Supporting information
Dynamic Manipulation of Modes in an Optical Waveguide
Using Dielectrophoresis
Aminuddin A. Kayani1, Khashayar Khoshmanesh1, Thach G. Nguyen1, Gorgi Kostovski1,
Adam Chrimes1, Mahyar Nasabi1, Daniel Heller2, Arnan Mitchell1 and
Kourosh Kalantar-zadeh1
1
School of Electrical and Computer Engineering, RMIT University, Melbourne, Victoria
3001, Australia.
2
Department of Chemical Engineering, Massachusetts Institute of Technology,
Cambridge, Massachusetts 01239, USA.
Email: aminkayani@gmail.com
Fax: +613 9925 2007
Abbreviations: DEP, dielectrophoretic; AC, alternating current; pDEP, positive DEP;
nDEP, negative DEP TE, transverse electric; WO3, tungsten trioxide; ZnO, zinc oxide;
SiO2, silicon dioxide
Keywords: dielectrophoresis, microfluidics, optofluidics, particle manipulation,
polymeric waveguide
1
1.
DEP spectra simulations
The response of the particles under the dielectrophoretic (DEP) force was predicted
by simulating the variations of Claussius-Mossoti factor, fCM at different frequencies. If the
Re[fCM] is positive, a positive DEP force is generated, attracting the particles to the regions of
strong electric field gradients. Alternatively, if the Re[fCM] is negative, a negative DEP force
is generated, repelling the particles from the regions of strong electric field gradients. It was
necessary to simulate the Re[fCM] spectrum to explore the crossover frequency, at which fCM
is zero and the particles undergo a change from negative to positive DEP or vice versa. This
simulation allowed the determination of appropriate DEP applied frequencies for
manipulating the particles’ motion during the experiments.
The particles used in the experiments were suspended in deionized (DI) water which
has a conductivity of 5 mS m-1 after the addition of the X-305 surfactant and a relative
permittivity of 77.6. The conductivity of particles is calculated as [1]:
σ overall  σ bulk  σ surface  σ bulk 
2K S
r
(1)
where σbulk is the bulk conductivity, σsurface is the surface conductivity, and Ks is the surface
conductance composed of the contributions of the Stern layer and diffuse layer formed
around the particles [2, 3]. Ks is 10, 30 and 200 pS m-1 for tungsten trioxide (WO3), zinc
oxide (ZnO) and silicon dioxide (SiO2), respectively [4, 5]. The bulk conductivities σp of
WO3 and ZnO are 100 and 48 mS m-1 while the bulk conductivity of SiO2 is negligible [6, 7].
The radius for the WO3, ZnO and SiO2 particles used in the experiments are 80 nm, 50 nm
and 72 nm. Using equation (1), the conductivities of the particles were obtained as 100.25,
49 and 5.6 mS m-1 for WO3, ZnO and SiO2 particles, respectively. The relative permittivity of
2
particles, εr was taken as 80, 8.6 and 4.5, respectively for the WO3, ZnO and SiO2
particles [8-11]. Using these values, the Re[fCM] for the particles used in the experiments were
calculated over a range of frequencies and plotted in Figure S1. The numerically calculated
crossover frequencies for the WO3, ZnO and SiO2 particles are 24, 8.5, and 1.6 MHz,
respectively.
Figure S1. Re[fCM] for the mesoparticles used in the experiments. Variations of Re[fCM] for WO3
(Ø80 nm), ZnO (Ø50 nm) and SiO2 (Ø72 nm) particles dispersed in DI water.
2.
DEP field simulations
To comprehend the performance of the optofluidic system, the DEP field was
simulated using Fluent 6.2 software package (Fluent Inc, Lebanon, USA) as detailed
previously [12]. In doing so, the electric potential was obtained by solving the Laplace
equation, ( 2  0) within the microchannel, by applying appropriate electric potentials at the
microelectrodes and zero electric flux at other surfaces. Consequently, the electric field was
obtained by taking the gradient of electric potential ( E   ) .
