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Supporting Information
Enhancing Nanoparticle Electrodynamics with Gold Nanoplate Mirrors
Zijie Yan, Ying Bao, Uttam Manna, Raman A. Shah & Norbert F. Scherer
The James Franck Institute, The University of Chicago, 929 East 57th Street, Chicago, Illinois
60637, United States
Videos
Video S1. Three dimensional optical trapping of a 30 nm Ag nanoparticle with an interferometric
trap constructed by interfering a Fourier-transformed Bessel beam with its own reflection from a
Au nanoplate.
Video S2. Optical binding of three Ag nanoparticles (100 nm dia.) confined by an optical line
trap near a coverslip and a Au nanoplate surface.
Video S3. Optical binding of four Ag nanoparticles (100 nm dia.) confined by an optical line trap
near a coverslip and a Au nanoplate surface.
Video S4. A Ag nanoparticle was trapped by an optical line near a coverslip surface and then
moved over a Au nanoplate.
All the videos play in real time.
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Figure S1. Scanning electron microscope images of Au nanoplates synthesized by a polyol
method. Sizes of the nanoplates can be up to 40 µm and thicknesses are in the range of 100-600
nm as estimated from the images of edges (e.g., the edge of the nanoplate shown in the bottomright panel). We have also checked the nanoplates by atomic force microscopy, and their
thicknesses are generally in that range.
Figure S2. Calculated skin depths of Au in the visible and near-infrared spectral range.
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Figure S3. Models of the Au thin film and nanoplate used in our FDTD simulations. The blue
arrows are the direction of (linear) polarization, and the purple arrows are the light propagation
direction (note that the purple dots in the top panels are just the end of the arrows that point into
the page).The yellow lines are monitors of the electric fields.
Figure S4. Optical images of a Au nanoplate and scattered/reflected light from a focused
Gaussian beam of 800 nm wavelength. The nanoplate was deposited at a glass/water interface.
When the laser beam was focused at the edges of the Au nanoplate, surface plasmon resonances
were excited that propagated through the nanoplate, inducing re-emission at other edges
(highlighted by green arrows). The re-emission does not happen when the laser was focused at
the central area of the nanoplate (away from the edge).
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Figure S5. (a) A montage of dark-field optical images of a trapped Ag nanoparticle that was
moved across the surface of a Au nanoplate. Each panel (separated by the white lines) of the
image shown was from an optical image taken at a different time. They were aligned based on
the contour of nanoplate edges. (b) Brightness (in terms of the averaged gray-scale value of
pixels) of the image of the nanoparticle at different positions. The brightness of the optically
trapped Ag nanoparticle increased 4-5-fold over the nanoplate mirror vs. over the transparent
glass coverslip adjacent to the nanoplate. The error bars are standard deviations of the brightness
in several images recorded at the same position.
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Figure S6. (a) Calculated intensity distributions of electric fields around Ag nanoparticles (dia.
100 nm) immersed in water and illuminated by a plane wave of λ = 800 nm. The beam is incident
from the bottom side with light polarization along the y-direction. (I). A single Ag nanoparticle
in water as a basis for comparison. (II). A Au plate is used to reflect the beam, and the Ag
nanoparticle is located at the first interference fringe (antinode). (III). A second Ag nanoparticle
is added at a x-separation of 0.6 µm from the first nanoparticle, which corresponds to the first
optical binding position of two nanoparticles. (b) Calculated interparticle forces of two Ag
nanoparticles in a plane wave (i.e., case a-I with an additional nanoparticle positioned along the
x-direction; image not shown) and in a standing wave (i.e., a-III). Note that the equilibrium
separation is larger for optical binding in the standing wave, which is consistent with the
experimental results shown in Fig. 3b in the main text. The spring constant of optical binding can
be obtained from the slope (absolute value) of the curve near the equilibrium separation. The
spring constant in the standing wave is ~3 times of that in the plane wave, but it is much less
than the ~ 25 times enhancement that we measured in experiments. In other words, the
enhancement of the interparticle force constant is > 20-fold more than expected from the
increased intensity due to standing wave interference. For clarification, we summarize the
relations of spring constants of optical binding and standard deviations of interparticle
fluctuations in the following table.
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Table 1. Summary of spring constants of optical binding and standard deviations of interparticle
fluctuations. Note that κ −1 ∝ σ 2 .
Definition
over glass
over nanoplate
Measured results
Expected from the increased intensity due to standing
wave interference (FDTD simulation)
Additional stiffness
standard
deviation
σ1
σ2
σ1 ≈ 5σ2
spring
constant
κ1
κ2
κ2 ≈ 25κ1
κ2 ≈ 3κ1
≈ 20κ1
Figure S7. Optical binding of Ag nanoparticles (100 nm dia.) over a dielectric mirror. (a)
Optical images of (I) two and (II) three Ag nanoparticles confined by an optical line trap (the
same as that used in the main text). The line trap is along the y-axis with the direction of linear
polarization along the x-axis. (b) Histograms and Gaussian fits of the interparticle separations
between the two Ag nanoparticles. (c) Histograms and Gaussian fits of the interparticle
separations between adjacent Ag nanoparticles of the three nanoparticles. Standard deviations (σ)
of the separations are also shown.
It is worth noting that it would be valuable to compare the enhancement of optical binding over a
Au nanoplate with that over a Au film. Unfortunately, regular gold mirrors are opaque to
transmitted light over a wide spectral range. Therefore, it is difficult to illuminate the Ag
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nanoparticles and image them. Here, we used a custom dichroic mirror (from Precision
Photonics) that offers > 99.99% reflectivity at 800 nm and > 99% transmittance between 400 750 nm, so we could create the interferometric optical traps while still imaging the nanoparticles.
The results show that the optical binding of two or three Ag nanoparticles over the dielectric
mirror has similar stability as those over the Au nanoplates. Since the dielectric mirror excludes
the possibility of plasmonic coupling between the particle and mirror, the comparison reinforces
our conclusion that the electrodynamic coupling of particle motions in three dimensions via
optical binding interactions plays an important role in enhancing the stabilities of optically bound
metal nanoparticles in a standing wave.
Figure S8. Calculated optical trapping potential of a single Ag nanoparticle (100 nm dia.) in a
standing wave (λ = 800 nm) at different distances (d) from a Au mirror surface. Optical forces
along the z-direction (normal to the mirror surface) are calculated first by FDTD simulations, and
then potentials are calculated by integrating the forces along the z-direction. An estimated
intensity (28.6 mW/µm2) of the line trap used in our experiments is adopted in the simulation.
We define zero as the potential minimum. For kBT energy, the standard deviation of z-axis
fluctuations is ~ 20 nm, i.e., the range of the green zone shown in the plot.
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