Combination of two basic types of synchronization in a coupled semiconductor laser system

Combination of two basic types of synchronization, anticipatory synchronization and lagged synchronization, is investigated numerically between two coupled semiconductor lasers. It is found that lagged synchronization produced by a backward coupling with a suitable delay can combine with the originally hidden anticipatory synchronization and produce a type of synchronization overcoming the original lagged synchronization produced by a forward coupling. We study the combination synchronization phenomenon when the delay of the backward coupling is different from that of the original anticipatory synchronization. Our results suggest that the synchronization combination phenomenon might allow an interpretation of an experimental observation by Sivaprakasam et al. [Phys. Rev. Lett. 87, 154101 (2001)] that the anticipating time is irrespective of the external-cavity round trip time, which to date remains to be understood.     

Pattern selection and stabilization in an annular CO laser

The formation and stabilization of spatio-temporal patterns in an annular CO₂ laser is studied. We give experimental and numerical evidence of the role of a small spatial perturbation (consisting of a thin metallic wire inserted in the optical cavity) in the selection and stabilization of patterns. Received 15 December 1999     

Pattern dynamics in an annular laser

Competition among modes in an annular CO₂ laser has been experimentally and numerically analyzed. During the coexistence of different patterns, each of them resulting from the interaction of two transverse modes with opposite angular momentum, chaos has been experimentally detected. A numerical model, derived from the Maxwell-Bloch equations and including symmetry breaking terms, enables the interpretation of the main experimental features. Received 10 March 2000     

Multiphase patterns in self-phase-locked optical parametric oscillators

Multiphase patterns are found in a mean-field model of a singly-resonant optical parametric oscillator that converts a pump field at frequency 3ω into signal and idler fields at frequencies 2ω and ω. A complex Ginzburg-Landau equation without diffusion and with a quadratic phase-sensitive nonlinear term is derived under single-longitudinal and paraxial propagation approximations. Owing to the phase-matched multistep parametric process ω + ω = 2ω, phase locking of the resonated signal field is possible with three distinct phase states. Three-armed rotating spirals, target patterns and light filamentation are found by a numerical analysis of the mean-field equation. Received 19 April 2001 and Received in final form 21 June 2001     

Thermomechanical effects in uniformly aligned dye-doped nematic liquid crystals

We show theoretically that thermomechanical effects in dye-doped nematic liquid crystals when illuminated by laser beams, can become important and lead to molecular reorientation at intensities substantially lower than that needed for optical Fréedericksz transition. We propose a 1D model that assumes homogenous intensity distribution in the plane of the layer and is capable to describe such a thermally induced threshold lowering. We consider a particular geometry, with a linearly polarized light incident perpendicularly on a layer of homeotropically aligned dye-doped nematics.     

The effect of the asymptotic response dynamics on the generalized synchronization

Generalized synchronization in a drive-response Chua circuits is investigated. A cascade of transitions to GS is observed with increasing the interaction strength. The mechanism on the transitions to GS is given based on the asymptotic behaviors of response dynamics.     

Statistical properties for a class of nonlinear squeezed states

Theoretical investigations of dynamical behavior in optical parametric oscillators (OPO) have generally assumed that the cavity detunings of the interacting fields are controllable parameters. However, OPOs are known to experience mode hops, where the system jumps to the mode of lowest cavity detuning. We note that this phenomenon significantly limits the range of accessible detunings and thus may prevent instabilities predicted to occur above a minimum detuning from being evidenced experimentally. As a simple example among a number of instability mechanisms possibly affected by this limitation, we discuss the Hopf bifurcation leading to periodic behavior in the monomode mean-field model of a triply resonant OPO and show that it probably can be observed only in very specific setups.     

Light-induced instabilities driven by competing helical patterns in long-pitch cholesterics

We study theoretically the dynamical reorientation phenomena when a long-pitch cholesteric liquid-crystal film with homeotropic alignment is illuminated by a circularly polarized lightwave. In the present case, the natural cholesteric pitch is of the order of (or larger than) the film thickness. The helical cholesteric structure is thus frustrated by the boundary conditions without illumination. However, above a light intensity threshold reorientation occurs and the bifurcation scenario depends strongly on the natural cholesteric pitch. Recalling that a long-pitch cholesteric is achieved in practice by adding a small amount of chiral agents in a nematic liquid crystal, the observed dynamics can be viewed as the result of the competition between intrinsic and extrinsic unidimensional helical patterns. The intrinsic part consists of the helical deformations induced by the chirality of the dopant, whereas the extrinsic part is related to the chirality induced by the optical field through the non-uniform angular momentum transfer of light to a nematic. The all-optical analog in the case of a pure nematic (without chiral dopant), is also discussed.     