3
Simulations showed that applying an alternating current (AC) signal of 15 Vp, the
electric field reaches a peak value of 1.6×106 V/m at the tip of microelectrodes and smoothly
decreases along the microelectrode structure (Fig. S2). Applying frequencies less than the
crossover frequency, induces positive DEP (pDEP) response and pushes the particles toward
the center of the microelectrode pairs. According to our observations, at low to medium flow
rates (0.5 to 2.5 µl min-1), the particles have enough time to immobilize between the opposite
microelectrodes. However at medium to high flow rates (3 to 4.5 µl min-1), although the
particles are descended to lower heights they will be dragged by flow before immobilization.
In this condition, the consequential microelectrodes act as discrete funnels due to their
symmetric shape and focus the passing particles along the centerline of the microchannel. In
our system, the abovementioned condition was obtained by applying a flow rate of 4 µl min-1
(corresponding to an average velocity of 1.66 mm s-1) and DEP voltage amplitude of 15 Vp.
Figure S2. Electric field simulation of the DEP microelectrodes. The contours of electric field (V/m)
at the bottom surface of DEP system obtained by numerical simulations.
Interestingly, the density of focused particles between the microelectrodes can be correlated
to the │DEP-y│, where DEP-y is the DEP force along the y-axis. For example, Fig. 3E in the
manuscript shows the dimensionless contours of │DEP-y│ at different planes along the
microchannel x-axis. It indicates the formation of packed particle regions along the inner
4
edge of microelectrodes. At the vicinity of the tips, the dense particle regions merge to form a
packed particle stream along the microchannel centerline. The configuration of the packed
particle stream after the tips depends on the balance of DEP force, which holds the particles
and the drag force which drags them.
3.
Waveguide simulations
The waveguide modes were simulated for TE polarizations using the rib waveguide
dimensions (described in the manuscript) and the wavelength of incident light, λ = 635 nm. A
fully vectorial mode matching technique [13] was employed to calculate the transverse
electric (TE) modal characteristics of the guided modes of the polymeric waveguide
assuming a DI water upper cladding media. In the mode matching simulations, the
computational window was fully open in the lateral direction. Therefore, the mode matching
simulation accurately modelled waveguide modes with lateral leakage [14, 15].
Figures S3 shows the electric field distributions of the major components of the TE
guided modes, which are composed of the fundamental, TE00 (Fig. S3A) and first order, TE10
(Fig. S3B) modes. The calculated propagation losses given are shown. From the simulations,
the TE00 mode propagates with negligible loss while the loss of the TE10 mode is much
smaller than that of higher order modes. Therefore, both the TE00 and TE10 modes propagate
in the waveguide with low loss.
5
A
B
TE00, neff =1.58869
Loss = Negligible
TE10, neff =1.57967+j7.53223×10-8
Loss = 0.65 dB cm-1
Figure S3. Waveguide modes for the quasi single mode waveguide. (A) TE00 mode; (B) TE10 mode.
4.
Refractive index profiles for the ZnO and SiO2 particles
The refractive indices for the ZnO and SiO2 particles (nparticle) are 2.0 and 1.47,
respectively. According to Equation (5) of the manuscript, the maximum refractive index
(nmax) of the media above the waveguide core when these particles are closely packed is 1.83
(ZnO) and 1.43 (SiO2). Under maximum packing conditions, the densely packed ZnO
mesoparticles are capable of coupling light from the rib waveguide, while SiO2 particles may
not be. Using Equation (6) of the manuscript, the refractive index of the media formed by the
packed ZnO particles in order for light to couple out of the rib waveguide ranges according
to: 1.59 (nmin) < nmedia < 1.83 (nmax).
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5.
Optical response
The optical mode intensity profiles observed at the quasi single mode waveguide
output, which corresponds to different particle packing conditions for the ZnO and SiO 2 are
included in this section.
