Self-Induced Oscillations in an Optomechanical System Driven by Bolometric Backaction

Abstract

We have explored the nonlinear dynamics of an optomechanical system consisting of an illuminated Fabry-Perot cavity, one of whose end-mirrors is attached to a vibrating cantilever. Such a system can experience negative light-induced damping and enter a regime of self-induced oscillations. We present a systematic experimental and theoretical study of the ensuing attractor diagram describing the nonlinear dynamics, in an experimental setup where the oscillation amplitude becomes large, and the mirror motion is influenced by several optical modes. A theory has been developed that yields detailed quantitative agreement with experimental results. This includes the observation of a regime where two mechanical modes of the cantilever are excited simultaneously.

Optomechanics

“…This will be the subject of the present section. These effects have already been observed in experiments Carmon et al, 2005;Kippenberg et al, 2005;Metzger et al, 2008).…”

“…(Marquardt et al, 2006). Self-induced oscillations in an optomechanical system have already been observed in experiments with bolometric forces Metzger et al, 2008) and in microtoroidal structures where radiation pressure dominates . Recently, a more detailed comparison of theory and experiment revealed interesting effects due to higher order mechanical modes that get involved in the nonlinear dynamics (Metzger et al, 2008).…”

Quantum noise in photothermal cooling

“…This approach has been proven to describe well experiments not only in the cooling regime [2,20] but also in the regime where self-sustained oscillations develop [34]. The force can thus be written as a time integral over a memory kernel of the instantaneous force due to the thermal deformation…”

Equations of a moving mirror and the electromagnetic field

“…Afterwards, we deduce equations that are correct up to first order in both the velocity and acceleration of the slab. With these results at hand, we conclude that the motion of the mirror and its interaction with the field give rise to a position-and time-dependent mass related to the effective mass taken in phenomenological treatments of this type of systems [4,10,13] and to a velocity-dependent force that is related to the cooling of mechanical objects [4,5]. Moreover, the field must satisfy a wave equation that depends on the slab's position, velocity, and acceleration.…”

“…Using certain experimental setups and certain types of materials one can manage to have mechanical objects in which one force predominates over the other. In this way, one has systems in which radiation pressure dominates [6,7,8], others in which thermal forces are much larger [9,10], and some others in which both types of forces are comparable [11]- [14].…”