Du chaos deterministe au bruit dans des systèmes optiques avec retard

An optical device with a variational structure driven by a delayed feedback, F(x(t — d)) = sinAx(t — d) is shown to display high dimensional chaos with dimension increasing linearly with two parameters, the delay d and the feedback frequency A . For large delay d and large frequency A, the system is shown to display Gaussian-Markovian statistics like a system driven b y a white noise. Decreasing the frequency A leads to effects very similar to those of a colored noise, and decreasing the dela y leads to quite special phenomena like phase transitions, giving rise to new peaks in the probability distribution . An analytica l description using the tools of stochastic equations agrees with the numerical results .Un système optique possédant une structure variationnelle, et forcé par une rétro-injection retardée, F(x(t - d)) = sin Ax(t- d), émet un signal lumineux chaotique dont la dimension croit linéairement avec deux paramètres, le retard d et la fréquence A. Pour de grandes valeurs du retard et de la fréquence, le signal émis a une statistique Gaussienne et Markovienne, comme la solution d'une équation de Langevin forcée par un bruit blanc. Lorsqu'on diminue la valeur du paramètre A, la statistique est modifiée comme celle d'une équation de Langevin forcée par un bruit coloré. Lorsqu'on diminue le retard, de nouveaux pics apparaissent dans la distribution de probabilité, comme dans les transitions de phase induites par du bruit coloré. Une description analytique utilisant les méthodes des signaux aléatoires permet d'interpréter les résultats numériques

Chaos and the Quantum Phase Transition in the Dicke Model

We investigate the quantum chaotic properties of the Dicke Hamiltonian; a quantum-optical model which describes a single-mode bosonic field interacting with an ensemble of $N$ two-level atoms. This model exhibits a zero-temperature quantum phase transition in the N \go \infty limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite $N$ and, by analysing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase-transition. Our considerations of the wavefunction indicate that this is connected with a delocalisation of the system and the emergence of macroscopic coherence. We also derive a semi-classical Dicke model, which exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.Comment: 51 pages, 15 figures, late

SPATIOTEMPORAL INSTABILITIES IN A SATURABLE HOMOGENEOUSLY BROADENED RING CAVITY

L'influence des effets transverses dus à la diffraction libre sur la dynamique nonlinéaire d'une cavité haute finesse est étudiée dans différentes configurations optiques. La nature des deux premières bifurcations semble être très robuste mais le seuil d'apparition du chaos est fortement diminué.The influence of transverse effects caused by free-space propagation on the nonlinear dynamics of a high finesse ring cavity is investigated for different optical configurations. The nature of the first two Hopf bifurcations is found to be robust against significative transverse effects but the threshold for chaos is lowered with respect to the plane wave case

LYAPUNOV VECTORS TREATMENT FOR BIFURCATIONS IN RETARDED DIFFERENTIAL SYSTEMS

L'analyse de Lyapunov est une méthode très efficace pour décrire les bifurcations des solutions périodiques dans les systèmes à retard.The Lyapunov analysis is shown to be very heuristic for describing bifurcation of T-periodic solution in delay systems

Theory of self phase-locked optical parametric oscillators

RevTeX file + 11 figures (.jpg format)The plane-wave dynamics of 3*omega => (2*omega, omega) subharmonic optical parametric oscillators containing a second harmonic generator of the idler wave omega is analyzed analytically by using the meanfield approximation and numerically by taking into account the field propagation inside the media. The resonant Chi(2):Chi(2) cascaded second-order nonlinearities induce a mutual injection-locking of the signal and idler waves that leads to coherent self phase-locking of the pump and subharmonic waves, freezing the phase diffusion noise. In case of signal-and-idler resonant devices, largely detuned sub-threshold states occur due to a subcritical bifurcation, broadening out the self-locking frequency range to a few cavity linewidths

Theory of self phase-locked optical parametric oscillators

RevTeX file + 11 figures (.jpg format)The plane-wave dynamics of 3*omega => (2*omega, omega) subharmonic optical parametric oscillators containing a second harmonic generator of the idler wave omega is analyzed analytically by using the meanfield approximation and numerically by taking into account the field propagation inside the media. The resonant Chi(2):Chi(2) cascaded second-order nonlinearities induce a mutual injection-locking of the signal and idler waves that leads to coherent self phase-locking of the pump and subharmonic waves, freezing the phase diffusion noise. In case of signal-and-idler resonant devices, largely detuned sub-threshold states occur due to a subcritical bifurcation, broadening out the self-locking frequency range to a few cavity linewidths