Bistable behaviour in squeezed vacua: I. Stationary analysis

A time-independent theoretical and numerical analysis of an optical bistable model of two-level atoms in a ring cavity, driven by a coherent field and in contact with a squeezed vacuum field is presented in the two cases of absorptive and dispersive optical bistability (OB). In the former case, a suitable choice of the phase of the squeezed vacuum field reduces the threshold for OB to occur compared with the normal vacuum case. In the latter case, regions of OB are identified as one or two disconnected simple closed curves depending on the cooperation parameter [0pt] : is the maximum possible value of the critical value of C at fixed values of the squeezed vacuum field parameters. Phase switching effects between different (output) states of the system is investigated in detail. In the absorptive case, one- or two-way optical switching is possible depending on [0pt] . We also present results which demonstrate more complicated switching behaviour in the dispersive case. Received 12 March 1999 and Received in final form 20 August 1999     

The pulse shape of a passively Q-switched microchip laser

The shape of the intensity pulse of a passively Q-switched microchip laser is investigated numerically and analytically. Our analysis is motivated by independent microchip laser experiments exhibiting nearly symmetric pulses in the case of a semiconductor saturable absorber and asymmetric pulses in the case of a solid state saturable absorber. Asymptotic methods are used to determine limiting behaviors of the pulse shape for both symmetric and asymmetric pulses. In the first case, we determine a sech² solution parametrized by one parameter which can be determined by solving two coupled nonlinear algebraic equations. In the second case, the pulse solution is decomposed into two distinct approximations exhibiting different amplitude and time scales properties. We review earlier approximations of the repetition rate and the pulse width. Received 2 August 1999     

Adaptive synchronization of weighted complex dynamical networks through pinning

This paper considers the problem of controlling weighted complex dynamical networks by applying adaptive control to a fraction of network nodes. We investigate the local and global synchronization of the controlled dynamical network through the construction of a master stability function and a Lyapunov function. Analytical results show that a certain number of nodes can be controlled by using adaptive pinning to ensure the synchronization of the entire network. We present numerical simulations to verify the effectiveness of the proposed scheme. In comparison with feedback pinning, the proposed pinning control scheme is robust when tested by noise, different weighting and coupling structures, and time delays.     

Effect of delay on phase locking in a pulse coupled neural network

Using a slightly simplified version of the integrate and fire model of a neural network with delay, I study the stability of the phase-locked state dependent on the coupling between the neurons and especially on a delay time. The coupling between neurons may be arbitrary. It is shown that the phase-locked state becomes less stable with increasing delay and that relaxation oscillations occur. Received 28 December 1999 and Received in final form 13 June 2000     

Coupling induced topological transition in a ring of chaotic oscillators

A ring of diffusively coupled R?ssler oscillators, which can develop the conventional rotating wave from high-dimensional chaos by increasing the coupling ɛ continuously is studied. The chaotic generator for the rotating wave emerges around ɛ = ɛ, where the topological transition induced by the coupling not only changes the topological structure of all the oscillators, which share a common strange attractor, but also changes them into being different from each other. Starting from this transition, infinitely long range temporal correlation and spatial order in the style of antiphase state are established gradually, which gives rise to the chaotic generator of the rotating wave. Received 15 March 2001     

Electron impact single and double ionization of argon

Stable two-mode, and three-mode oscillations due to the spatial hole burning effect were observed experimentally with the increase of the pump power ratio in a laser-diode pumped sub-nanosecond microchip Cr,Yb:YAG self-Q-switched multimode laser. The stability of the output pulse trains was attributed to the mode coupling through antiphase dynamics between different modes. Modified multimode rate equations including the spatial hole-burning effect in the active medium and the non-linear absorption of the saturable absorber were proposed. Numerical simulations of the antiphase dynamics of such a laser were in good agreement with the experimental data, and the antiphase dynamics were explained by the evolution of the inversion population and the bleaching and recovery of the inversion population of the saturable absorber.     

Stochastic and coherence resonance in lasers: homoclinic chaos and polarization bistability

We report Stochastic Resonance and Coherence Resonance phenomena in experiments using CO₂ lasers. First, we consider a polarized laser with feedback; for suitable feedback parameters, the laser intensity undergoes homoclinic chaos consisting in the return to a saddle focus, where noise controls the permanence time around the saddle. Second, we discuss a quasi-isotropic laser where noise induces switching between two intensity components with mutually orthogonal polarization.     

Globally coupled systems with prescribed synchronized dynamics

A system of globally coupled maps whose synchronized dynamics differs from the individual (chaotic) evolution is considered. For nonchaotic synchronized dynamics, the synchronized state becomes stable at a critical coupling intensity lower than that of the fully chaotic case. Below such critical point, synchronization is also stable in a set of finite intervals. Moreover, the system is shown to exhibit multistability, so that even when the synchronized state is stable not all the initial conditions lead to synchronization of the ensemble. Received 22 October 1999     

Radiation pressure induced instabilities in laser interferometric detectors of gravitational waves

The large scale interferometric gravitational wave detectors consist of Fabry-Perot cavities operating at very high powers ranging from tens of kW to MW for next generations. The high powers may result in several nonlinear effects which would affect the performance of the detector. In this paper, we investigate the effects of radiation pressure, which tend to displace the mirrors from their resonant position resulting in the detuning of the cavity. We observe a remarkable effect, namely, that the freely hanging mirrors gain energy continuously and swing with increasing amplitude. It is found that the “time delay”, that is, the time taken for the field to adjust to its instantaneous equilibrium value, when the mirrors are in motion, is responsible for this effect. This effect is likely to be important in the optimal operation of the full-scale interferometers such as VIRGO and LIGO. Received 12 July 1999     

Modulation instability induced by periodic power variation in soliton fiber ring lasers

Modulation instability with subsideband generation induced by periodic power variation in soliton fiber ring lasers is reported. We found that different wavelength shifts of subsideband generation are related to different periodic power variation. The period of power variation and wavelength shifts of subsideband can be changed by altering the linear cavity phase delay. It is also found that the periodic power variation is caused by the interaction between the nonuniform polarization state of the circulating light and the polarizer in the laser cavity.