Numerical modeling of the formation of dynamically configurable L2 lens in a microchannel

A. Gupta, J. Kitting, I.H. Karampelas
Flow Science, Inc.,
United States

Keywords: optofluidics, L2 lens, laminar flows, refractive index, focal length, dynamically configurable lens


The aim of this presentation is to describe the numerical modeling of a dynamically reconfigurable liquid-core liquid-cladding (L2) lens in a microfluidic channel, followed by a quantitative validation against the experimental results [1]. The lens is formed in a microchannel by three laminar co-flowing streams of fluids with different refractive indices. The core stream, which is sandwiched between the cladding streams, has a higher refractive index, causing the light to bend while passing through the layers of microfluidic streams. Based on the relative flow magnitudes of the core flow rates and the cladding flow rates, different lens shapes (defined by the curvatures) are formed. Each curvature leads to a different focal length, thus governing the path of light rays passing through the microchannel. L2 lenses have several advantages over conventional lenses. They are dynamically configurable which means that their focal lengths can be changed in real time by adjusting the fluid flows of the core and the cladding streams. The laminarity of the flow allows a smooth interface between the core and the cladding streams despite the roughness of the wall channel. Lastly, these systems are co-fabricated, simplifying the pre-alignment of the lens. This case study is divided into two parts – variable core flow rates and constant core flow rates. Variable core flow rates always result in the formation of bi-convex lenses. Constant core flow rates may form bi-convex, plano-convex or other lens shapes based on the relative flow rates of the core and the cladding flows. Finally, the numerical results are validated against the experimental results using regression analysis. It was found that the numerical modeling results are in excellent agreement with the experimental results. Such numerical validations highlight the importance of numerical modeling in design phases of optofluidic systems and give researchers valuable insights to the hydraulics governing the formation of the lenses.