Voltage-programmable liquid optical interface

Voltage-programmable liquid optical interface

(Parte 1 de 2)

Voltage-programmable liquid optical interface C. V. Brown*,G .G .W ells,M .I .N ewtona nd G. McHale

Recently, there has been intense interest in photonic devices based on microfluidics, including displays1,2 and refractive tunable microlenses and optical beamsteerers3–5 that work using the principle of electrowetting6,7. 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 forces8–10. We have demonstrated this voltageprogrammable surface wrinkling effect in periodic devices with pitch lengths of between 20 and 240 m and with response times of less than 40 ms. By a careful choice of oils, it is possible to optimize either for high-amplitude sinusoidal wrinkles at micrometre-scale pitches or more complex nonsinusoidal profiles with higher Fourier components at longer pitches. This opens up the possibility of developing rapidly responsive voltage-programmable, polarization-insensitive transmission and reflection diffraction devices and arbitrary surface profile optical devices.

The device structure is shown in Fig. 1. The side view (Fig. 1a) shows the glass substrate coated with patterned gold/titanium conducting electrodes, on the top of 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 Fig. 1b.

Electrically induced wrinkling at the oil surface will be considered first for a device with an electrode pitch p of 80 m. When a small volume (0.1 ml) of 1-decanol was initially dispensed onto the device it formed a spherical cap with a contact angle of 58. Every other stripe in the electrode array was biased with an a.c.

voltage of magnitude V0 (r.m.s.) and the interdigitated stripes between them were earthed as shown in Fig. 1. This created a

highly non-uniform, periodic electric field profile in the plane of the oil layer. A polarizable 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 field8–10. When the r.m.s. electrode voltage was greater than V0 ¼ 20 V the dielectrophoretic forces spread the oil into a thin film of uniform thickness h ¼ 12mm, 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 m, 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 interdigitated electrode geometry is commonly used in biological particle manipulation9,1 but dielectrophoretic actuation in fluids has previously been limited to nanodroplet formation and lab-on-a-chip applications12.

The wrinkle at the oil–air interface and the associated periodic variation in the optical path for light travelling through the film has been directly visualized here using a Mach–Zehnder interferometer13. The device was illuminated in transmission mode with He–Ne laser light at a wavelength of 633 nm. One of the mirrors of the interferometer was tilted to produce parallel intensity interference fringes localized at the position of the oil layer. The individual interference fringes were oriented parallel to the x-direction and a periodic change in the oil thickness h(x) caused a directly proportionate periodic shift of the fringes in the y-direction. The interferograms shown as insets in Fig. 2 show the fringe patterns when voltages (20 kHz a.c.) of V0 ¼ 80 V (top left inset) and V0 ¼ 160 V (top right inset) were applied between adjacent in-plane electrodes.

Knowledge of the refractive index of the oil (noil ¼ 1.438 for 1-decanol, ref. 14) allowed the peak-to-peak amplitude A of the wrinkle at the oil–water interface to be calculated directly from the interferometer fringe patterns. The results are shown as filled circles in Fig. 2, where the square of the r.m.s. amplitude of the applied voltage is plotted as the abcissae. The solid line shows the

Under an applied periodic potential the appearance of the wrinkle at the oil–air interface decreases the dielectric energy of the system, but this in turn causes an increase in the area of the oil–water interface. The interfacial surface tension provides a restorative force that resists the undulation deformation on the spread oil film. The observed dependence on the square of the voltage is reproduced by a simple calculation using the following approximations: (i) the wrinkle amplitude is small (A p); (i) the periodic potential profile due to the electrodes, V(x, y), is described by a Fourier series expansion to second order only; and (i) the potential profile is unperturbed by the presence of the oil–air interface. Equating and minimizing the sum of the electrostatic and surface tension energies with respect to the peak-topeak amplitude A of the wrinkle yields equation (1):

0V z xy z x y0V a b 0V

A p

Figure 1 | Structure of the device. a, Side view. A thin layer of oil coats a dielectric layer (shown cross-hatched), which has been deposited onto a glass substrate containing an array of gold/titanium interdigitated striped electrodes (shown by the black electrodes). b, Plan view of the interdigitated electrode geometry.

School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham, NG11 8NS, UK. *e-mail: carl.brown@ntu.ac.uk


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This reproduces the intuitive result that, at a particular voltage, higher wrinkle amplitudes will result from using oil with a higher dielectric constant and lower surface tension. Substituting the values from the linear regression fit to the data in Fig. 2 and

the values of 1oil ¼ 8.1 and g ¼ 28.4 mN m21 (ref. 14) for the dielectric constant and surface tension of 1-decanol into equation

(1) yields h ¼ 5:5mm. This is the correct order of magnitude but lower than the average thickness of h ¼ 12mm estimated from the fringe pattern at the edge of the spread film (see Supplementary information).

The switching speed was measured by monitoring the timedependent intensity of the reflection mode first-order diffraction peak in response to a sudden change in the amplitude of the voltage V0. The device was illuminated in reflection with laser light at a wavelength of 543 nm and the applied voltage (20 kHz a.c. square-wave) was discontinuously switched between a low value, V0 ¼ 10 V, and a high value every 5 ms. The low value was just sufficient to maintain the uniformity of the oil coating. The high value of the voltage was adjusted to achieve a peak in the intensity of the first diffracted order for each particular oil film thickness. For the three different thicknesses h ¼ 20, 18 and 14 m, the r.m.s.

amplitudes of the high voltages were V0 ¼ 93, 90 and 86 V, respectively. From simultaneous transmission measurements of the high-voltage fringe displacements on the Mach–Zehnder interferometer this was found to correspond to a wrinkle of amplitude A ¼ 0.36 m for all cases. Data are shown in Fig. 3 for the low to high voltage transition labelled ‘Switch’, and for the high to low voltage transition labelled ‘Relax’. The times for the intensity to change from the value at 0 ms to 90% of the difference between the initial and asymptotic intensities were 35, 40, 49 ms (switching) and 79, 89, 108 ms (relaxing) for h ¼ 20, 18 and 14 m, respectively.

