Optofluidic Resonance of a Transparent Liquid Jet Excited by a Continuous Wave Laser

We report a new optofluidic resonating phenomenon that naturally links the optical radiation pressure, total internal reflection, capillary wave, and Rayleigh-Plateau instability together. When a transparent liquid jet is radiated by a focused continuous wave laser beam, the highly ordered periodic jet breakup is unexpectedly triggered and maintained. The capillary wave enables the liquid-gas interface to serve as a rotating mirror reflecting the laser beam in a wide range of angles, including the critical angle for total internal reflection. The liquid jet acts as an optical waveguide to periodically transmit the laser beam to the upstream of the jet. The periodic optical beam transmittance inside the liquid jet exerts time-dependent optical pressure to the jet that triggers the Rayleigh-Plateau instability. The jet breakup process locks in at the frequency corresponding to the peak growth rate of the Rayleigh-Plateau instability of the liquid jet, which agrees with the prediction from the dispersion relation of a traveling liquid jet.

Figure 1

(a) Schematic of the optofluidic resonance experiment. A focused CW laser beam intercepts the jet at point $C$. (b) Immediately after the laser is on, the jet breakup is still random. (c) The jet breakup point sometimes randomly moves up above $C$, showing the laser hits the droplet and generates multiple reflections inside the droplet. (d) Breakup point moves down and below $C$. (e),(f) $\sim 100\mathrm{ms}$ after laser is on, the jet breaks up orderly. The exit of the nozzle is alternatively illuminated (e) or dark (f), indicating the laser beam is periodically transmitted upstream to the origin of the liquid jet. (Laser: 520 nm, 1.9 W; $R=75\mu \mathrm{m}$; ethanol; flow rate: $1.4\mathrm{mL}/\min .$)

Figure 2

Breakup point location history covering the entire process after laser is on, with the laser-jet intersecting point fixed (ethanol; $R=109\mu \mathrm{m}$; ${\beta }^2=5$; laser: 532 nm, $P_L=3.3\mathrm{W}$).

Figure 3

(a) Envelope of the laser power ($P_L$) and the laser interception location ($L_C$) for triggering optofluidic resonances (${\beta }^2=6$). (b) The difference between the interception location and breakup point at different laser power $P_L$ and Weber number. (Ethanol; fixed $L_C/R=83$; $R=109\mu \mathrm{m}$; laser wavelength: 532 nm.)

Figure 4

Ray optics simulation. (a) Comparison of the simulation and experimental images at different stage of the traveling capillary wave (central axial plane) (ethanol; $R=109\mu \mathrm{m}$; ${\beta }^2=6$; $P_L=3.3\mathrm{W}$). (b) Optical force near the nozzle exit in a complete breakup period. “Near” is defined as within the distance of $2\pi R$ from the nozzle exit (ethanol; ${\beta }^2=6$; $P_L=3.3\mathrm{W}$).

Figure 5

The initially in-resonance ethanol jet keeps ordered breakup for $\sim 28t_R$ (or $\sim 6\mathrm{ms}$) after the CW laser is turned off ($R=109\mu \mathrm{m}$; $v_j=1.45\mathrm{m}/\mathrm{s}$; $P_L=3.3\mathrm{W}$).