Fundamental limits in high-Q droplet microresonators

Abstract

Liquid droplet whispering-gallery-mode microresonators open a new research frontier for sensing, optomechanics and photonic devices. At visible wavelengths, where most liquids are transparent, a major contribution to a droplet optical quality factor is expected theoretically from thermal surface distortions and capillary waves. Here, we investigate experimentally these predictions using transient cavity ring-down spectroscopy. With our scheme, the optical out-coupling and intrinsic loss are measured independently while any perturbation induced by thermal, acoustic and laser-frequency noise is avoided thanks to the ultra-short light-cavity interaction time. The measurements reveal a photon lifetime at least ten times longer than the thermal limit and indicate that capillary fluctuations activate surface scattering effects responsible for light coupling. This suggests that droplet microresonators are an ideal optical platform for ultra-sensitive spectroscopy of highly transparent liquid compounds in nano-liter volumes.

Figure 1. Experimental arrangement.

A visible diode laser is focused close to the droplet rim to excite WGMs. Ringing signals are observed where directly-transmitted light and the scattered light are detected.

Figure 2. WGM excitation along a laser-frequency sweep (13-Hz frequency) for a paraffin droplet (300-μm radius).

The three radial modes excited by scattering show different linewidths. Lower-Q modes are visible on the background.

Figure 3. Transient ringing waveforms recorded during a single, very-fast linear laser sweep (∼10¹⁷ Hz/s) across the resonances corresponding to WGM1 and the weak mode WGM2.

Figure 4. Fitting of the WGM3 resonance with Eq. 5 (red line) after subtraction of the linear power background and 4000-waveform averaging.

The overall lifetime is τ₃ = 4.8 ± 0.1 ns (errors are 1σ standard deviation; time resolution is 5 ps). The inset shows a recording in the spectral domain performed by a slow laser-frequency scan (transit time through resonance ~0.4 ms) along with a Gaussian fit (red line): the measured FWHM is 160 ± 1 MHz (Q = 2.93 ± 0.02·10⁶).

Figure 5. Lifetime values extracted from the fit of ringing waveforms of paraffin droplets with different radii (the red point corresponds to a silicone oil droplet).

Figure 6. Thermal broadening/narrowing effect and hysteretic response of a WGM resonance as seen on both sides of a slow linear wavelength scan (scan range ∼1 GHz).