Tunable Liquid Microlenses formed from Dynamically
Re-Configurable Double Emulsions
by
Sara Nagelberg
B.S., McGill University (2013)
Submitted to the Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
ARCHIVES
MASTER OF SCEINCE
MASSACHu
OF ICH-
at the
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JUL 3 0 2015
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Department of Mechanical Engineering
May 8, 2015
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Certified by
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_
Mathias Kolle
Assistant Professor Of Mechanical Engineering
Thesis Supervisor
Accepted by
redacted
_Signature
___
David E. Hardt
Professor of Mechanical Engineering
Chairman, Committee on Graduate Students
I'IiT
111
PELaborat
for
MITMECHE
Photonip
e
Tunable Liquid Microlenses formed from Dynamically
Re-Configurable Double Emulsions
by
Sara Nagelberg
Submitted to the Department of Mechanical Engineering on May 8, 2015 in Partial
Fulfillment of the Requirements for the Degree of Master of Science in Mechanical
Engineering
Abstract
Micro-scale optical components capable of on-demand reconfiguration of their internal morphology and composition would enable unprecedented control of light propogation on the microscale. Double emulsions formed from immiscible hydrocarbons and
fluorocarbons offer a promising platform as reconfigurable micro-optical lenses. These
droplet-based lenses can be reconfigured to strongly focusing, nearly transparent, or
strongly scattering geometries. The dynamic variation of the lenses' optical interfaces
can greatly enhance the lenses' ability to manipulate light. Finite Difference Time
Domain and Raytracing techniques were used to characterize the optical properties of
the drops and the simulations were verified experimentally immersing the lenses in an
aqueous fluorescent medium in order to visualize their light manipulation capabilities.
The lenses show a rapid response to external light stimuli or heat gradients and are
susceptible to chemical triggers.
Thesis Supervisor: Mathias Kolle
Title: Assistant Professor of Mechanical Engineering
3
1
Introduction
Micron-sized lenses find use in a variety of applications including plenoptic cam-
eras [1], integral imaging or 3D displays, and solar collection [2]. They may also find
use in microfluidics in order to collimate diverging light coupled into the system using
an optical fiber [3].
Dynamically tunable micro-lenses formed from hydrocarbon-fluorocarbon double
emulsion drops [4] are presented here. These droplet-based lenses can easily be produced in large quantities The interface between the two phases can be adjusted by
changing the relative surface tensions in the drop, allowing the focal length of the
lenses to be varied dynamically through chemical triggers or optically.
Simulations of the optical response of the drops were done using the Finite difference
Time Domain solver MEEP (MIT Electromagnetic Equation Propagation) [5] as well
as ray tracing methods in MATLAB. These simulations show how the focal length
and depth of the lenses vary when the optical interface between the two emulsion
constituents is modified.
The simulations also show how different rotations of the
drops relative to the incident light can be used to direct light.
This ability of the droplet-based lenses to focus, scatter, or redirect light was experimentally observed by placing the drops in an aqueous solution of Rhodamine B.
The drops were shown to be able to collimate diverging light from the tip of an optical
fiber, as well as to focus light from a plane wave source.
The drops also show an interesting response to an infrared laser. When the infrared
laser is focused in the vicinity of a liquid lens, it will orient itself such that the internal
phase is closer to the focus of the laser. This capability of the drops offers opportunities
for the development of a thermally or optically addressed dynamic 3D display.
5
2
Background
Microlens arrays can be made by shaping the optical interface of a surface on the
micron scale. For example, microlens arrays have been fabricated by creating an arrangement of posts using photolithography and then heating the posts until they melt.
The lenses' shape is dominated by surface tension resulting in a spherical interface [6].
Alternatively microlens arrays have also been created using gradient refractive index
(GRIN) through ion exchange [7]. In both cases, the resulting microlenses have a fixed
focal length.
Micro-lenses formed by control of liquid configurations are an appealing option for
several reasons. The surface roughness of liquid interfaces is significantly smaller than
the wavelength of visible light (the surface roughness of a water-air interface is several
angstroms [8]) ideal for high quality optical interfaces. Liquids can also be tuned after
the lens is formed. Liquid lenses with a variable focal length have been fabricated by
taking advantage of electro-wetting [9-11]. In these cases, the contact angle between
the solid and liquid is manipulated by applying a voltage. In order to negate the effect
of gravity the lens is enclosed in a second, density-matched liquid and hysteresis can
be minimized using a lubricating liquid.
Variable focal length lenses have also been fabricated using microfluidics where the
amount of liquid in a cavity behind a membrane is varied [12-14]. In essence, these
lenses work similarly to the human eye. By varying the pressure in the microfluidic
channel, the curvature of the lens is adjusted, and therefore the focal length. Flows of
liquid have also been used to create variable lenses within the plane of the micro-fluidic
channel [3].
The liquid lenses presented here are formed from double emulsions. The method
for creating the double emulsions developed by Dr.
