A tuneable micro-optofluidic biconvex lens with mathematically predictable focal length

Abstract

Recent research efforts have been increasingly focused on the development of microlenses. Of great interest are in-plane optofluidic lenses due to the possibility of integrating them directly into a microfluidic network. Furthermore, the tunability of optofluidic lenses makes them more adaptive to lab-on-a-chip (LOC) system for biological and chemical analysis. However, the predictability of the performance of the current optofluidic lenses is limited by the lack of a simple explicit mathematical model. Previously, we proposed a model based on dipole flow theory to calculate the flow field in a circular chamber where the optofluidic lens is formed. However, this method assumes that both the core and cladding liquids have the same viscosity. In this article, hydrodynamic spreading theory is used to model the opening angles of the core stream and the cladding stream at the entrance of the circular chamber. Subsequently, the curvature of the lens interface for each corresponding opening angle of the core stream can be determined. The focal length of the optofluidic lens formed in the circular chamber can be analytically formulated, which can help to determine the position of focal point for a given flow condition. Experiments were carried out to verify this new model. Ray-tracing method was used experimentally and numerically to measure the focal length. The theoretical results agree well with both experimental and numeric results.