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

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. The backaction induced by the bolometric light force produces negative damping such that the system enters a regime of nonlinear oscillations. We study the ensuing attractor diagram describing the nonlinear dynamics. A theory is presented that yields quantitative agreement with experimental results. This includes the observation of a regime where two mechanical modes of the cantilever are excited simultaneously.

Figure 1

The experimental setup. The light inside the optical cavity is focused onto a cantilever, where it exerts a force. Both the transmitted light intensity and its sidebands at the cantilever frequency are recorded (Transmission and Amplitude, respectively).

Figure 2

Attractor diagram. (a) Amplitude $A$ of self-induced oscillations vs cantilever equilibrium position $x_0$. The color scale displays the net power fed into the cantilever from the radiation field, i.e., the right-hand side of Eq. (4). Contour lines indicate possible oscillation amplitudes (attractors) for various damping constants ${\Gamma }_1$. Red dots stem from numerical simulations, for the experimental value of ${\Gamma }_1$ (and a laser input power of $I=0.3I_0$). The inset shows the same plot as a function of $(A,\overline{x})$ instead of $(A,x_0)$. (b),(c) Whenever $x(t)$ (thick black line) passes through the optical resonances (green bars), the light intensity (red line) displays spikes, leading to delayed increases in the radiation force (dashed blue line), which was plotted as $(\theta -\overline{\theta })\times 200$. Plots (b) and (c) correspond to the positions indicated in the attractor diagram (a).

Figure 3

Experiment vs theory. The transmitted light intensity (left) and the amplitude of self-induced cantilever oscillations (right), from a numerical simulation (red full curves) and from the experiment (blue data points), at increasing input power levels (top to bottom). Theoretical transmission curves display the (rescaled) time-averaged circulating light intensity from the simulation. Amplitude curves are obtained from the sidebands in the intensity (see main text). For clarity, the hysteresis observed upon sweeping $x_0$ has been shown only in the middle panel. The region of instability (shaded interval) grows with increasing input power. Simultaneous self-induced oscillations of the first two mechanical modes set in at the highest power displayed (in the two intervals indicated in the plot). The calculated amplitude of the second mode is shown as a dashed line.