Lauren Zarzar with Professor
Tim Swager's group in the MIT Department of Chemistry, utilizes fluorocarbons and
hydrocarbons in an aqueous solution. Fluorocarbons are ideal for forming these double
emulsions because they are both lipophobic and hydrophobic at room temperature,
7
(1)
(2)
(3)
YH
W
C
YFH
'F
VI
6.0
YH
YFH'
4.0-
F, OF 4 40
a
\FH
(
'H
F
(E
zH
Ei
F
YFH
'F
II
-
b
V
00
AF
-2.0
-4OT
Fluorosurfactant diffusion
20
4-
0.8
0
0.1
0.2
0.4
0.6
0.1% Zonyl
F/H/W
H/F/W
Janus Droplet
0.1% SOS
fw
III
IV
V
VI
Vil
d
Figure 1: Droplet Morphology. a) Sketch of effect of surface tensions
on drop morphology b) Hexane-perfluorohexane drops reconfigure due to
variation in surface tension as zonyl diffuses through a solution of SDS.
c) difference in surface tension as a function of surfactant concentration.
d) Optical micrograph of the various geometries of the drops. Reproduced
with permission from [4].
and the temperature above which they will from a homogenous mixture (the critical
temperature T,) with hydrocarbons is relatively low (< 700 C). By gently heating the
fluorocarbon and hydrocarbon to a temperature above T, they can be mixed to form a
homogeneous solution. When drops of this mixture are then cooled back below T, in an
aqueous solution, they will phase separate to form drops that are compartmentalized
into the two distinct materials [4].
100 pm), surface tension is the dominant
On the length scale of the drops (~
force [15] and thus determines the morphology of the emulsions. The interfaces will
therefore be spherical and the contact angles are:
2
cos
2
2
-
2
H F - HY FH
-YFHYH
2
2
cos OF = YH
-F
2
2
~ "FH
(1)
(2)
"YFH'YF
where -YF is the inter-facial tension between the fluorocarbon and the water, -yH between the hydrocarbon and the water, and -YFH between the fluorocarbon and the
hydrocarbon [4].
By changing these inter-facial tensions it is possible vary the drop through the var-
8
ious geometries depicted in Figure 1. This can be accomplished by adding surfactants
such as Zonyl or sodium dodecyl sulfate (SDS) to change -yF and
7H. Changing the
relative concentrations of these two surfactants allows the contact angle (and thus the
curvature) of the internal interface to be controllably varied. A change in curvature
translates into a change in focal length when the drop is used as a liquid lens.
9
10
3
Simulations
3.1
Background on Optical Modeling Techniques
As the emulsion droplets range in size from a few microns in diameter to hundreds of
microns, the optical properties were simulated using two methods. The first method, for
the smallest of the drops, was Finite Difference Time Domain (FDTD) calculation using
the open source software MEEP (MIT Electromagnetic Equation Propagation) [5].
The larger drops could be simulated using simple ray-tracing techniques implemented
in MATLAB.
3.1.1
Finite Difference Time Domain Simulations using MEEP
Electromagnetism can be summarized by Maxwell's equations:
aB
VxE=-,
at
V xH=~aD + j,
at
V-B=O,
V D =p
where E is the electric field, H is the magnetic field, D is the displacement field,
B is the magnetic induction field, and p and . are the charge and current densities
respectively.
The Finite Difference Time Domain (FDTD) technique numerically solves Maxwells
equations by dividing time and space into discrete units and stepping forward in time
to solve for the electric field and magnetic field at each point in space and time. The
computational cell is divided into a uniform grid in both time and space, and the
derivatives in Maxwell's equations are approximated as finite differences. MEEP then
uses a leap frog algorithm to step forward in time. At a time t the electric field E
at each grid point is calculated from the surrounding electric field grid points at a
time t - At and the magnetic field at surrounding points at time t -
t. Similarly,
the magnetic field H is then found at time t + A. This leap frog method is repeated
11
through the entire simulation. Reflections at the edge of the computational cell are
avoided using a perfectly matched layer [16].
Increasing Resolution
pp
1
0.7
-
0.8
.
0.6
0.5
0.4
0.3
0.2
01
0
10000
8000
E
6000
0
4000
E2000
CL
0
20
40
Resolution
60
Figure 2: FDTD Resolution. Simulations of 500nm wavelength light
propagating through a 10 pm diameter double emulsion drop with resolution a) 8, b) 10, c) 16, d) 32, e) 128 grid points per pm. f) plot of the
computation time required for each of the simulation cells. For extremely
low resolution the light will not even propagate, however for extremely high
resolution, the computation time is very high.
The FDTD simulation technique is both powerful and straightforward to use, however comes at the cost of being computationally expensive, as it needs to calculate the
electric and magnetic fields at every point in space for each time step. In order for
the solution to converge, the temporal resolution must be at least twice the spatial
resolution.
Therefore for a 2D simulation, the computation time is proportional to
third power of the resolution, and for a 3D simulation cell, the computational time
increases as fourth power of the resolution. The effect on the output of the simulation
by varying the resolution can be seen in Figure 2.
12
3
12.5
3
2
(V
1.5
.4-,
C
0.5
0
3
3-
d
C
2.5
2
2
1.5
._
1.
