A. Tallet

Daisy patterns in the passive ring cavity with diffusion effects

Near-field patterns with three to fifteen petals set on a single circle are numerically observed in the ring cavity device. Three to six petal daisies result from usual finite size effects. We point out the non-trivial formation of seven to fifteen petal daisies, with a top-hat input, and a small diffusion term that controls this daisy-type pattern formation, preventing the usual hexagonal structure to be formed.

Rotating spiral waves in a nonlinear optical system with spatial interactions

Abstract The formation of multi-petals and multi-spirals is analysed with the help of a generalized dispersion relation, taking advantage of the invariance of the rotation frequency of a pattern. It results in an eigenvalue problem, which allows us to predict the rotation frequency and the radial curvature of the pattern, in good agreement with exact calculations: A stationary pattern is predicted to look like petals, while a uniform rotating pattern is predicted to have some curvature, leading to a spiral shape.

Spatial patterns in a passive ring cavity with atoms

Abstract We present numerical simulations of a simplified model for the ring cavity device in the case of round-trip time equal to the atomic radiative lifetime. Real pattern effects are of primordial importance, especially in small systems where the boundary conditions seem the key for the pattern selection. For a plane-wave input, our system displays not only hexagons, as in the mean-field model, but also stationary rolls, squares and octagons with a weakly chaotic structure. All these structures are also obtained in the case of bell-shaped input profile with large aspect ratio; they even appear regular and wonderful, as if boundary effects stabilize them.

Quasi-trapping of Gaussian beams in two-level systems

Large scale quasi-trapping of Gaussian beams in a two-level-atom medium is displayed. The well-known ray theory provides a condition for the possibility of quasi-straight ray paths only in the case of a strongly saturated medium. For weak saturation, the ray paths can never be quasi-straight lines; the beam necessarily undergoes reshaping, as emphasized by Wagner et al. [ Phys. Rev.175, 256 ( 1968)]. Nevertheless, the moment theory displays a quasi-constant mean-radius condition that gives rise to fairly good trapping. These conditions are supported by numerical simulations. Quasi-trappings are displayed over many tens of Rayleigh lengths. Experiments, such as conical emission, that might involve trapping are discussed.

Why does a Ginzburg-Landau diffraction equation become a diffusion equation in the passive ring cavity?

The Swift-Hohenberg diffusion-type equation is shown to be the normal form of the purely diffraction-type Ginzburg-Landau equation for the passive and saturable ring cavity in the vicinity of nascent hysteresis.

Raman emission versus dopplerons in a two-level atomic cell

Dopplerons are the signature of the nonlinear response of moving atoms driven by a continuous standing-wave laser beam. They display maxima on the velocity-dependent atomic population difference at velocities nearly equal to ±(c/ω)[(δ(ω2 + 2Ω2)1/2/(2p + 1)], where Ω is the Rabi frequency associated with an individual beam field and δω is the detuning between the driving frequency and the center of the Doppler linewidth. Probing the device with a weak signal yields gain for Doppler broadenings of the magnitude of the detuning, exclusively on the atomic-resonance-frequency side, with a maximum shifted from the driving frequency by the generalized Rabi frequency associated with a standing wave, defined by (δω2 + 4Ω2)1/2. The existence of dopplerons is demonstrated by peaks occurring at frequencies shifted from the driving frequency by even harmonics of doppleron frequencies. The intensity of the peaks is shown to depend on the Doppler width, and the complexity of the gain curve is shown to increase as the pump intensity does.

Threshold and large amplitude self-oscillations in a saturable Rayleigh-gain ring cavity

Periodic instabilities which occur in the output beam of a ring cavity containing a short cell of passive homogeneously broadened two-level atoms are studied as a function of the atomic detuning and the mode spacing in a high-finesse cavity. The output characteristics are found to be very sensitive to the round-trip time of the light through the cavity and to the refractive index. Conditions for the occurrence of large-amplitude self-oscillation are given in terms of these two parameters. >

Kinetics of the formation of domain walls in the degenerate optical parametric oscillator

Summary form only given. In a degenerate optical parametric oscillator (DOPO) the non-trivial homogeneous signal amplitude presents a /spl pi/-phase indetermination, giving rise to the formation of walls separating the two /spl pi/-phase domains. The kinetics of the phase separation from an initial 50%-50% mixture of positive and negative domains, is studied with the help of the average domain size, proportional to the inverse of the interface length.

Patterns and Quasi-Patterns in a the Single Feedback Mirror Device

Spontaneous transverse pattern formation in nonlinear optical feedback systems is a subject of rapidly growing interest. Especially, the scheme of a I<err-medium with a single feedback mirror proposed by Firth et al. [I] has been proved to bc a very fertile concept for studies of optical pattern formation because it uncovers the fundamental role of the coupling between diffraction and the nonlinearity of the medium. Experimentally we realized large-aperture patterns in a single feedback mirror system using a high sensitive optically addressable liquid crystal light valve (LCLV) as a dispersive optical nonlinearity [2]. A more complex and fascinating situation is predicted for a single feedback mirror system including polarization modulation [3] where the system has a lot of formal similarities to dispersive nonlinear ring resonators like optical bistability and related phenomena. In this context the initial detuning from maximum transmission becomes an important and experimentally easy accessible control parameter. Depending on this parameter we investigate transitions between different types of spontaneously formed patterns. With increasing control parameter we observed localized bright spots which evolve on arbitrary positions and switch in a smooth melting-process to negative hexagons followed by transitions to stripes and positve hexagons. This sequence of different patterns is periodically repeated until the reorientation of the liquid crystal layer saturates. Using a short pulse of a second laser we induce the switching of localised states at defined positions. Due to transverse effects like self-focusing, a bright spot on a dark homogeneous background becomes a stable and robust solution. We discovered the typical scaling behaviour of noncritical slowing down in the switching characteristics related to the existence of an unstable branch which separates the basins of attraction of two stable states. Besides the applications as solitary units for binary information encoding, localized states can be considered as fundamental building elements describing the behaviour of complex systems 141. We present first experimental results showing the interaction of solitary spots and how they form regular patterns. Additionally, numerical simulations are carried out which confirm the experimental results.

From disorder to ordering in the pattern formation of a ring cavity device

this prediction is confirmed by numerical simulations of our model equations on a periodic domain for a variety of parameter values. Although rolls dominate close to threshold, other exotic structures exist and appear to be stable. Figure 1 shows the stationary solution that prevails at 50% above threshold for B = 2 (A = 0), 0 = 1. The underlying structure consists of rolls, and we see several defects including dislocations, a disclination at the top, and a Roman arch. Figure 2 shows the solution at 10% above threshold for the same parameter values. Again rolls are the dominating structure, but we also see a target pattem. In either case, decreasing the intensity causes the pattems to melt and form straight parallel rolls. ‘Optical Sciences Center, University of Arizona, Tucson AZ 85721, USA ‘Department of Physics and Applied Physics, University of Strathclyde, Glasgow G4 ONC, Scotland