Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light

Synchronization of many coupled oscillators is widely found in nature and has the potential to revolutionize timing technologies. Here, we demonstrate synchronization in arrays of silicon nitride micromechanical oscillators coupled in an all-to-all configuration purely through an optical radiation field. We show that the phase noise of the synchronized oscillators can be improved by almost 10 dB below the phase noise limit for each individual oscillator. These results open a practical route towards synchronized oscillator networks.

Figure 1

Concept and devices. (a) Concept of mediating coupling between mechanical oscillators (yellow) through a global optical field (blue). The optical field provides energy for each mechanical oscillator to vibrate at their natural frequencies ${\mathrm{\Omega }}_{i,j}$ and also provide coupling between each mechanical oscillator forming an all-to-all coupling topology. When the optical coupling is strong, the oscillators synchronize and vibrate at a common frequency. (b) A schematic of each individual double disk. The edges are partly suspended to allow for mechanical vibration. (c) Cross section of a double disk showing the mechanical and the optical mode shapes. (d) Optical microscope images of coupled optomechanical double-disk oscillator arrays. The oscillators are mechanically separated by a narrow gap ($\sim 150\mathrm{nm}$) and coupled solely through the optical evanescent field. The squares and strings are support structures for tapered optical fibers.

Figure 2

Experimental configuration. (a) Optical supermode spatial structures. The colored halos show where the optical cavity field resides for different types of arrays. The more opaque colors illustrate higher cavity field intensities when compared to the rest of the cavities. The supermodes that spatially span over all cavities with equal intensities are identified by dashed lines. (b) Experimental setup. The coupled optomechanical oscillator array is placed in a vacuum chamber and excited by a tunable infrared (IR) camera through a tapered optical fiber. The optical power and polarization are controlled by an variable optical attenuator (VOA) and a fiber polarization controller (PC). The optical transmission is detected by an amplified photodiode (PD) and analyzed by an oscilloscope and a spectrum analyzer.

Figure 3

Synchronization in arrays of OMOs. Optical power spectrum of the (a) three-, (b) four-, and (c) seven-OMO system as the input optical power increases. The vertical scale is from $-110$ to 0 dBm for each trace. Synchronization is characterized by the sudden noise floor drop and the emergence of a single frequency in the optical power spectrum as indicated in the graphs. The disorder in natural mechanical frequencies and incoherent dynamics before the onset of synchronization is evident from the rf peaks and the broad noise floor. The seven-resonator array (c) shows multiple changes of noise shapes before eventually synchronizing, indicating the presence of multiple oscillation states as a result of many OMOs.

Figure 4

Phase noise in synchronized arrays. (a) Phase noise in a two-OMO system at a 10 kHz carrier offset as the laser power is increased. The noise increases due to mode competition between possible oscillation states and then decreases by $\sim 3\mathrm{dB}$ below the noise level of the one-OMO oscillation state. (b) The phase noise of the synchronized oscillation signal for different sizes of OMO arrays. The gray curve is the phase noise level predicted by theory for near-identical synchronized oscillators. (c) Power spectrum of a state where four OMOs are oscillating (black) and of a state where two OMOs are oscillating (purple). The phase noise drops by $\sim 3\mathrm{dB}$ following the transition. The inset shows an enlargement near the peak and captured IR images for the two- and four-OMO synchronized state, respectively.