01
0
0.5
0
0
40
30
20
10
z (PM)
50
3
0
10
0
20
40
50
3
e
2.5
2.5
2
2
1.5
1.5
)1
0.5
0.5
-10
-5
0
SPM)
5
10
01
-10
-5
0
x Pm
5
10
Figure 3: Comparison of 2D and 3D Simulations of Double Emulsions. Finite Difference Time Domain simulations of 500nm wavelength
light through 10 pm diameter double emulsion drop at a resolution of 16
points per pm. a) Intensity distribution for a two dimensional computational cell. Symmetry is assumed for the 3 rd dimension, so the drop is
modeled as the cross-section of an infinite fiber. b) Cross-section of full
three dimensional simulation. c, d) Optical intensity profile along optical
axis of 2D and 3D simulations respectively. e, f) Intensity profile at focal
plane.
Each of the simulation cells in Figure 2 was run for 264 time unitsi, with increasing
resolution.
In the case of a low resolution simulation (8 grid points per pm) the
simulation could not even capture the propagation of the light. The 10 grid points
'This time was chosen based on the time it takes the monochromatic source to turn on and then the light
to propagate through the cell, allowing for a steady state to be reached.
13
per pm simulation varies greatly from the high resolution 128 grid point simulation.
The 16 grid point resolution simulation captures most of the information of the high
resolution, and the 32 is almost indistinguishable. In 3D the computation time is even
higher and increases even more quickly, so the 16 grid points per pm resolution was
used.2
Given that the computational time is so long for a high resolution 3D simulation,
it is appealing to use 2D simulations to gauge the general behavior of the system. A
comparison of 2D and 3D simulations of a double emulsion can be seen in Figure 3.
While the intensity at the focus is significantly increased for the 3D simulation, the
overall behavior is similar. In both cases the distance from the center of the drop
to the point of highest intensity is 16 pm (marked with a dashed line in Figure 3).
In this comparison both simulations were run at a resolution of 16 grid points per
pm. Throughout the rest of this work, 3D simulations shown are done with this same
resolution, but 2D simulations were completed at a higher resolution of 32 grid points
per pm.
3.1.2
Ray-Tracing
For emulsion droplets significantly larger than the wavelength of interest
(
drop
radius ~ 100 pm) ray-tracing techniques are sufficient for understanding the basic
behaviour of the system. To this end a simple ray-tracer was created in MATLAB.
The ray-tracer is implemented using MATLAB's object oriented environment. Each
Ray object had properties 3 including the position, direction, amplitude, and an array of
past locations. The rays are propagated through the drop by locating each intersection
point and then calculating the refraction using Snell's law.
The amplitude of the
transmitted and reflected waves was determined using the Fresnel equations [17].
For a three dimensional ray-tracer it is simpler to model refraction and reflection in
terms of vector representations of light rays. Consider a ray traveling in the direction
2
3
Even at this resolution a single simulation takes several days to run.
1n MATLAB, object fields are referred to as properties.
14
dj
ft
n2
\W2
Figure 4: Vector Diagram for Snell's Law.
index
d 1 refracting through a surface with normal n' from a material with refractive
plane
ni to a material with refractive index n2 . Refraction will take place within the
formed by n' and d 1 . Therefore consider a vector
t perpendicular to n' in this plane
such that
d,
=
sin O 1 t+ cos 6 1n
(3)
sin 62 t- cOS 02
(4)
and
d2=
as can be seen in Figure 4. From equation 3, t must then be:
-d
t
+ cos 0 1n
sin
15
1
(5)
The outgoing angle
02
can be determined using Snell's law:
ni sin 01 = n2 sin 6 2
Using the identity sin 2 9 + cos 2 9
=
CO
(6)
1 Snell's law can be written in terms of the cosines
=
-
(1
(
-
(7)
cos 1)
Substituting Equations 5, 6, and 7 into Equation 4 yields a vector form for Snell's Law:
2=
-di + (
n2
n2
V/i-
cos
(
\2
)[1
-cos29]) n;
(8)
The angle 01 between the incoming ray and the surface normal is easily obtained
from the dot product:
cos 01 = di - n
(9)
since d1 and n' each have unit length.
Similarly, rays are reflected at the same angle that they are incident of the surface
d.
sin O 1 - cos
=
1 in
(10)
The ray-tracer handles reflected rays by recursively calling the same algorithm for
propagating the ray through the drop for each reflection.
The Fresnel equations are
used to determine the amplitude of the transmitted and reflected rays. Total internal
reflection occurs when
sin0 1 >
-,
n,
or equivalently
1
<
1-
(
cos9
One tn2 y
Once the rays are propagated through the system the intensity can either be de-
16
termined coherently or incoherently. If coherent illumination is assumed, the intensity
is determined by summing the complex amplitude of the rays and then squaring the
absolute value. For incoherent illumination, the intensity of each ray is determined by
squaring the absolute value of the amplitude and then the intensities of all the rays is
summed.
