Dynamic beam shaping using electrowetting effects

Abstract

A geometric model was developed to describe the meniscus shape of a rectangular electrowetting lens under arbitrary voltages for small Bond numbers. The model assumes the meniscus being a part of a toroidal surface. Seven variables (cell width, cell length, the saline solution volume, and the four contact angles on the four sidewalls) determine the meniscus shape. From the model, the optical parameters of the two primary radii of the meniscus and its optical tilt and pan angle can be obtained.

Based on the toroidal model, ray tracing analyses were conducted on single electrowetting lenses and lens arrays. The largest beam angle change and tilt angle change were 0-16.7 degrees and 0-9.3 degrees, which were too small to be useful for a dynamic optical beam shaper. The effects of refractive index, cell size, and cell numbers were studied, the findings of which led to an enhancement design with different geometry and a secondary lens array. The beam angle control range improved to 4.7-49.9 degrees. The beam tilt angle control range increased to 0-35.5 degrees. Although the optical efficiency dropped by 14-15%, the enhancement design demonstrated that electrowetting is a good candidate for a dynamic optical beam shaper.

Experimental validation of the geometric model was conducted by comparing the dynamic image shifts of a wire mesh produced with suitably designed electrowetting cells and the corresponding image obtained through ZEMAX image simulation. The experimental 2 × 2 × 12.7 mm rectangular electrowetting cells were fabricated and used as test samples for experimental validation. Focal length change, radius of one primary curvature change, tilt meniscus along one sidewall, and tilt meniscus along diagonal direction were studied. The model prediction had an excellent match with the first two cases. For the latter two cases, the model predicted the general trend and shape but under-predicted optical changes at the corners of the experimental cells.

The model was compared with the Surface Evolver simulation, which obtained the meniscus shape via energy minimization. The difference between the geometric model and the energy minimizing simulation is calculated. The largest standard deviation of the differences over cell widths is less than 2%.

The applicability of the electrowetting technology on dynamic beam shaping in lighting applications is demonstrated in this study.