In this work, we study the nonlinear dynamics of two elastically coupled micro-membranes. These MHz-resonators are capacitively driven by a pair of integrated interdigitated electrodes. Each membrane is suspended over a 350 nm air gap constituting a Fabry-Pérot cavity used to optomechanically read-out its displacement with a 633 nm laser. The linear regime analysis of the system reveals a strong constitutive difference of the resonators natural frequencies as well as a weak coupling regime. The system is strongly driven to reach a nonlinear regime that is described with a two coupled Duffing resonators model. We report the emergence of classical chaos when the resonant driving force is modulated with a low frequency (kHz) pump. The experimental bifurcation diagrams corresponding to the change of low frequency pump and amplitude of this modulation are numerically reproduced. We discuss the dissipative aspect of the problem that plays a crucial role in the pump frequency range allowing the chaotic regimes to be reached. This system constitutes an interesting base for the fundamental investigation of the collective dynamics of an array of nonlinear resonators. Additionally, our bifurcation diagrams exhibits several brutal dynamical changes often referred as “extreme events”. We consider using these highly sensitive points in the parameters space as working points for chaos based sensing applications.
In ordinary consciousness, noise is associated with the term “hindrance”; it is considered as a nuisance that can lead to communication or signal transmission failure or prevent the detection of a weak signal to be measured. However, under certain conditions the impact of noise can be counter-intuitively a resource. In nonlinear systems, noise can induce novel regimes leading to the formation of synchronized structures, coherence between the output and the input of resonators or even to the amplification of weak signals. In other words, noise can play a constructive role, with potential benefits for signal processing or measurement for instance.
Single or coupled Nano-Opto-ElectroMechanical resonators whose design is based on suspended photonic crystal membrane could be used as a toy-system to pursue two main goals: stochastic amplification and chaos. As such noise-aided processes might have a strong impact in noise-assisted applications including signal processing or sensing.
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