3.2
FDTD Simulations of Focusing and Scattering Droplets
When placed in an aqueous fluorocarbon surfactant solution, such as Zonyl, the
emulsions will adopt a configuration such that the fluorocarbon phase is on the outside.
In general, the fluorocarbon has a lower index of refraction than the hydrocarbon phase
on the inside. The resulting drop works well to focus light. If however, a hydrocarbon
surfactant is used, the higher refractive index hydrocarbon phase will be on the outside
of the drop, and the drop will scatter light, as can be seen in Figure 5.
Due to the presence of gravity, the drops do not form in a concentric morphology,
but the lower density material floats. In most cases, the hydrocarbon phase is lighter
than fluorocarbon.
In the case of the focusing drop shown in Figure 5a with the
fluorocarbon phase on the outside, the inner hydrocarbon drop floats.
The two lens configuration extremes, highly scattering and strongly focusing, resemble the geometries of retinal cell nuclei found in nocturnal and diurnal mammals [18-20].
Simulations of the droplets' optical behavior show that they focus and scatter light in
a very similar way as individual retinal cell nuclei. Therefore, the tunable lenses could
represent a versatile experimental model system for elucidating the detailed function
of the observed biological retinal architectures by performing experiments that might
be difficult or impossible to realize in the biological systems.
17
12
ab
10
6.1-
C
nw
n,
n
2
0
Figure 5: FDTD Simulations of Light Scattering by two Extreme Emulsion Droplet Geometries. The refractive indexes of the
two droplet phases are ni = 1.387 (heptane), n 2 = 1.27 (FC-770). The surrounding medium has a refractive index of nm = 1.33 (water). a) Strongly
focusing drop in solution with Zonyl. Heptane is the inner phase and
FC-770 as the outer phase. b) The same droplet in SDS strongly scatters light as the two phases switch position.
3.3
Focusing Dependence on Inner Radius of Curvature
When the emulsions are immersed in an aqueous solution with an appropriate
mixture of hydrocarbon and fluorocarbon surfactants, Janus drops will form. Since
the surface tensions of the drop depend on surfactant concentrations, the curvature of
the inner drop will depend on the ratio of the surfactant concentrations. A diagram
of the geometry of such a drop can be seen in Figure 6. V
-
A i
Volume
liquid B
of liquid
Volume of
the
h
volume ratio, Rd is the radius of the drop, Ri is the radius of curvature of the internal
interface of the drop.
The interface between the two liquids is modeled as sphere with radius Ri located
a distance d from the center of the drop. Geometrically, it can be shown that d solves
18
Figure 6: Diagram of Emulsion Geometry. Rd is the radius of the
drop, Ri is the radius of curvature of the internal interface and d is the
distance between the drop
center and the sphere modeled for the internal
interface.
the equation:
(d + Rd - Ri)2(d2 + 2d( Ri -- Rd) - 3( Rd + Ri)2) + 16d 1+?2V
The contact angle is related o
rva
COSO =
= 0.
(11)
of theRintrnalditerfahe relation
R2 + R2 - d2
i
2RdRj
(12)
Combining these gives a relation between the contact angle, inner radius of curvature
and the volume ratio.
Figure 7 shows several 2D FDTD simulations of double emulsions with varying
radii of curvature. As expected, stronger focusing can be seen for the smaller radius of
curvature. The far field distribution was approximated by Fraunhofer diffraction [21].
The far field angular distribution of intensity is wider for a smaller radius of curvature.
For a flat interface between heptane (n
=
1.387) and FC770 (n = 1.27) the far-field
distribution is very similar to the case when there is no drop present. The flat interface
19
1
C
0)
-20
0
20
-20
-20
20
0
0
20
-20
0
20
0
-20
20
-20
0
20
(W)
g
12
10
8
6
4
0
10
30
20
40
50
Radius of Curvature of Inner Interface (Pm)
Figure 7: FDTD Simulations of Double Emulsions with Various
Internal Radii of Curvature. The two-dimensional simulations were
done with a resolution of 32 grid points per pm for 500 nm light incident
on 10 pm diameter droplets with internal radii of curvature a) 3.96, b) 6,
c) 9, d) 20, and e)oo (flat interface). f) The same simulation with no
drop present. The far-field distribution of the drop with the flat internal
interface and the aperture when no drop is present are very similar. g) The
width of the far-field distribution.
drops are nearly transparent.
3.4
Transparent Janus Droplets
One potential application of the emulsions is to create a screen that can easily be
switched between opaque (scattering drops) and clear (transparent drops). To achieve
this transparency the drops need to have no net focusing power, that is to say that
rays that enter the drop parallel, leave the drop parallel. This can be accomplished
20
if refraction at the second edge of the drop essentially "undoes" the refraction at the
first edge. This can happen for a convex lens if one of the indexes of refraction is lower
than that of the surrounding medium. This is almost the case for the flat Janus drop
formed from FC770 and heptane. Figure 8a shows how parallel rays interact with this
drop.
