchy of rational soliton solutions. We show that rogue waves can emerge in the genuine turbulent regime and that their coherent deterministic description provided by the rational soliton solutions is compatible with an accurate statistical description of the random wave provided by the wave turbulence theory. Furthermore, the simulations reveal that even in the weakly nonlinear regime, the nonlinearity can play a key role in the emergence of an individual r…
Nonlinear spectrum broadening cancellation by sinusoidal phase modulation
2017
International audience; We propose and experimentally demonstrate a new approach to dramatically reduce the spectral broadening induced by self-phase modulation occurring in a Kerr medium. By using a temporal sinusoidal phase modulation, we efficiently cancel to a large extend the chirp induced by the nonlinear effect. Experimental validation carried out in a passive or amplifying fiber confirm the interest of the technic for the mitigation of spectral expansion of long pulses.
Emergence of spectral incoherent solitons through supercontinuum generation in photonic crystal fibers
2011
International audience; We report an experimental and numerical study of the spontaneous emergence of spectral incoherent solitons through supercontinuum generation in a two zero-dispersionwavelengths photonic crystal fiber. By using a simple experimental setup, we show that the highly nonlinear regime of supercontinuum generation is characterized by the emergence of a spectral incoherent soliton in the low-frequency edge of the supercontinuum spectrum. We show that a transition occurs from the discrete spectral incoherent soliton to its continuous counterpart as the power of the laser is increased. Contrary to conventional solitons, spectral incoherent solitons do not exhibit a confinement…
Vibrating soliton pairs in a mode-locked laser cavity
2006
International audience; We show numerically the existence of vibrating soliton pairs that are consistent with observations performed with a passively mode-locked fiber laser. These vibrating pairs are new types of multisoliton complexes that exist in the vicinity of the phase-locked soliton pairs discovered a few years ago [Opt. Lett. 27, 966 (2002)]. The pairs are found numerically with a laser propagation model that includes nonlinear dissipation and cavity periodicity, and they can appear following a Hopf-type bifurcation when a cavity parameter is tuned.
Control of nonlinear instabilities in Bessel beams using shaped longitudinal intensity profiles
2017
International audience; We show that tailored longitudinal intensity shaping of a non-diffracting Bessel beam can strongly reduce four wave mixing induced oscillations and stabilize nonlinear propagation at ablation-level intensities
The Peregrine breather of order nine and its deformations with sixteen parameters solutions to the NLS equation
2015
Abstract We construct new deformations of the Peregrine breather ( P 9 ) of order 9 with 16 real parameters. With this method, we obtain explicitly new families of quasi-rational solutions to the NLS equation in terms of a product of an exponential depending on t by a ratio of two polynomials of degree 90 in x and t; when all the parameters are equal to 0, we recover the classical P 9 breather. We construct new patterns of different types of rogue waves as triangular configurations of 45 peaks as well as rings and concentric rings.