Stimulated Brillouin Cavity Optomechanics in Liquid Droplets

Liquid droplets are ubiquitous in nature wherein surface tension shapes them into perfect spheres with atomic-scale smooth surfaces. Here, we use stable droplets that cohost equatorial acoustical and optical resonances phase matched to enable the exchange of energy and momentum between sound and light. Relying on free-space laser excitation of multiple whispering-gallery modes, we harness a triple-resonant forward Brillouin scattering to stimulate optomechanical surface waves. Nonlinear amplification of droplet vibrations in the 60–70 MHz range is realized with spectral narrowing beyond the limit of material loss, thereby activating the droplet as hypersound-laser emitter.

Figure 1

(a) Pictorial view of the optical setup. A high-$Q$ optical microresonator is obtained suspending a silicone-oil droplet by the tip of a silica holder (not to scale). A red laser beam is focused tangentially to the droplet rim to excite optical and acoustic WGMs. The generated vibration propagates along an equatorial trajectory and scatters (Brillouin) the incident light. A time-domain oscillation ($\sim 14\text{−}\mathrm{ns}$ period) on the transmitted power, resulting from the beat between the laser and Stokes fields, is shown as an example by the monitor screen. (b) Optical resonances are shown as observed on the transmission of a $140\text{−}\mu \mathrm{m}$-radius droplet along an ascending and descending wavelength scan, from left to right, respectively. Fast amplitude oscillations and thermal broadening effects are visible on each resonance. Inset: Camera view of the out-scattered radiation when the laser is resonant with the strongest mode.

Figure 2

FFT of the droplet transmission signal. The Fourier spectrum shows several oscillations with the largest peaks from 70 to 500 MHz (pump power of $360\mu \mathrm{W}$). The inset shows a Fabry-Pèrot spectral analysis of the microcavity transmitted light (maximum pump power) that points out the generation of a new optical field due to (Stokes) forward SBS.

Figure 3

Acoustic mode FEM simulation. Different longitudinal modes resonating along the circumference with an azimuthal mode number $m=45$ are numerically analyzed and plotted along with their resonance frequencies. (i)–(iii) Top: Three acoustic modes in ascending transverse order are shown in a 3D artistic illustration with purposely exaggerated modulation depth. (i)–(iii) Bottom: The three modes are shown with their absolute displacement fields (see scale on color bar): left, at the liquid-phase boundary ($\theta -\phi$ plane); right, at the radial-polar plane ($r-\theta$). (iv) The first mode seen at the equatorial plane ($r-\phi$). The FEM simulation is carried out with comsol multiphysics^® for silicone-oil droplets, using Young’s modulus $E=1.641\mathrm{GPa}$, density $\rho =971\mathrm{kg}{/\mathrm{m}}^3$, Poisson’s ratio $\nu =0.17$, and cavity radius $R=140\mu \mathrm{m}$. The model considers an azimuthal slice of the droplet corresponding to one quarter wavelength of the acoustic mode.

Figure 4

Stokes linewidth and power versus pump light power coupled to the droplet. The Stokes beat-note power (black squares) increases with pump and exhibits a knee with slope change at a threshold power of $\sim 180\mu \mathrm{W}$ (error bars are statistical uncertainties from Lorentzian fits). The beat-note linewidth (blue points) narrows exponentially with increasing power from an initial value of $11.1\pm 0.2\mathrm{MHz}$ (35% wider than the value expected from the intrinsic material loss; see ref. [21]) down to $780\pm 4\mathrm{kHz}$ at the maximum power level (dotted square on the graph). The narrowest observed line shape is shown in the inset with a red line representing a Lorentzian fit.