As long as one of the indexes of refraction is below that of the surrounding medium
and the other is above, it should be possible to satisfy the condition that rays that
enter the drop parallel, leave the drop parallel. By curving the internal interface this
can be accomplished even when one of the indexes of refraction is significantly higher
than that of the surrounding medium and the other is only slightly lower. The amount
curvature required can be determined using the paraxial approximation and the ray
transfer matrix method.
The ray transfer matrix considers a ray that starts at an initial input plane and
travels to a final output plane both perpendicular to the optical axis. For a ray starts
a distance x 1 from the optical axis with angle 01 from the optical axis, the position
and angle of the ray at the output plane can then be approximated by:
X2
A
B
x1
[2
C
D
01
(13)
The matrix for one of the droplet-based lenses is:
A
B
[1
C
D
n2nm
nRd
01-d
n
nm_
Into Drop
Internal Interface
Out Of Drop
1
1
0
1
[i-n2
n 2 Ri
Through Second Phase
0
1
Rd+d-i
1
0
a-
0
1
nm-ni
n1Rd
nm
n2
Through First Phase
(14)
In order for rays that enter parallel to exit parallel, component C of the above
matrix should be equal to zero.
The resulting equation can be numerically solved
simultaneously with Equation 11 for the radius of curvature of the inner interface Ri.
21
n1
Figure 8b shows parallel rays through a drop where ni
=
1.6 and n2
=
1.31. While
the focal length of this drop is infinite, the rays become more condensed as they exit
the drop. Such a drop might be useful as a micro-beam expander/condenser.
a)
n
m
T)
n
~
2a
la
b )n m
n2b
Figure 8: Raytracing through Transparent Drops. a.) A Janus
drop formed from heptane(nia = 1.38) and FC770 (n 2 a = 1.27), the radius
of curvature at the interface is R, = 24.8 x Rd. b) Example of a higher
refractive index drop (nib = 1.6 and n2b = 1.31 ) with curved interface
Ri = 1.01 x Rd.
3.5
Rotations of Droplet-Based Lenses
Since the fluorocarbon and hydrocarbon liquids in the drops are not perfectly
density-matched, the drops do not exhibit spherical symmetry even when they form
complete double emulsions.
Flat interface Janus drops can be used similarly to prisms to redirect light. Figure 10
shows how the drops can accomplish this.
For small angle deflections, the far-field
distribution resembles that of the aligned drop, but shifted. Large angle deflections
however are not possible as at glancing angles a large amount of light is reflected at
the interface between the two materials.
22
Sbd8
6
n
L
2
Figure 9: 3D FDTD Simulation of Rotations of Double Emulsion
Drops. 500 nm light sent through 10 pm diameter drops formed from
heptane (n1 = 1.387) and FC-770 (n2 =1.27) at rotations a =a) 01,
b) 300 , c) 600, d) 900.
AAM,,
-5-,
CDC
-2012
0
-50
0
50 -50
0
0
so -so
50 -50
0
56-
f
-4-
E
0
20
40
>0
Ro tati on An gle a (4)
Figure 10: 2D FDTD Simulations of Flat Interface Janus Drops
at Various Rotations. 500 nm wavelength light sent through 10 Pm
diameter drops formed from heptane (n = 1.387) and FC-770 (n2 = 1.27)
at rotations a = a) 00, b) 100, c) 30', d) 60'. f) Far-field deflection angle
as a function of droplet rotation.
23
24
Experimental Characterization of the Droplets
4
4.1
Emulsion Materials
The emulsions can be formed from a variety of different transparent optically distinct materials provided that the two materials are both hydrophobic and immiscible.
Several different combinations of liquids and their indexes of refraction can be seen in
table 1. The optimal material choice depends on desired application. The transparent
drops discussed in section 3.4 can only be created for an emulsion where one of the two
phases has a refractive index lower than the surrounding medium (1.33 for water). On
the other hand, better focusing can be accomplished if both phases have an index of
refraction higher than the surrounding medium.
Fluorocarbons
Perfluorohexane
3M Fluoronert FC770
Methooxyperflourobutane
Index
1.25
1.27
??
Hydrocarbons
Heptane
Hexane
Hexadecane
Index
1.39
1.38
1.43
Table 1: Refractive Indexes of Materials Used to Create Dynamically Reconfigurable Double Emulsions. Values obtained from ChemSpider online
database [22].
The drops are made by simply combining the fluorocarbon and hydrocarbon in the
desired volume ratio (usually 1:1) in a small capped vial and heating until the two
materials mix. The point when they mix is easily observed as the phase boundary
will vanish and the solution will remain transparent when gently agitated. Care is
taken to not overheat the mixture, as the liquid will start to evaporate, changing
the volume ratio. A slightly larger volume of the desired surfactant solution (usually
4
0.1% by weight either Zonyl or SDS) is simultaneously heated. A warm pipette is
used to transfer the fluorocarbon-hydrocarbon mixture to the surfactant solution. The
resulting solution is shaken to form small drops and allowed to cool back below the
critical temperature, at which point the hydrocarbon and fluorocarbon will separate
within each drop.
'The heating can be accomplished on a hot plate or simply using hot air from a hairdryer.
