Ripplon laser through stimulated emission mediated by water waves

Lasers rely on stimulated electronic transition, a quantum phenomenon in the form of population inversion. In contrast, phonon masers1–3 depend on stimulated Raman scattering and are entirely classical. Here we extend Raman lasers1–3 to rely on capillary waves, which are unique to the liquid phase of matter and relate to the attraction between intimate fluid particles. We fabricate resonators that co-host capillary4 and optical modes5, control them to operate at their non-resolved sideband and observe stimulated capillary scattering and the coherent excitation of capillary resonances at kilohertz rates (which can be heard in audio files recorded by us). By exchanging energy between electromagnetic and capillary waves, we bridge the interfacial tension phenomena at the liquid phase boundary to optics. This approach may impact optofluidics by allowing optical control, interrogation and cooling6 of water waves. Novel nanolasers7–9 benefit from using metallic materials. In a similar way, it is possible to exploit different wave systems that extend the concepts of Brillouin lasers1–3, which rely on acoustical waves, to capillary waves. At a scale smaller than the width of a hair (capillus in Latin), the effects that arise from cohesive forces between intimate particles of liquid push to minimize the liquid’s surface. Unlike acoustical waves that can propagate in all phases of matter, capillary waves are unique to liquids. Liquid interfaces, such as the ones in a glass of water, tend to be viewed as stationary smooth surfaces that exchange minimal energy with electromagnetic waves. Yet liquid phase boundaries, including those in droplets, actually look like a stormy sea when monitored with Angstrom resolution10–12 and can therefore scatter and Dopplershift light. During this scattering process, light can transfer part of its energy to capillary waves through redshift. Scattering from density variations, while coherently generating acoustic waves, is known as a Brillouin laser1–3. Raman scattering1,3 refers to the scattering from fluctuations in charge distribution while the molecule’s centre of mass remains stationary. In such scattering processes, energy conservation considerations suggest the stimulated optical generation of coherent oscillations if ‘redder’ (Stokes) scattering governs over the ‘bluer’ (anti-Stokes) scattering. Thermodynamically the Boltzmann distribution13 implies a sufficient Stokes enhancement for Raman and Brillouin lasers1, as can be seen in Fig. 1. In contrast, capillaries have rates (10 Hz) much lower than optical frequencies (1014 Hz), suggesting that their Stokes and anti-Stokes lines are almost equal. In other words, there will be no optocapillary energy exchange because the Stokes-created ripplons will be balanced by the anti-Stokes-annihilated ripplons. To mitigate this Stokes–antiStokes balance, it is possible to ‘help’ the Boltzmann distribution in the task of enhancing the capillary Stokes line. For example, the Stokes line can be resonantly enhanced (over the anti-Stokes line) by operating at the sideband of an optical resonance (Fig. 1b). Such a usage of sideband control is important in the cooling of gasses6 and in the excitation of phonon lasers14. It would therefore seem that forcing the optical cavity of a liquid droplet5,15–20 to operate at its non-resolved sideband regime would allow ripplon laser emission. Yet, just as low acoustic attenuation is needed for Brillouin lasers1–3, low viscosity is required for capillary oscillations. Low-viscosity (runny) liquids are, however, experimentally challenging because of their inherently fast evaporation rates. One recently demonstrated resonator system that is both small and resistant to evaporation uses optical tweezers to submerge a microdroplet near an optical coupler18. Here we use this technique18 to cancel out evaporation, but use runny liquids that transform the system from the capillary overdamped to the capillary underdamped operation regime. Our hybrid optocapillary resonator is an octane microdroplet in water. Octane and water are chosen here for their low viscosities (0.54 and 1.0 mPa s) and for their high transparency, which allow a capillary quality factor (Qcap) of 18 together with an optical quality factor (Qopt) of 1 × 10 . When the circumference of the droplets is an integer number of optical wavelengths, an optical whispering gallery mode (Fig. 2a, the arrow along the equatorial line) is possible. The transverse profile of this mode is calculated21 to reside at the droplet interface (Fig. 2a, inset on the bottom right). Similar to its optical modes, the droplet can also resonate when its size is near an integer number of capillary wavelengths. The eigenfrequencies22, fi, of the capillary shape oscillations (Fig. 2b) are