Voltage-programmable liquid optical interface
C. V. Brown*,G.G.Wells,M.I.NewtonandG.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 dielec-
trophoretic forces8–10. We have demonstrated this voltage-
programmable surface wrinkling effect in periodic devices
with pitch lengths of between 20 and 240 mm 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 non-
sinusoidal 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 con-
ducting 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 con-
sidered first for a device with an electrode pitch pof 80 mm.
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 V
0
(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 dielec-
trophoretic force) in the direction of the increase in magnitude of
the electric field8–10. When the r.m.s. electrode voltage was greater
than V
0
¼20 V the dielectrophoretic forces spread the oil into a
thin film of uniform thickness
h¼12 mm, 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 mm, 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 dielec-
trophoretic forces in these regions cause the oil to collect there pre-
ferentially. The interdigitated electrode geometry is commonly used
in biological particle manipulation9,11 but dielectrophoretic actua-
tion 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 indi-
vidual 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 V
0
¼80 V (top left inset)
and V
0
¼160 V (top right inset) were applied between adjacent
in-plane electrodes.
Knowledge of the refractive index of the oil (n
oil
¼1.438 for
1-decanol, ref. 14) allowed the peak-to-peak amplitude Aof 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
linear regression fit to the data: A¼(5.107 10
25
)V
0
2þ0.118,
in micrometres.
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 (Ap); (ii)
the periodic potential profile due to the electrodes, V(x,y), is
described by a Fourier series expansion to second order only; and
(iii) the potential profile is unperturbed by the presence of the
oil–air interface. Equating and minimizing the sum of the electro-
static and surface tension energies with respect to the peak-to-
peak amplitude Aof the wrinkle yields equation (1):
A¼1610
3
g
p41oil 1air
ðÞ
exp 4p
h
p
V2
0ð1Þ
Oil layer
h(x)
0 V
z
x
yzx
y
0 V
ab
0 V
±V0±V0
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, Pl an view of the interdigitated
electrode geometry.
School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham, NG11 8NS, UK. *e-mail: carl.br[email protected]c.uk
LETTERS
PUBLISHED ONLINE: 21 JUNE 2009 | DOI: 10.1038/NPHOTON.2009.99
NATUREPHOTONICS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturephotonics 1
© 2009 Macmillan Publishers Limited. All rights reserved.
