Stochastic resonance with phase noise in an integrated nano-electro-mechanical photonic crystal membrane

Summary form only given. In a large number of experiments or devices, noise is usually viewed as an undesirable disturbance, hindering the measurement sensitivity or device performances. In some circumstances however, noise-induced phenomena can help, as in the case of stochastic resonance whereby a small coherent signal gets amplified resonantly by application of external noise. Stochastic resonance occurs in a wide class of nonlinear systems, in neurobiology [1], mesoscopic physics [2], photonics [3], atomic physics [4], mechanics [5, 6]... Stochastic resonance is a kind of synchronization of the switching events. If a weak periodic forcing is applied to the oscillator, the initially symmetrical double-well potential gets tilted asymmetrically up and down, periodically raising and lowering the potential barrier. Although the periodic forcing is too weak to let the membrane switch periodically from one potential well into the other one, noise-induced hopping between the potential wells can become synchronized with the weak period forcing. This time coincidence takes place when the average waiting time between noise-induced interwell transitions is comparable with half the period of the periodic forcing. Thus stochastic resonance corresponds to the noise-assisted amplification of a weak coherent input that is too feeble to induce hopping between the two stable states. In order to match these conditions, an in-depth characterization of these time-scales is performed for our mechanical resonator which consists of an InP suspended photonic crystal membrane (Fig. 1a) with a thickness of about 260 nm and a 10×20μm2 surface. The coherent weak signal is introduced by applying a modulated electrostatic force on the membrane and driving its out-of-plane motion. This force is generated by applying an AC-bias at the frequency of the fundamental mechanical resonance, on integrated interdigitated electrodes placed underneath the membrane at a distance of about 400 nm (Fig. 1a). In the same manner, phase noise is added on the AC applied voltage, which is proportional the actuation force. Last, the mechanical response of the membrane is probed optically in an interferometric testbed, in which the membrane is used as one of the end mirrors.