Modal Spectroscopy of Optoexcited Vibrations of a Micron-Scale On-Chip Resonator at Greater than 1 GHz Frequency

We analyze experimentally and theoretically $>1\mathrm{GHz}$ optoexcited mechanical vibration in an on-chip micron-scaled sphere. Different eigen-mechanical modes are excited upon demand by the centrifugal radiation pressure of the optical whispering-gallery-mode, enabling an optomechanical modal spectroscopy investigation of many vibrational modes. Spectral analysis of the light emitted from the device enables deduction of its natural vibrational modes in analogy with spectroscopy of a molecule’s vibrational levels, and its eccentricity perturbation is shown to induce spectral splitting.

Figure 1

(a) Schematics of the radiation-pressure instability in the context of Fabry-Perot resonator. (b) Experimental setup: continuous-wave optical input is evanescently coupled via a tapered fiber to a whispering-gallery-mode cavity. One of the natural mechanical modes of the structure is optoexcited by the centrifugal radiation pressure and modulates the optical output in return. Inset shows a micrograph of the whispering-gallery-mode cavity. (c) Rendering of the cavity at mechanical equilibrium. (d) Rendering of the calculated 538 MHz mode. The calculated deflection is exaggerated in the rendering.

Figure 2

Column 1 shows the electrical spectrum of photocurrent upon detection of continuous pump wave modulated by the vibrating microsphere. Column 2 shows the same photocurrent signal except measured in the time domain (horizontal dotted lines in column 2a stands for transmission of 0 and 1). The experimental data is taken at a pump power which is 10 times higher than that of the vibration threshold power. The corresponding calculated mechanical modes are presented in column 3. Also calculated is the nodes geometry in column 4 wherein the lines represent the calculated boundaries at $\pi /2$ and $-\pi /2$. The calculated deflection is exaggerated in the plots. Movies of the vibrational modes are available in Ref. [25].

Figure 3

Higher resolution spectral scans (over two scan-width spans 3a,b) of the fundamental spectral component in Fig. 2a. (3a) contains a temporal-spectral scan and (3b) contains a conventional spectral scan. Using the Lorentzian fit in figure 3b, we infer a FWHM linewidth for the oscillation peak (and hence the mechanical mode) of 300 Hz. The data are collected for excitation at $10X$ the threshold power.

Figure 4

(a) Experimental spectrum of an anisotropic toroidal cavity reveals spectral-line splitting (light and dark lines). (b) Calculation shows the corresponding degenerate modes oriented with different rotation. Deformation is exaggerated in figures.