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curved membrane enclosure.
[20–23]
Importantly, internal pres-
sure within an enclosed membrane leads to a spherical lens,
whereas, here, the wetting induced elastocapillary effect leads
to aspherical geometry.
[19]
This particular effect differentiates
our system from other conventional optofluidic lenses in which
a curved liquid meniscus or a liquid drop is used as a lens,
[24]
and which essentially remains spherical.
The dual effect of difference in refractive indices (r.i.) of
liquid (ca. 1.33–1.52) and solid (r.i. ca. 1.41) and the curved
interfaces in the layer results in a lensing effect. The focal
length of these lenses can be tuned by number of geometric,
material, and interfacial properties. The layers that house the
lenses can be bonded to a rigid substrate, but can also be gen-
erated on a flexible one, which allows their surface profile and
resultant optical properties to be altered further via axial com-
pression of the substrate. The lenses can be used also as optical
filters, which thus allows compact design of optical elements in
many applications.
Figure 1a shows these lenses prepared in elastomeric layers
of poly(dimethylsiloxane) (PDMS) bonded to a rigid glass
slide. Layers of uniform thickness were prepared by cross-
linking Sylgard 184 between two parallel plates that were
separated by spacers of desired thickness ca. 0.5–1.5 mm.
[17]
The layers were embedded with channels at different vertical
heights: t
min
≈ 5–160 μm, by using cylindrical rods of diameter
d ≈ 0.45–1.2 mm as templates.
[17–19]
These channels remain
circular when filled with air; the elastomeric layer too remains
undeformed, but when filled with a wetting liquid, e.g., silicone
oil (surface tension, γ ≈ 22 mJ/m
2
), excess interfacial energy
of wetting is converted into elastic energy of the channel wall,
which bulges out
[18]
at the region of minimum thickness, t
min
,
as depicted by the side view in Figure 1b. The channel cross-
section deforms from being circular to oval-shaped and remains
symmetric about the location of t
min
. Over time the bulging
height increases further because of diffusion of the liquid, how-
ever small, into the solid network; finally a definite time-invar-
iant profile is attained in about 24 h. Thus, the smooth surface
of a soft elastomer becomes undulating with a spatially varying
curvature which can be used as an aspherical lens. When light
is incident upon the curved elastomer, a line of focused light
is generated, the magnified image of which, when captured
by using a camera fitted with a microscope lens, shows sharp
edges surrounding the line (Figure 1a).
Figure 1f shows curvature κ as a function of distance x from
the location of t
min
for channels of constant diameter d = 450 μm
but different minimum skin thickness t
min
= 20–98 μm. For all
cases, κ remains positive in the vicinity of t
min
, but decreases
away from it, eventually turning negative and then again posi-
tive, and finally asymptotically converging to zero far away from
Design of an Adaptable Optofluidic Aspherical Lens
by Using the Elastocapillary Effect
Abhijit Chandra Roy and Animangsu Ghatak*
Dr. A. C. Roy, Dr. A. Ghatak
Department of Chemical Engineering
Indian Institute of Technology
Kanpur 208016, India
E-mail: aghatak@iitk.ac.in
DOI: 10.1002/adom.201400081
Aspherical optical lenses comprise curved surfaces, the cur-
vature of which varies spatially to generate a sharp image of
an object that is devoid of common optical aberrations. These
lenses are used extensively in a variety of applications: optical
metrology,
[1]
spectroscopy,
[2]
laser diodes,
[3]
acousto-optics,
[4]
holographic gratings,
[5]
grating sensors,
[6]
and laser physics.
[7]
The lenses are used also in applications which require light to
be focused in two dimensions, e.g., light-sheet microscopy,
[8]
line-illumination microscopy,
[9]
and depth-of-focus enhance-
ment.
[10]
These applications all demand minimum optical aber-
ration, a sharp line of focus, and also compact lens modules
for ease of operation.
[11]
Conventionally, however, fabrication of
aspherical lenses is a problem as they involve intricate design
of a surface that precisely follows a specific profile.
[12]
The top-
down approach to fabricating such surfaces involves machining
and polishing a curved solid by using high-precision turning
machines, operation of which requires a highly skilled techni-
cian as well as precise control of temperature, humidity, and
vibration in the surroundings;
[13–15]
all of these increase the
manufacturing cost. The rate of rejection of faulty pieces also
remains very high. The other strategy of generating aspherical
profiles is to draw a preformed material at elevated temperature
to form a cylindrical lens of desired curvature.
[16]
Here too, the
starting material must be of a desired shape, and it is expected
to sustain high temperature. The drawing process tends to gen-
erate a spherical surface rather than an aspherical one, because
of the effect of surface tension. Essentially, there exists no
simple way of manufacturing aspherical lenses, which has a
cascading effect on research in many different fields.
We present a method of generating aspherical lenses by
using an elastocapillary instability induced by surface tension
of a soft rubbery solid. In particular, we have prepared thin
elastomeric layers embedded with microchannels of different
shapes and size of cross-section. When these channels are
filled with a wetting liquid, interfacial energy is released, which
bulges out the portion of the film at the vicinity of the channel,
forming a surface with spatially varying curvature.
[17–19]
Thus,
in contrast to conventional optofluidic lenses,
[20,21]
the bulging
deformation of the elastomeric film occurs spontaneously
without any fluidic pressure being exerted to alter the cur-
vature of an enclosed membrane, nor the need for a prefixed
Adv. Optical Mater. 2014, 2, 874–878