E. Ressayre

Striped and circular domain walls in the DOPO

A family of circular and striped domain walls with oscillatory tails have been observed with the propagation model for the DOPO that is more general than the mean-field model. The same structures are observed with diffraction inside or outside the cell, showing that diffraction and nonlinearity may be decoupled. They result from the switching of the signal amplitude, from the positive to the negative solution. They are formed for positive and negative signal detunings of order unity, in a wide range of input pump amplitude. A second-order MacLaurin expansion mapping model is found to agree well with the propagation model.

Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator

We study the dynamics of the formation of circular domain walls, which are large-intensity structures, in a degenerate optical parametric oscillator. We show that the mean-field and the propagation models predict the same increase in the domain size proportional to t(1/3) .

Self-induced generation of an off-axis frequency shifted radiation from atoms

Abstract The transient resonant linear response at wavelength λa of an N two-level atom vapor driven by a strong pulse with wavelength λf = λa - |Δλ| is shown to promote an emission of radiation peaked at wavelength λc = λa + |Δλ| in a conical shell around the propagation axis of the incident beam. In the limit of weak excitation, i.e. for an incident Rabi frequency much smaller than the detuning, the cone angle is found to be equal to 2λμ(2N/ch|Δλ|) 1 2 where μ is the transition dipole moment.

Simulation and analysis of the flower-like instability in the single-feedback mirror experiment with rubidium vapor

Flower-like patterns are numerically investigated when the schematic Rb four-level relevant transition is reduced to the lower two Zeeman sub-levels via the adiabatic elimination of the upper states. These flower-like patterns are the signature of small aspect ratio while typical patterns like squares are displayed in the opposite limit. Depending on the relative weights of diffraction effects and nonlinearities, they display, or not, self-similar shapes in the near and the far field.

Kinetics of domain walls in the degenerate optical parametric oscillator

The kinetics of the domain walls that occur in the degenerate optical parametric oscillator are studied within the propagation model. The formation of large intensity peaks for null and positive signal mistuning is shown to be associated with a dynamical scaling law ~t1/3. In the parameter range where the degenerate optical parametric operator reduces to potential systems, the growth law ~t1/2 is observed. It is also obtained for negative mistuning of order unity, and up to three times above the threshold, i.e.?beyond the validity range of the Swift-Hohenberg model equation. In addition, we describe the labyrinth formation which displays self-similar growth with the law ~t1/5.

Beyond the Mean-Field Model of the Ring Cavity

Abstract The ring cavity device with large diffraction path in the free-space of the cavity cannotbe described within the mean-field model. It is shown to generate a large variety of monoconicaland multiconical patterns with wave and/or Turing modes, for anonlinear medium either made of two-level atoms or with a χ (2) crystal.Even in the limit of a single-longitudinal mode operation, monoconical structures can be differentfrom those predicted by the mean-field model. For instance, chaotic localized structures with anatomic medium and square patterns with a DOPO are presented.

Lyapunov analysis of the ruelle-takens route to chaos in an optical retarded differential system

Abstract The Lyapunov analysis of low-dimensional instabilities in retarded differential systems predicts both the Hopf bifurcation thresholds and the fundamental frequencies. A demonstration is made in a saturable thin sample ring cavity.

Role of the phase mismatch on the structures generated in an optical parametric oscillator

The effects of the phase mismatch are analysed within the propagation model for the degenerate optical parametric oscillator (DOPO). The transverse structures generated via a modulational instability are found to be strongly dependent on the mistuning of the signal and the phase mismatch. Islands of squares, quasi-hexagons and zigzags are found to emerge from a sea of stripes, in the plane defined by the two mistunings.

Gain and reflectivity characteristics of self-oscillations in self- feedback and delayed feedback devices

Abstract In counterpropagating waves devices, multiwave mixing involves gain and reflectivity properties for the forward and the backward probes and idlers that are shown to be related to both gain and reflectivity of the intrinsic system without any mirror. In the later case, gain and reflectivity of a probe field are shown to vary strongly with the angular frequency of the probe; actually the reflectivity is especially depending on whether it is associated with a convective instability or an absolute instability, vanishing in the first case but diverging in the second case. The occurrence of a self-oscillation at a given frequency in either a half-cavity device or a Fabry-Perot interferometer is demonstrated to depend not only on the gain that such a probe would realize through the system without mirrors but also on its reflectivity properties at the cell exit. For example the self-oscillation in a Fabry-Perot interferometer occurs in the Rabi frequency domain not because a probe might be strongly amplified, as usually stated, but because its reflectivity at the cell exit has to be negligible. Differently, the half-cavity device chooses its own threshold frequency for the self-oscillation to occur where the probe reflectivity matrix has elements of magnitude of order unit, irrespective of its gain. In both cases the behaviour is seen to be a consequence of the boundary conditions imposed by the optics.

Phase Transitions Induced by Deterministic Delayed Forces

The frontier between noise and deterministic chaos was recently shown1 to be free, in the sense that the very simple deterministic retarded equation n n