Spectral properties of thermal fluctuations on simple liquid surfaces below shot-noise levels

We study the spectral properties of thermal fluctuations on simple liquid surfaces, sometimes called ripplons. Analytical properties of the spectral function are investigated and are shown to be composed of regions with simple analytic behavior with respect to the frequency or the wave number. The derived expressions are compared to spectral measurements performed orders of magnitude below shot-noise levels, which is achieved using a novel noise reduction method. The agreement between the theory of thermal surface fluctuations and the experiment is found to be excellent, elucidating the spectral properties of the surface fluctuations. The measurement method requires relatively only a small sample both spatially (few μm) and temporally (∼20s). The method also requires relatively weak light power (∼0.5mW) so that it has a broad range of applicability, including local measurements, investigations of time-dependent phenomena, and noninvasive measurements.