25
The two primary combinations used are Flourinert FC770 (trademark 3M) with
heptane and perfluorohexane with either heptane or hexane. The advantage of FC770
over perfluorohexane is that it has a higher boiling point, so less will evaporate during
the heating process. The advantage of heptane over hexane is that it has a higher
critical temperature with the fluorocarbons, which allows for double emulsions at room
temperature.
4.2
Visualizing the Light Manipulation Power of the Lenses
In order to visualize the optical power of the liquid lenses, fluorescent dye was
added to the aqueaous medium to visualize the path of light. This method has been
used in the past [3] to characterize liquid lenses. Rhodamine dye at sufficiently low
concentrations will fluoresce along the beam path of the laser without overly reducing
the intensity of the beam. This allowed the path of light to be traced over distanced
os several pm.
4.2.1
Illumination of the Lenses Using an Optical Fiber
A green (532 nm) laser diode was coupled into a 50 pm core optical fiber, the other
end of which was submerged into an aqueous solution containing a small amount of
Rhodamine B (- 5 ppm). The fluorescence of the Rhodamine could then be photographed easily, allowing the laser beam to be visualized as can be seen in Figure 12.
As the drops have a higher density than water, they sink to the bottom of any
container they are placed in. Therefore, a substrate with similar optical properties
to the surrounding medium was needed to hold the drops. Water beads designed for
craft purposes (typically made from sodium polyacrylate) work nicely. These gel beads
could as easily be swollen in a solution of Rhodamine as a pure water solution. As these
beads were designed to be nearly invisible in water, their refractive index matches that
of the solution very closely. There is some variation in refractive index however and a
very small amount of glucose could be added to the water-rhodamine solution in order
to index match more closely.
26
Optical
Fiber
Illumination
SSource
To
Tube Lens
Scattering
Computer
Screen
Objective
CCD
WaterA
Bead
Gel
Figure 11: Schematic of Setup Used to Visualize Light. A 50 Jrm
core optical fiber sends light into the cuvette containing the rhodamine
solution and water bead used as substrate for the drops. The drops and
fluorescence was imaged through a custom microscope setup.
The gels were swollen inside of cuvette in order to hold them in place. An aqueous
solution containing the surfactant (Zonyl or SDS, < 0.1%) and Rhodamine B (~5ppm)
was then added above the gel. The surfactant was added just before the experiment
was conducted, as the SDS would gradually push the Rhodamine out of the gel. A
small number of the emulsion lenses were then added to the cuvette. The laser light
path and drops were imaged using a custom built horizontal microscope setup.
A full schematic of the optical setup can be seen in Figure 11. The optical fiber
is gripped above the cuvette and can be positioned using an x-y-z translation stage
with pm-scale precision. The cuvette is similarly held on a three-axis translation stage.
The six degrees of freedom allows a single drop to be positioned in front of the microscope and simultaneously to align the illumination fiber. The microscope consists
of an Olympus UplanFLN 4x objective, a Thorlabs infinity corrected tube lens and a
Thorlabs USB 3.0 camera.
27
Figure 12: Photograph of the Rhodamine Solution with the Green
Laser Coupled in Through the Optical Fiber. a) Macroscopic view
of cuvette with laser coupled in through the fiber. b) Image of a fiber tip
in the rhodamine solution through a 5x objective. Scale bar lOOµm.
4.2.2
Utilizing a Flat Waveguide
The greatest disadvantage of using the optical fiber in order to couple light into
the liquid lenses is that it resulted in a partially diverging beam. Since the size of the
fiber core is comparable to the lens size, the fiber can not be approximated as a point
source nor as a plane wave source, the two ideal conditions for measuring the focusing
power of the lenses. In order to get a plane wave source, a long, thin flat waveguide
was used to send light into the drop solution.
The 532nm laser was coupled into a cover-slip (VWR) using a Thorlabs N-BK7
right angle prism. The light was then contained within the coverslip by total internal
reflection. A diagram of this can be seen in Figure 13.
The primary disadvantage of this setup is that the light is sent in horizontally. Since
the drops orient themselves vertically due to gravity this essentially means that light
is sent in perpendicular to the optical axis. In order to send light through the optical
axis of the drop lenses this system needs to be rotated 90° . Initial attempts at rotating
28
Microscope objective
Immersion oil to
smooth interface
Slight gap
Figure 13: Laser Coupled Into Solution Using a Flat Waveguide.
The 532nm laser was coupled into a microscope coverslip through a N-BK7
right angle prism. Index matching immersion oil was used to aid the transmission of light from the prism to the coverslip.
this setup were done by adding a layer of teflon to the coverslip to act as a "cladding"
and used to seal the bottom of the cell. The sides of the cell were sealed with nail
polish. Thin slices of the water beads were placed into the cell as a substrate for the
drops. The rhodamine solution was added from the top using a needle and syringe.
The emulsions were added last by applying a small amount of solution above the cell
and allowing gravity to pull the drops onto the gel substrate.
4.2.3
Results
Figure 14 shows the optical fiber coupling light into drop formed from FC-770 and
heptane.