5.1 ZnO particles
The DEP force polarity, for the ZnO particles (Sigma Aldrich, n = 2.0), changed from
negative to positive as the frequency was decreased from 13 to 3 MHz. First, the experiments
were conducted by keeping the applied DEP voltage constant at 15 Vp while varying the
frequency. The ZnO particles were repelled from the center by applying a 13 MHz frequency
at 15 Vp (Fig. S4A) and the corresponding mode intensity profile showing a single lobe was
observed (Fig. S4D). The frequency of the AC signal was then reduced to 8 MHz. The DEP
repelling forces became weak as particles began to move towards the center of the
microchannel leaving a narrow strip in between the microelectrode pairs devoid of particles
(Fig. S4B). The corresponding mode intensity profile observed was a single lobe with
reduced intensity compared to the previous case. This change was attributed to the increase in
the media refractive index above the waveguide core which caused the waveguide to become
increasingly evanescent. As the DEP frequency was further reduced to 3 MHz, a stream of
packed ZnO particles was formed at the microchannel center (Fig. S4C). The ZnO particles
agglomerated close to the DEP microelectrode surface. The corresponding mode intensity
profile was the single lobe with the intensity significantly reduced (Fig. S4F). There seems to
be lateral leakage of light, possibly caused by the agglomeration of ZnO particles, which
formed a media of high refractive index that induced the coupling light into the neighboring
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waveguides in the platform structure as the waveguides in the platform were spaced ~ 40 µm
apart.
To increase the packing density of the particles and to induce stronger coupling of
light into the particle concentration, the second series of experiments using ZnO were
conducted by keeping the frequency constant at 1.5 MHz, while varying the DEP voltage
from 0 to 15 Vp at 5 Vp increments (Fig. S4G-S4L). At 5 Vp, a weak pDEP force trapped the
ZnO particles in the center of the microfluidic channel (Fig. S4G) causing the intensity of the
mode to be reduced (Fig. S4J). As the DEP voltage was increased, the particle packing was
increased as well (Fig. S4H) which caused further reductions in the intensity of the mode
(Fig. S4K). When the DEP voltage applied was 15 Vp, the ZnO particles formed a distinct
narrowband of packed particles (Fig. S4K) while the intensity of the mode was significantly
reduced (Fig. S4L).
8
DEP: 15Vp 13 MHz
A
x (µm)
DEP: 15Vp 8 MHz
B
x (µm)
0
50
160
250
C
160
50
y
x (µm)
0
0
325 360
DEP: 15Vp 3 MHz
250
325 360
50
160
250
p
q
r
y
y
p = 33 µm
q =31 µm
r = 32.5 µm
s = 34.6 µm
t = 32.1 µm
weakly repelled
nDEP EParticles
nDEP
from waveguide surface
F
DEP:
15V
8
MHz
13 MHz
E
F
D
DEP: 15Vp
G
TE
DEP: 5Vp 1.5 MHz
x (µm)
H
160
250
DEP: 10Vp 1.5 MHz
x (µm)
TE
250
DEP: 15Vp 1.5 MHz
x (µm)
0
325 360
50
160
250
p
q
r
p
q
r
s
t
p = 33 µm
q = 31 µm
r = 32.5 µm
s = 34.6 µm
t = 32.1 µm
pDEP
K
325 360
y
pDEP
DEP: 5Vp 1.5 MHz
I
y
p = 31 µm
q =35 µm
r = 43.5 µm
s = 42.6 µm
t = 43.1 µm
J
160
50
325 360
y
Particles weakly trapped
above waveguide surface
TE
0
0
50
DEP: 15Vp 3 MHz
p
TE
t
s
pDEP
Particles repelled from the
waveguide surface
D
325 360
DEP: 10Vp 1.5 MHz
TE
s
t
pDEP
L
DEP: 15Vp 1.5 MHz
TE
Figure S4. ZnO particles and intensity profiles with variation of DEP frequency and AC voltages.
(A) ZnO particles flowing at 4 µl min-1 were repelled from the center at 15 Vp and f = 13 MHz;
(B) ZnO particles flowing at 4 µl min-1 were weakly repelled at 15 Vp and f = 8 MHz; (C) ZnO
particles were packed at 15 Vp and f = 3 MHz; (D) TE mode intensity profile at DEP: 15 Vp and
f = 13 MHz; (E) at DEP: 15 Vp and f = 8 MHz; and (F) at DEP: 15 Vp and f = 3 MHz. (G) ZnO
particles trapped in the center at 5 Vp and f = 1.5 MHz; (H) at 10 Vp and f = 1.5 MHz; (I) and at 15 Vp
and f = 1.5 MHz; (J) Waveguide TE mode profile at DEP: 5 Vp and f = 1.5 MHz (K) at DEP: 10 Vp
and f = 1.5 MHz; and (L) at DEP: 15 Vp and f = 1.5 MHz.
