# Tunable Liquid Optics: Electrowetting Controlled Liquid Mirrors Based on Self-Assembled Janus Tiles

**Introduction**

The authors present the fabrication of tunable liquid lenses that are mechanically stable. They use reflection, rather than refraction, to focus an incident beam of collimated light. They employ electrowetting by applying a voltage across the microlens to tune the focal length, and demonstrate that classical electrowetting theory explains the trend in focal length with applied voltage.

**Reflection Based Lens via Self-Assembly of Janus Tiles at the liquid-liquid Interface**

A microlens is initially created by placing a drop of oil on top of a pool of water. To keep the fluid lenses mechanically stable, the water and oil must be density matched, thus limiting the types of liquids that can be used. This design constraint severely limits the maximal refractive index contrast that can be obtained. Therefore, the authors optically enhance the liquid-liquid interface so that the optical properties of the liquids are of minimal importance. This is done by coating the interface with micromirros (Janus tiles). These “Janus tiles” are thin hexagonal slices of silicon that are formed using photolithography, and are coated with a thin layer of gold on one side to create a hydrophobic surface. A depiction of these particles is shown below in Figure 2.

The Janus tiles are mixed with oil, and this mixture is deposited onto a pool of water. A concave interface is created as shown below in Figure 3 and the Janus tiles self-assemble with a high packing density at the interface. The gold side of the tiles is hydrophobic, while the bare silicon is hydrophilic, so the tiles self-assemble at the oil water interface with the gold side facing towards the oil. This creates a reflective concave lens at the oil-water interface. Thus when collimated light is incident on the lens, the light is reflected and focused at a distance of 1 focal length away.

The focal length (f) of the micromirror is a function of the contact angle (<math>\theta</math>) between the oil-water interface and the Cytop surface and the volume of the oil drop (<math>\Omega</math>).

(1) <math>f^3 = \frac{3\Omega}{8\pi (1-cos(\theta))(2-cos^2(\theta)-cos(\theta))}</math>

From classical electrowetting theory, the relationship between the contact angle and the applied voltage is given by

(2) <math> cos(\theta)(V) = cos(\theta_0) - \frac{\epsilon_0 \epsilon_r}{2d\gamma_{wo}}V^2</math>

V: Applied Voltage

<math>\theta_0</math>: Contact angle when V = 0

<math>\gamma_{wo}</math>: Interfacial energy per area of water-oil interface

<math>\epsilon_0</math>: Electric permittivity of free space

<math>\epsilon_r</math>: Electric permittivity of dielectric insulator

d: dielectric thickness

Combining equations (1) and (2), and Taylor expanding f with respect to V yields a linear relationship between f and <math>V^2</math> for small voltages.

The authors measured the focal length of the lens for various applied voltages, and showed that the relationship between f and <math>V^2</math> is indeed linear as predicted by theory. The authors demonstrate a 2-fold range of focal length. The sensitivity of focal length to voltage could be enhanced by decreasing the thickness of the dielectric.

**Implications related to Soft Matter Physics**

This paper is an excellent demonstration of applications of interface science, self-assembly, and electrowetting to device development. The authors suggest employing this technology as a projector, where a point sourse is placed one focal length away to obtain a collimated beam.

**Reference**

M. A. Bucaro, P. R. Kolodner, J.A. Taylor, A. Sidorenko, J. Aizenberg, and T. Krupenkin. "Tunable Liquid Optics: Electrowetting Controlled Liquid Mirrors Based on Self-Assembled Janus Tiles." Langmuir 2009, 25, 3876-3879