Liquid Droplet Microresonators

Abstract

We provide here an overview of passive optical micro-cavities made of droplets in the liquid phase. We focus on resonators that are naturally created and suspended under gravity thanks to interfacial forces, illustrating simple ways to excite whispering-gallery modes in various slow-evaporation liquids using free-space optics. Similar to solid resonators, frequency locking of near-infrared and visible lasers to resonant modes is performed exploiting either phase-sensitive detection of the leakage cavity field or multiple interference between whispering-gallery modes in the scattered light. As opposed to conventional micro-cavity sensors, each droplet acts simultaneously as the sensor and the sample, whereby the internal light can detect dissolved compounds and particles. Optical quality factors up to 107⁻108 are observed in liquid-polymer droplets through photon lifetime measurements. First attempts in using single water droplets are also reported. These achievements point out their huge potential for direct spectroscopy and bio-chemical sensing in liquid environments. Finally, the first experiments of cavity optomechanics with surface acoustic waves in nanolitre droplets are presented. The possibility to perform studies of viscous-elastic properties points to a new paradigm: a droplet device as an opto-fluid-mechanics laboratory on table-top scale under controlled environmental conditions.

Keywords: cavity optomechanics; cavity ring-down spectroscopy; droplet micro-cavity; free-space laser excitation; optical Q-factor; whispering gallery modes.

Figure 1

Photos of Pisa baptistery’s dome (left) and of its internal gallery structure (right).

Figure 2

Left: 3D rendering of the optical scheme for excitation of a droplet cavity by a free-space laser beam (Reproduced with permission from [27]). Right: photograph of a liquid-paraffin droplet (~1.5 mm diam) hanging from the tip of a silica fiber with acrylic coating (250-μm outer diam).

Figure 3

Whispering gallery mode (WGM) resonances recorded from the transmission (black line), back-scattering (red) and side-scattering (blue) of a pendant liquid paraffin droplet excited by a 640-nm laser beam with incident power of 5 mW. The observed coupling efficiency for the central mode is about 6%. In the inset, a camera view of the side scattered light evidences the presence of different WGMs.

Figure 4

Fano-resonance behavior observed varying the distance between the laser beam and the droplet. The relative distance is decreased by ~1.6 μm (b) and 2.8 μm (c) from the WGM optimal coupling position (a).

Figure 5

Laser light coupling, detection and frequency locking scheme. D1, D2, photodetectors; RF, radio-frequency; AM, amplitude modulation; MZ, Mach–Zehnder modulator; L, lens (Reproduced with permission from [27]).

Figure 6

Pound–Drever–Hall (PDH) error signals (black line) generated after demodulation of the directly transmitted power with sidebands at about 1 GHz (paraffin oil droplet) using a diode laser emitting around 1560 nm (incident power 2 mW). The WGM scatter spectrum (red line) shows peaks that are centered exactly at the PDH signal zero crossing points (All plots are reproduced with permission plots from [27]).

Figure 7

WGM resonance along a laser frequency sweep on the directly-transmitted beam (black line) and the corresponding error signal generated by (a) spatial interference on the back-scattered light (blue line) and (b) Pound–Drever–Hall technique (red line) (All plots are reproduced with permission plots from [41]).

Figure 8

Ringing lineshapes observed during a fast laser-frequency sweep through the narrowest WGM shown in Figure 3, for a paraffin oil droplet (red line is recorded from direct transmission, blue line from back-scattering).

Figure 9

WGMs recorded on the transmission of a pure H₂O droplet using a laser at 475 nm.

Figure 10

Photon decay rate for increasing olive-oil/seed-oil concentration levels (Reproduced with permission from [27]).

Figure 11

Real-time WGM shift measurements. Noise spectrum of the cavity-laser locking signal with application of a sinusoidal, slow mechanical perturbation. A wavelength-shift resolution limit is extrapolated from the noisefloor (dashed line). In the inset, the response of the droplet to a pulsed perturbation that mimics a particle binding to the surface is shown (All plots are reproduced with permission from [27]).

Figure 12

Optical resonances are shown as observed on the transmission of a 140-μm radius droplet along an ascending and descending wavelength scan, from left to right, respectively. Fast oscillations and broadening effects are observed on the resonances. In the inset, a camera image of the out-scattered radiation when the laser is resonant with the strongest mode (Reproduced with permission from [61]).

Figure 13

Left: FFT of the droplet transmission on resonance. The spectrum shows a large oscillations centered at 70 MHz (pump power of 360 μW). Right: Finite element method (FEM) simulation. A surface acoustic mode with high transverse order is shown in a 3-D artistic illustration (yellow sphere) with purposely exaggerated modulation depth along with its absolute displacement fields (scale on color bar) at liquid-phase boundary (θ-φ plane) and at radial-polar plane (r-θ) (All plots are reproduced with permission from [61]).

Figure 14

Stokes linewidth and power vs. pump light power injected into the droplet. The Stokes beat-note power (black squares) increases with pump and exhibits a knee with slope change at a threshold ~180 μW. The narrowest observed lineshape is shown in the inset with a red line representing a Lorentzian fit (All plots are reproduced with permission from [61]).