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5.2 SiO2 particles
The suspended SiO2 particles (Microspheres Nanospheres, n = 1.47) were tested using
various DEP parameters that formed distinct particle assembly conditions in the
microfluidics. The DEP force polarity for the SiO2 particles changed from negative to
positive as the applied DEP frequency was decreased from 2.4 MHz to 800 kHz.
First, the experiments were conducted by keeping the DEP voltage constant at 15 Vp
while varying the DEP frequencies. At the DEP voltage of 15 Vp and frequency of 2.4 MHz,
the SiO2 particles flowed through the microfluidic channel with a weak repelling force which
kept the particles from flowing to the microchannel center (Fig. S5A). When the frequency
was reduced to 1.6 MHz, the SiO2 particles began to form a particle stream above the
waveguide core (Fig. S5B) and when the frequency was further reduced to 800 kHz, a dense
particle stream was formed (Fig. S5C). The mode intensity profiles corresponding to the
particle concentrations formed by the applied DEP forces are presented in Figures S4D, S4E
and S4F. As predicted, the SiO2 particles did not couple the light from the quasi single mode
waveguide. The packed concentrations of SiO2 particles also did not have an impact on the
behaviour of the guided modes and hence the application of stronger pDEP forces (at a
constant frequency) was not conducted. Interestingly, it was observed in the case of the
strong particle focusing at 15 Vp and frequency of 800 kHz, the intensity of the guided mode
was slightly reduced. This could be attributed to the waveguide becoming increasingly
evanescent due to the presence of highly concentrated SiO2 particles which caused a change
in the media refractive index above the waveguide. The media refractive index may have
exceeded that of DI water but not exceeding the index of the waveguide core.
10
A
DEP: 15Vp 2.4MHz
x (µm)
B
160
250
DEP: 15Vp 800kHz
x (µm)
x (µm)
0
50
C
DEP: 15Vp 1.6MHz
0
0
325 360
50
y
160
250
50
325 360
160
250
325 360
q
r
s
y
y
p = 7.1 µm
q = 6.4 µm
r = 18.8 µm p
s = 22.1 µm
t = 17.8 µm
q
r
s
t
p = 5.2 µm
q = 5.3 µm
r = 6.1 µm
s = 21.9µm
t = 19.8 µm
p
t
Particles repelled from the
waveguide surface
D
DEP:
DEP:15V
15Vpp2.4
2.4MHz
MHz
E
DEP: 15Vp 1.6 MHz
TE
TE
TE
F
DEP: 15Vp 800 kHz
TE
Figure S5. SiO2 particles and intensity profiles with variation of DEP frequency and AC voltages.
(A) SiO2 particles flowing at 4 µl min-1 were repelled from the center at 15 Vp and f = 2.4 MHz;
(B) SiO2 particles were packed at 15 Vp and f = 1.6 MHz; (C) SiO2 particles were densely packed at
15 Vp and f = 800 kHz; (D) TE mode intensity profile at DEP: 15 Vp and f = 2.4 MHz; (E) at DEP:
15 Vp and f = 1.6 MHz; and (F) at DEP: 15 Vp and f = 800 kHz.
6.
Particle density distribution
The single sided symmetry of the DEP microelectrode pattern is presented in
Figure S6A. The density of particles in any y direction was assumed to be proportional to the
intensity of the DEP-y force at that point and therefore, the particle density distribution
function presented in Figure S6B is obtained. At x = 350 m, maximum trapping occurs
causing the formation of a particle packed stream, when combined with hydrodynamic forces.
This particle density distribution is used to plot the refractive index profiles in Figure 5A of
the manuscript.
11
A
B
(a)
Figure S6. Calculation of the particle density distribution correlating the density of particles to the
distribution of the DEP-y field. (A) DEP electrode single sided symmetry diagram; (B) DEP field
intensity distribution at various x locations.
7.
Video files of the optical responses for the WO3 particles
Three video files showing the mode intensity profile captured during the experiments
using WO3 particles are included. The first video file (SI Movie 1.wmv), shows the mode
intensity profile when the WO3 particle suspension fills the microfluidic channel. The second
and third video files (SI Movie 2.wmv and SI Movie 3.wmv), show the mode intensity
profiles while applying a DEP signal of 15 Vp and changing the applied frequency from
15 MHz to 5 MHz and 15 MHz to 30 MHz, respectively.
12
8.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
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