Synchronization of Micromechanical Oscillators Using Light

Synchronization, the emergence of spontaneous order in coupled systems, is of fundamental importance in both physical and biological systems. We demonstrate the synchronization of two dissimilar silicon nitride micromechanical oscillators, that are spaced apart by a few hundred nanometers and are coupled through an optical cavity radiation field. The tunability of the optical coupling between the oscillators enables one to externally control the dynamics and switch between coupled and individual oscillation states. These results pave a path toward reconfigurable synchronized oscillator networks.

Figure 1

Design of the optically coupled optomechanical oscillators (OMOs). (a) Schematic of the device illustrating the mechanical mode profile and the optical whispering gallery mode. (b) False-colored scanning electron micrograph (SEM) image of the OMOs with chrome heating pads (blue) for optical tuning by top illumination. (c),(d) The symmetric (S) and antisymmetric (AS) coupled optical supermodes. The deformation illustrates the mechanical mode that is excited by the optical field. (e) The dynamics of the coupled OMOs can be approximated by a lumped model for two optically coupled damped-driven nonlinear harmonic oscillators.

Figure 2

Controlling the OMO system. (a) Schematic of the experimental setup. The pump and probe light are launched together into the cavities and are detected separately by photodiodes (PD). (b) Anticrossing of the optical mode as the relative temperature of the $L$ OMO ($T_L$) and the $R$ OMO ($T_R$) is changed through varying the tuning laser power. The tuning laser is focused on to the two OMOs respectively to obtain the negative and positive relative temperatures. (c) Transmission spectrum of the maximally coupled state indicated by the white horizontal line in (b). S (blue) and AS (red) optical supermodes with optical coupling rate $\kappa$. NT: normalized transmission.

Figure 3

rf spectra of the OMOs and synchronization (a), (b) rf power spectra of cavity $L$ (a) and $R$ (b) as a function of laser frequency when the coupling is turned off. The horizontal white lines indicate the onset of self-sustaining oscillation. Power spectral density (PSD). (c) When the coupling is turned on, at an input power $P_{\mathrm{in}}=(1.8\pm 0.2)\mu \mathrm{W}$ cavities $L$ and $R$ do not synchronize and oscillate close to their natural frequencies. (d) At $P_{\mathrm{in}}=(11\pm 1)\mu \mathrm{W}$ synchronization occurs after the horizontal solid white line after a brief region of unsynchronized oscillation (between the dashed and solid white lines). (e) The system oscillate directly in a synchronized state at input optical power $P_{\mathrm{in}}=(14\pm 1)\mu \mathrm{W}$. (f), (g), (h) Corresponding numerical simulations for the OMO system based on the lumped harmonic oscillator model described in the text. Normalized power spectral density (NPSD).

Figure 4

Pump-probe measurements of the oscillations of individual OMO operating as in Fig. 3d. (a), (b) The uneven probe intensity distribution of the cavities, observed by an infrared CCD camera when the pump laser is off. (c) Normalized transmission (NT) spectrum for the probe resonances. The red (blue) dashed line corresponds to the probe wavelength region for probing the $L$ ($R$) OMO, as illustrated in (a), (b). (d) The red (blue) curve is the $L$ ($R$) cavity probe transmission rf spectrum when the two OMOs are asynchronous: a strong peak at $f_L$ is observed but with very different amplitude for two probing conditions. (e) Same curves shown in (d) but with the OMOs synchronized: the two probing conditions have almost identical amplitudes.