An amplitude-programmable phase diffraction grating15 has been demonstrated in transmission mode using wrinkles with a shorter pitch of p ¼ 20 m in a filmof 1-decanol oil having an averagethickness of h ¼ 3mm. Figure 4 showstheintensities of thezero-,first- and second-order peaks due to the diffraction of light at 543 nm transmitted through the film with its periodic surface wrinkle as a function of the voltage V0 (20 kHz a.c.) (see also Supplementary information).

The ratio of the peak intensity in the first order to the zero-order peak intensityat low voltage is 32.6%. This is close to the value of 3.8% that would be predicted by the Fraunhofer approximation for a ‘thin sinusoidal phase grating’16.

Still shorter pitches on the scale of micrometres or lower appear feasible, but there are technological challenges in creating a sufficiently thin film of oil. Still higher diffraction efficiencies may be possible by making the fluid surface (rather than the substrate) fully reflective17,18. It is also possible that the surface wrinkle could be produced at the interface between two density-matched liquids, for example, a high-refractive-index oil and water, in an encapsulated device that could be used in any orientation3 (see Supplementary information).

Figure 5 shows oil film surface shapes that aremoreinteresting than the simple sinusoidalprofiles that have been discussed above. Each of


Intensit y (a.u.)

14 µm 18 µm

20 µm

Figure 3 | Transient response of the intensity of the reflection mode first diffracted order as a function of time. Data were taken at a wavelength of 543 nm (0.08 Wcm22) after a wrinkle of amplitude A ¼ 0.36mma t the surface of 1-decanol was turned on (‘Switch’) or off (‘Relax’) at time 0 ms. Measurements are shown for oil layers of three different thicknesses coating the same device as used in Fig. 2, for which the pitch was p ¼ 80mm.

Second order

Zero order

First order

Figure 4 | Intensity of the zero-, first- and second-order peaks due to the diffraction of light at 543 nm. Intensities of the transmitted diffracted orders at 543 nm (0.08 Wcm22) are shown for a film of 1-decanol with average thickness h ¼ 3 m as a function of the magnitude of the voltage (20 kHz a.c.) applied between adjacent in-plane electrodes. The orders were observed at angles of 08 (zero), 1.568 (þ1) and 3.118 (þ2). For this device the dielectric layer was 2 m thick and was fabricated from SU-8 photoresist (see Supplementary information), and the electrode pitch was p ¼ 20mm, which also corresponded to the wrinkle pitch.

Wrinkle amplitude, µ m)

0 V 0 V

Voltage (V)

Figure 2 | Plot of the peak-to-peak amplitude A of the wrinkle at the oil–air interface and interferograms at different voltages. The insets present interferograms showing periodic displacements of tilt fringes at a wavelength of 633 nm (0.61 mWcm22 at device) in a Mach–Zehnder interferometer. These fringe patterns were produced by a layer of 1-decanol oil coating a device with a dielectric stack of thickness 1.13mm (see Supplementary information) with voltages (r.m.s. 20 kHz a.c.) of 80 V (top-left inset) and 160 V (bottom-right inset). The electrode (and wrinkle) pitch was 80mm. The peak-to-peak amplitude A of the wrinkle at the oil–air interface was obtained from the interferometer fringe patterns and is plotted against the square of the a.c. voltage, V20.


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the solidlinesshows an individualsurface profilethat has been created for a particular voltage (represented using different colours) and for a particular average oil film thickness (shown by the horizontaldotted line on which it lies). By using oil with a lower dielectric constant

(hexadecane, 1oil ¼ 2.05), combined with a longer electrode pitch (p ¼ 240 m), it has been possible to program non-sinusoidalpro- files and so switch on other Fourier components with higher spatial frequencies. These higher Fourier components are most prominent at the lowest film thickness, h ¼ 6:0mm, where the surface of the oil film lies closer to the highly non-uniform fringing electric fields at the electrode edges.

In conclusion, we have presented a new and potentially versatile concept of using dielectrophoretic forces to create fluid-based optical switching devices. As an example photonic device application we have demonstrated a switchable phase diffraction grating where the intensity modulation of the undeviated zero order, as well as the diffracted orders, are intrinsically polarization insensitive; the zero- and first-order intensities can be fully modulated at speeds below 40 ms. The voltage-programmable optical effect uses a straightforward device structure and is static, reproducible and stable19–21 when switched on. This combination of properties in a single device is significant compared with existing technologies based on, for example, birefringent liquid crystals22,23, electro-optic or acousto-optic modulators24,25, or deformable polymer layers26. Our further demonstration of more complex non-sinusoidal surface wrinkle profiles suggests the possibility of producing aperiodic or arbitrary surface profiles using independently addressable electrodes for application in two-dimensional spatial light modulator arrays.

Videos showing the modulation of the diffraction pattern in response to a slowly ramping voltage (i) in transmission mode using the 20-m pitch, and (i) in reflection mode using the 80-m pitch are available as Supplementary Information. The

Supplementary Information also provides additional experimental details and discussion of equation (1).

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