Voltage-programmable liquid optical interface

Abstract

There has been intense recent interest in photonic devices based on microfluidics that include displays [1,2] and refractive tunable microlenses and optical beamsteerers [3][4][5] that work using the principle of electrowetting [6,7]. Here we report a novel approach to optical devices in which static wrinkles are produced at the surface of a thin film of oil as a result of dielectrophoretic forces [8][9][10]. We have demonstrated this voltage programmable surface wrinkling effect with periodic devices with pitch lengths of between 20 µm and 240 µm and with response times of less than 40 µs. By careful choice of oils, it is possible to optimise either for high amplitude sinusoidal wrinkles at micrometer-scale pitches or for more complex non-sinusoidal profiles with higher Fourier components at the longer pitches. This provides the possibility for rapidly responsive voltage programmable polarisation insensitive transmission and reflection diffraction devices and for arbitrary surface profile optical devices. * E-mail: carl.brown@ntu.ac.uk, Tel: 44 115 8483184 2 The structure of the device is shown in figure 1. The side view, in figure 1(a), shows the glass substrate coated with patterned gold/titanium conducting electrodes, on which there is a thin solid dielectric layer (either photoresist or a dielectric stack), upon which is coated a thin layer of oil. The electrodes were arranged as an array of stripes parallel to the y direction in the xy plane. This geometry allowed every other electrode to be electrically connected as shown in the plan view in figure 1(b).The electrically induced wrinkling at the oil surface will be considered first for a device with an electrode pitch of p = 80 µm. When a small volume (0.1 µL) of 1-decanol was initially dispensed onto the device it formed a spherical cap with a contact angle of 5°. Every other stripe in the electrode array was biased with an A.C. voltage with r.m.s. magnitude V O and the inter-digitated stripes between them were earthed, as shown in figure 1. This creates a periodic electric field profile in the plane of the oil layer which is highly non-uniform. A polarisable dielectric material in a region containing non-uniform electric fields experiences a force, known as a dielectrophoretic force, in the direction of the increase in magnitude of the electric field [8][9][10]. When the r.m.s. electrode voltage was greater than V O = 20 Volts the dielectrophoretic forces spread the oil into a thin film with a uniform thickness, h = 12 µm, across the area covered by the electrodes.Increasing the voltage between neighbouring electrodes gave rise to a periodic undulation at the surface of the oil. The period of the wrinkle was equal to the electrode pitch, 80 µm, and the peaks and troughs of the wrinkle lay parallel to the electrode fingers along the y-direction. This undulation arises because the highest electric field gradients occur in the gaps between the electrodes and so the dielectrophoretic forces in these regions cause the oil to collect there preferentially. The...

Analysis of a static undulation on the surface of a thin dielectric liquid layer formed by dielectrophoresis forces

“…The value of W E shows a minimum for ε oil = 1.5 in figure (5). This occurs for all the numerical solutions if the range of Ak is extended, and the numerical solutions have a parabolic dependence on Ak to a good approximation.…”

“…For example, in a diffractive light modulation device a relatively small, fixed, wrinkle amplitude of A = 0.7-0.9 µm (depending on the refractive index of the liquid) at 543 nm wavelength is required to extinguish the zero order of coherent light transmitted through a transparent liquid [5].…”

“…The result of performing the double integration in equation [5] to first order in Ak is given in equation [6] where…”

“…After performing the y-integrations in equation [5] the exponential terms were replaced with Taylor series expansions, using the assumption that Ak << 1, before the x-integrations were performed.…”

“…We have previously shown that an interdigital array of striped co-planar electrodes can be used to spread a droplet of oil into a thin uniform film and that a static periodic deformation, or wrinkle, forms on the spread film at the oil/air interface [5]. The period p of the wrinkle was found to be equal to the period of the electrode stripes, which is half of the electrical period since neighbouring stripes on the array were oppositely biased at potentials O V + and O V − .…”