The light path without the drop present is imaged first as a comparison.
While the focus of the drop can not be seen, the drop does serve to collimate the light
leaving the fiber. The white boxes in Figure 14 represent the area used in the analysis
seen in Figure 15. The green image channel was used in the analysis.
Since the light is diverging from the fiber, the lens acts more to collimate the light
than to focus it. Although coupling light into the lens through the optical fiber did not
allow the focus of the lens to be visualized, it does reveal evidence that the drops might
find use has collimating lenses at the end of optical fibers especially in micro-optofluidic
29
Figure 14: Liquid Lens Used to Collimate Light Exiting an Optical Fiber. a) fiber is misaligned from the drop and the light is diverging.
b). Fiber aligned with the drop results in a tighter beam. The white box
represents the area show in Figure 15.
160
140
150
100
S50
0
0
C
d
120
120
I
100
80,
80
60
60
401
0
I
600
400
200
Distance (pill)
0
80
80
70
70
60
60
400
600
200
Dist attce (pill)
rI 50
40
40
30
30
-200
-100D
0
100
Disttinti (Pill)
200
-200
-100
0
100
Distance (Pill)
Figure 15: Intensity of the Rhodamine Fluorescense. a) Fluorescent intensity from the green image channel from Figure 14a and
b)Figure 14b. c) Intensity along optical axis when the drop is not in
the beam path and d) when the drop is aligned. e, f) Cross-section of the
fluorescence of the rhodamine due to the beam without the drop and with
the drop respectively.
30
200
50
-
60
40
C
W
20
L
0
10
d
e12
8
.
'
10
C
6
42
4
-U
C
2 E
0
Figure 16: Intensity of the Rhodamine Fluorescense using the
Prism Setup. a) Bright field microscope image of a FC770-heptane drop
from above b) Bright field illumination turned off and laser turned on.
c) Intensity of fluorescence taken from the red image channel of the image
in b. d) Cross-section of 3D simulation of double emulsion drop; the dotted
line represents the plane in (e). e) Off optic-axis intensity from 3D FDTD
simulation of FC770-heptane drop.
devices.
The Flat waveguide method of coupling light into the droplets did allow the focus of
the lenses to be visualized (Figure 16). This method however did not allow for testing
various configurations of the drops. as the light was not aligned with the optical axis
of the lens. Figure 16d shows the cross-section that is expected from the setup.
31
4.2.4
Total Internal Reflection Rings
An interesting phenomenon that can be observed for these drops is coupling into
total internal reflection modes. The optical interface inside of the drops breaks the
spherical symmetry allowing this coupling to occur. Light that enters the drop near
the edge will be reflected around the drop's internal interface and back into the camera
(Figure 17). The effect appears as bright rings around the three-phase contact line.
Although this total internal reflection can occur whenever the spherical symmetry
is broken, the reflected light will only reach the camera when rays exit the drop at an
angle close to the angle at which they enter.
Incoming Light
TIR
n
n,
n2
n, >n
Reflected Rays
Figure 17: Total Internal Reflection Rings. Drops are illuminated
and imagined from above. Ray diagram on the right shows how the rays
are reflected around the inner interface of the drop through total internal
reflection.
4.3
Tuning Lens Orientation with an Infrared Laser
The emulsion lenses exhibit interesting behavior when placed into an optical trap.
An optical trap, also referred to as optical tweezers uses an optical intensity gradient to
move small, optically distinct particles or cells around in a medium [23]. When the light
hits the particle, it is refracted. A difference in optical intensity across the width of the
particle causes in a net change of momentum of the light, resulting in a change in net
force on the particle. If the particle has a higher refractive index than the surrounding
medium it will be drawn towards the area of higher light intensity, similarly if it has a
32
CCD
To Computer
ri
Laser
Tube Lens
M2
BS1
Illumination
Source
LaserB2
Li
L2
L3
Objective
M1
Sample
Figure 18: Schematic of the Optical Trap. A laser beam is expanded
and collimated before being coupled into a custom microscope setup. The
location of the optical trap can be manipulated by rotated mirror M1 and
M2. The insets a) and b) show 10 pm polystyrene colloids being manipulated with this optical trap.
lower refractive index, it will be pushed away. The shape and location of the trap can
be controlled dynamically using scanning mirrors or beam shaping [24, 25].
A custom optical trap was constructed in our lab (Figure 18) A Thorlabs 915nm
wavelength laser diode was used as the laser source.
The trap could be controlled
this
manually by adjusting the angle of either mirror MI or mirror M2. In the future
trap could be automated by adding a spatial light modulator to the beam path, or by
replacing M2 with a scanning galvo-mirror system.
When the focusing conformation of the drops (high index core, low index shell) are
refractive
placed into the optical trap, they behave as would be expected. The higher
33
index core is pulled towards the focused laser, and the lower refractive index shell is
pushed away as can be seen in Figure 19. However the reversed scattering drops do
not behave as expected; the lower index core is also drawn towards the focused laser!
