Chaotically spiking attractors in suspended-mirror optical cavities

Generation of Optical Frequency Comb via Giant Optomechanical Oscillation

Optical frequency combs (OFCs) are essential in precision metrology, spectroscopy, distance measurement, and optical communications. Significant advances have been made recently in achieving micro-OFC devices based on parametric frequency conversion or electro-optic phase modulation. Here, we demonstrate a new kind of microcomb using a cavity optomechanical system with giant oscillation amplitude. We observe both optical and microwave frequency combs in a microtoroid resonator, which feature a flat OFC with 938 comb lines and a repetition rate as low as 50.22 MHz, as well as a flat microwave frequency comb with 867 comb lines. To generate such giant oscillation amplitude, we excite an overcoupled optical mode with a large blue detuning that is assisted with the thermo-optic nonlinearity. A new type of nonlinear oscillation, induced by competition between the optomechanical oscillation and thermo-optic nonlinearity, is also observed.

Canard resonance: on noise-induced ordering of trajectories in heterogeneous networks of slow-fast systems

We analyse the dynamics of a network of semiconductor lasers coupled via their mean intensity through a non-linear optoelectronic feedback loop. We establish experimentally the excitable character of a single node, which stems from the slow-fast nature of the system, adequately described by a set of rate equations with three well separated time scales. Beyond the excitable regime, the system undergoes relaxation oscillations where the nodes display canard dynamics. We show numerically that, without noise, the coupled system follows an intricate canard trajectory, with the nodes switching on one by one. While incorporating noise leads to a better correspondence between numerical simulations and experimental data, it also has an unexpected ordering effect on the canard orbit, causing the nodes to switch on closer together in time. We find that the dispersion of the trajectories of the network nodes in phase space is minimized for a non-zero noise strength, and call this phenomenon canard resonance.

Self-excited oscillation and synchronization of an on-fiber optomechanical cavity

We study a fully on-fiber optomechanical cavity and characterize its performance as a sensor. The cavity is formed by patterning a suspended metallic mirror near the tip of an optical fiber and by introducing a static reflector inside the fiber. Optically induced self-excited oscillation (SEO) is observed above a threshold value of the injected laser power. The SEO phase can be synchronized by periodically modulating the optical power that is injected into the cavity. Noise properties of the system in the region of synchronization are investigated. Moreover, the spectrum is measured near different values of the modulation frequency, at which phase locking occurs. A universal behavior is revealed in the transition between the regions of phase locked and free running SEO.

Devil's staircase in an optomechanical cavity

We study self-excited oscillations (SEOs) in an on-fiber optomechanical cavity. While the phase of SEOs randomly diffuses in time when the laser power injected into the cavity is kept constant, phase locking may occur when the laser power is periodically modulated in time. We investigate the dependence of phase locking on the amplitude and frequency of the laser-power modulation. We find that phase locking can be induced with a relatively low modulation amplitude provided that the ratio between the modulation frequency and the frequency of SEOs is tuned close to a rational number of relatively low hierarchy in the Farey tree. To account for the experimental results, a one-dimensional map, which allows evaluating the time evolution of the phase of SEOs, is theoretically derived. By calculating the winding number of the one-dimensional map, the regions of phase locking can be mapped in the plane of modulation amplitude and modulation frequency. Comparison between the theoretical predictions and the experimental findings yields a partial agreement.

Synchronization in an optomechanical cavity

We study self-excited oscillations (SEO) in an on-fiber optomechanical cavity. Synchronization is observed when the optical power that is injected into the cavity is periodically modulated. A theoretical analysis based on the Fokker-Planck equation evaluates the expected phase space distribution (PSD) of the self-oscillating mechanical resonator. A tomography technique is employed for extracting PSD from the measured reflected optical power. Time-resolved state tomography measurements are performed to study phase diffusion and phase locking of the SEO. The detuning region inside which synchronization occurs is experimentally determined and the results are compared with the theoretical prediction.

Coexisting attractors and chaotic canard explosions in a slow-fast optomechanical system

The multiple time scale dynamics induced by radiation pressure and photothermal effects in a high-finesse optomechanical resonator is experimentally studied. At difference with two-dimensional slow-fast systems, the transition from the quasiharmonic to the relaxational regime occurs via chaotic canard explosions, where large-amplitude relaxation spikes are separated by an irregular number of subthreshold oscillations. We also show that this regime coexists with other periodic attractors, on which the trajectories evolve on a substantially faster time scale. The experimental results are reproduced and analyzed by means of a detailed physical model of our system.

Forced and self-excited oscillations of an optomechanical cavity

We experimentally study forced and self-excited oscillations of an optomechanical cavity, which is formed between a fiber Bragg grating that serves as a static mirror and a freely suspended metallic mechanical resonator that serves as a moving mirror. In the domain of small amplitude mechanical oscillations, we find that the optomechanical coupling is manifested as changes in the effective resonance frequency, damping rate, and cubic nonlinearity of the mechanical resonator. Moreover, self-excited oscillations of the micromechanical mirror are observed above a certain optical power threshold. A comparison between the experimental results and a theoretical model that we have recently derived and analyzed yields a good agreement. The comparison also indicates that the dominant optomechanical coupling mechanism is the heating of the metallic mirror due to optical absorption.

Mixed-mode oscillations via canard explosions in light-emitting diodes with optoelectronic feedback

Chaotically spiking attractors in semiconductor lasers with optoelectronic feedback have been recently observed to be the result of canard phenomena in three-dimensional phase space (incomplete homoclinic scenarios). Since light-emitting diodes display the same dynamics and are much more easily controllable, we use one of these systems to complete the attractor analysis demonstrating experimentally and theoretically the occurrence of complex sequences of periodic mixed-mode oscillations. In particular, we investigate the transition between periodic and chaotic mixed-mode states and analyze the effects of the unavoidable experimental noise on these transitions.

Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows

Infinite cascades of periodicity hubs were predicted and very recently observed experimentally to organize stable oscillations of some dissipative flows. Here we describe the global mechanism underlying the genesis and organization of networks of periodicity hubs in control parameter space of a simple prototypical flow, namely a Rössler's oscillator. We show that spirals associated with periodicity hubs emerge and accumulate at the folding of certain fractal-like sheaves of Shilnikov homoclinic bifurcations of a common saddle-focus equilibrium. The specific organization of hub networks is found to depend strongly on the interaction between the homoclinic orbits and the global structure of the underlying attractor.