Fig. 1. Nanobeam-double optomechanical cavities (OMCs). (a) Schematic of asymmetric photonic coupling of a tapered fiber contacting one end of the nanobeam-double OMCs. The distances between the tapered fiber and the two original single cavities are different, which breaks the symmetric refractive index distribution and leads to only one excited optical mode of the double cavities in (d). The inset image presents a schematic of the nanobeam-double OMCs. The green parts are cavity defect regions formed by gradually varied hole radius. The gray parts are cavity mirrors for both optical and mechanical modes. (b) Top-view scanning electron microscope (SEM) micrograph of the nanobeam-double OMCs. (c) Normalized displacement of the mechanical symmetric supermode (SSM) and antisymmetric supermode (ASM). (d) Normalized Ey of the excited optical mode by the asymmetric photonic coupling fiber. (e) Mechanical cavity coupling rate with center mirror cell quantity and center mirror radius.

Fig. 2. Experimental setup and optical and mechanical results. (a) Schematic of the experimental setup for mechanical and optical measurement. (b) Optical transmission spectrum with laser power of −20, 0, and 5 dBm. (c) Power spectral density (PSD) for the three types of mechanical modes observed in the spectrum analyzer. The inset displays the detailed PSD of the fundamental modes. The dotted lines are the fitting results reflecting two mechanical-mode couplings.

Fig. 3. Optical control of the two mechanical-mode couplings. (a) Normalized mechanical power spectrum density for various pump wavelengths. The red dashed lines reveal the resonance frequencies of two coupled modes. The inset presents an enlarged view of the mechanical spectrum at laser wavelength of 1551.04 nm with the two-component fits. (b) The non-Hermitian parameter space diagram of mechanical-mode coupling with pump power and pump wavelength. The blue and yellow sheets each represent a mechanical mode.

Fig. 4. (a) Thermal oscillation PSD of the nanobeam-double OMCs for various optical wavelengths. The gray and pink regions refer to the thermal stable state and thermal self-oscillation, respectively. (b) Mechanical-mode coupling in the stable region (black line) and self-oscillation region (red lines). The blue dashed lines indicate two mechanical modes.

Fig. 5. (a) Optical resonance wavelengths and (b) optical mode isolation as a function of the contact position along the length direction of the nanobeam-double OMCs. The insets in (a) illustrate the normalized electric y component of the optical modes of the two optical cavities.

Fig. 6. Superposed asymmetric mechanical modes of the nanobeam-double OMCs. The two curves are the experimental results of the power spectral density (PSD) for the optical fiber on the various ends of the nanobeam.

Fig. 7. Calculated non-Hermitian parameter space diagram of normalized mechanical frequency difference with pump power and detuning Δ. The blue and yellow sheets each represent a mechanical mode.

Fig. 8. Mechanical frequency of the corresponding spectra in Fig. 3(a) versus optical wavelength. The orange and blue circles reveal the resonance frequencies of two coupled modes. The inset shows the error bar of the fitted frequency, which is almost negligible.

Fig. 9. (a) Optical transmission of the double cavity at a high pump power of 5 dBm. The gray region reveals the optical thermal stable state (including thermal bistability), and the red region denotes the optical thermal self-oscillation. (b) Experimental observation of thermal self-oscillations in a single optomechanical cavity. (c) Details of the pulse front dominated by free carrier dispersion.