Analysis of natural frequency for imaging interface in liquid lens

Transmission beam can be modulated at the liquid-liquid interface inside an electrowetting liquid lens. The fluctuation characteristics of the interface has a decisive effect on the beam modulation. A closed cylinder in capillary constant scale is analyzed and the natural frequencies of a flat interface are obtained using capillary wave hydrodynamics. Results in modes 0 and 1 are in good agreement with previous experiments in the literature. The influences of the radius, the height ratio and the height-to-diameter ratio of a liquid lens on the interface eigenfrequencies are analyzed.