-20 pm
Figure 19: Single Drop Follows Laser Focus. An infrared laser is
coupled into a solution containing heptane-perfluorohexane drops through
a 60x objective. The inner phase (heptane) moves in the direction of the
laser focus, while the overall drop appears to remain stationary.
This re-orienting effect can be observed for surpisingly large distances between
drop and focused laser spot. Figure 20 shows a number of heptane-perfluorohexane
emulsion drops following the focused infrared laser. In this case the laser was coupled
in through a lOx objective through the water-air interface. The numerical aperture of
the lOx objective lens (0.3) is usually too low for optical trapping. This observation
along with the behavior of the scattering drops (low refractive index inner phase, high
refractive index outer phase) has led us to the conclusion that the double-emulsions
are not reacting to the optical intensity gradient, but instead to another force in the
system- most likely the light induced thermal gradient.
Since the surface tension between aqueous and organic liquids is temperature dependent [26], the change in orientation and morphology of the drop emulsions could
be due to a thermally induced gradient in surface tension across the drop. The minimization of surface energy could result in the drop being oriented towards the heat
source.
34
Figure 20: Drops "Watching" The Laser Focus. An infrared laser is
coupled into a solution containing heptane-perfluorohexane drops through
a lOx objective. The inner phase (heptane) moves in the direction of the
laser focus.
35
36
5
Conclusion
Double Emulsions Droplets formed from two immiscible hydrophobic materials can
be switched between several configurations that change the optical properties of the
drops significantly. When they are in a state where a material with higher refractive
index surrounds a lower refractive index material they will strongly scatter light. In
the opposite configuration - lower refractive index on the outside - the drops will focus
light. By tuning the surface tensions of the droplet, they can form intermediate states
which can be transparent or used to direct light.
Visualization of the drops capability to manipulate light using rhodamine B showed
that the droplet lenses could be used to collimate light from the tip of an optical fiber,
which could prove useful in optofluidic devices. Unfortunately, this method did not
allow to quantitatively characterize the lensing abilities of the drops. Since the light
from the fiber tip was diverging, it was not possible to get a focal point from the lens.
The flat waveguide setup minimizes this problem, however it has not yet been used
along the optical axis of the droplet lens. Optimization of a vertical version of this flat
waveguide setup should provide more experimental characterization of the lenses.
By changing the radius of curvature of the internal interface the amount that the
droplet-based lenses focus or scatter light can be manipulated. In the future in will also
be interesting to see what capabilities can be realized by changing the volume ratio of
the constituents, and by creating double emulsions with other materials. For example,
higher refractive index materials could be used to create drops that closely resemble
the geometry of nocturnal mammal nuclei [18-20] in order to better understand the
natural system. Density matched materials might allow droplet-based lenses that don't
orient themselves so strongly to the gravitational field. The rich parameter space of
materials and volume ratios might even be exploited to create drops that minimize lens
aberrations.
The glowing total internal reflection (TIR) rings observed for some drop configurations are an interesting phenomenon that might be useful for sensing or for contact
37
angle determination.
It is only for a fairly narrow set of geometries that the light
coupled into these TIR modes will be reflected back in the same direction. The width
of the rings as well as their presence might be used as in indicator for the specific
configuration of the drop.
The demonstrated ability of tuning the droplets' orientation and possibly morphology with an infrared laser is also extremely interesting. While we hypothesis that the
change in orientation is due to a thermal gradient, the precise mechanism responsible
for the laser-induced switching needs to be investigated in more detail. To this end,
the change in droplet conformation under various heating conditions could be studied.
The thermal gradient could be manipulated in several ways including changing the
beam shape or intensity, adding a molecular absorber to the surrounding medium or
possibly through resistive heating or thermo-electric heating and cooling.
The beam shape of the stimulating laser could be manipulated using a spatial light
modulator.
The effect of multiple beams on the geometry of the drops could also
be investigated, using diffractive optics, a spatial light modulator or time sharing of a
single beam using a scanning mirror. The range of the force associated with the optical
intensity gradient could simultaneously be evaluated for a given beam profile by adding
small (1 - 3 pm) tracer particles, which would help to further distinguish between the
relevance of optical intensity gradients and thermal gradients. Adding a chemical agent
with high infrared absorption to the surrounding medium would increase the thermal
gradient, which could yield faster switching at lower optical intensities.
The capacity to switch the droplets electrically would also be beneficial in many
application scenarios. Local thermal gradients could be generated using miniaturized
resistive or thermo-electric heaters.
This may be accomplished by placing a small
resistive filament (such as a Tungsten light bulb filament) in the solution near a drop
and observing the changes in geometry as a voltage is applied. In both cases, optically
heating and resistively heating, it would be interesting to simultaneously monitor the
temperature distribution around the droplets, which could be accomplished with a
thermographic camera.
38
Double Emulsions formed from hydrocarbons and fluorocarbons in an aqueous solution exhibit a variety of interesting optical effects. These optical properties can be
manipulated using chemical triggers and thermal gradients. Macroscopically these effects might be visualized in order to create integral imaging displays. Additionally the
drops could find use in on-chip microscopy systems, sensors, or fiber couplers.
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