Near-Field Mediated Plexcitonic Coupling and Giant Rabi Splitting in Individual Metallic Dimers

Abstract

Strong coupling between resonantly-matched localized surface plasmons and molecular excitons results in the formation of new hybridized energy states called plexcitons. Understanding the nature and tunability of these hybrid nanostructures is important for both fundamental studies and the development of new applications. We investigate the interactions between J-aggregate excitons and single plasmonic dimers and report for the first time a unique strong coupling regime in individual plexcitonic nanostructures. Dark-field scattering measurements and finite-difference time-domain simulations of the hybrid nanostructures show strong plexcitonic coupling mediated by the near-field inside each dimer gap, which can be actively controlled by rotating the polarization of the optical excitation. The plexciton dispersion curves, obtained from coupled harmonic oscillator models, show anticrossing behavior at the exciton transition energy and giant Rabi splitting ranging between 230-400 meV. These energies are, to the best of our knowledge, the largest obtained on individual hybrid nanostructures.

Full text

Near-Field Mediated Plexcitonic Coupling and Giant Rabi Splitting in
Individual Metallic Dimers
Andrea E. Schlather,
†,∥
Nicolas Large,
‡,∥
Alexander S. Urban,
§,∥
Peter Nordlander,
‡,§,∥
and Naomi J. Halas*
,†,‡,§,∥
†
Department of Chemistry,
‡
Department of Electrical and Computer Engineering,
§
Department of Physics and Astronomy, and
∥
Laboratory for Nanophotonics, Rice University, 6100 Main Street, Houston, Texas 77005, United States
*
SSupporting Information
ABSTRACT: Strong coupling between resonantly matched localized surface
plasmons and molecular excitons results in the formation of new hybridized energy
states called plexcitons. Understanding the nature and tunability of these hybrid
nanostructures is important for both fundamental studies and the development of
new applications. We investigate the interactions between J-aggregate excitons and
single plasmonic dimers and report for the first time a unique strong coupling
regime in individual plexcitonic nanostructures. Dark-field scattering measurements
and finite-difference time-domain simulations of the hybrid nanostructures show
strong plexcitonic coupling mediated by the near-field inside each dimer gap, which
can be actively controlled by rotating the polarization of the optical excitation. The
plexciton dispersion curves, obtained from coupled harmonic oscillator models, show anticrossing behavior at the exciton
transition energy and giant Rabi splitting ranging between 230 and 400 meV. These energies are, to the best of our knowledge,
the largest obtained on individual hybrid nanostructures.
KEYWORDS: Plexcitons, surface plasmons, molecular excitons, Rabi splitting, dark-field spectroscopy, individual hybrid nanostructures
Future nanodevices will most likely include hybrid
nanostructures that combine the intrinsic properties of
dissimilar materials to forge new and interesting tunable
properties.
1−6
Although plexcitonics (i.e., the study of
plasmon−exciton coupling) is still an experimentally and
theoretically challenging subject, several studies have reported
plexcitonic nanostructures composed of metallic nanostructures
interacting with molecular materials
6−13
and semiconduc-
tors.
14−18
In a plexcitonic device, the localized surface plasmon
resonance (LSPR) of a metallic nanostructure couple with the
excitons of a complementary material. The resulting hybrid
nanostructures provide a uniquely adaptable platform for the
design and the implementation of functional optical devices at
the nanoscale. Important, already demonstrated applications
include chemical sensors,
19
pH meters,
20
light harvesting,
21
and
optically active devices.
22,23
The molecular complexes can also
be used to tune the optical properties of the metallic
nanostructure through a local modification of the dielectric
environment.
24
These are all examples of light-matter coupling
in the weak regime, where the LSPR modes are perturbed by
the presence of the molecule. Several concepts such as
hybridization,
25
Fano resonances,
26
and Rabi splitting
27
have
been successfully transferred from atomic and molecular
physics to describe analogue phenomena seen in plasmonic
systems. In the strong coupling regime,
7−13,25−32
the coupling
between a molecular exciton and a plasmonic cavity results in
anticrossings of the hybrid plexciton dispersion curves and the
formation of two hybrid energy states separated by a Rabi
splitting energy. More recently, dynamic tuning
12,28
and
ultrafast manipulation
7,9,10
of the plexcitonic coupling have
been investigated in such hybrid nanostructures. However, all
of these studies have involved arrays of nanostruc-
tures,
7,9,12−14,16,29
or ensembles of nanoparticles.
8,10,11,15,30
Previous studies have shown that coupling between
elementary excitations can be mediated by the near-field and
in particular by the highly enhanced electric field near the
surfaces of plasmonic nanostructures, known as “hot
spots”.
31−35
The strong and localized field in a plasmonic hot
spot enhances the interaction between LSPRs and the local
excitons, much as it enhances other molecular excitations.
Plasmonic dimers are the canonical geometry for the generation
of high-intensity hot spots, where the local field is sufficient to
give rise to surface enhanced Raman spectroscopy at the single
molecule level.
36
Plasmonic dimers have been widely studied
due to their simple geometry and the tunability of their far-field
scattering properties in the visible/NIR range.
37
Here, we
investigate the strong coupling between individual nano-
structured plasmonic dimers and J-aggregate complexes. By
tuning the dimensions of a plasmonic dimer we are able to
create spectral overlap with the J-aggregate exciton transition as
well as large near-field enhancements. This allows us to report
for the first time a unique strong coupling regime in individual
plexcitonic nanostructures.
Received: April 24, 2013
Revised: May 21, 2013
Letter
pubs.acs.org/NanoLett
© XXXX American Chemical Society Adx.doi.org/10.1021/nl4014887 |Nano Lett. XXXX, XXX, XXX−XXX

Results. The plasmonic dimers used to probe the LSPR-
exciton interaction were created using planar fabrication on an
ITO-coated SiO2wafer. The J-aggregates used to form our
structures have been shown to exhibit strong coupling in a
number of other plexcitonic systems,
8,10,12,13,38
due to their
narrow exciton transition linewidths and high oscillator
strengths at room temperature. J-aggregates were formed
from monomers of a cyanine dye in a polyvinyl alcohol
(PVA) matrix (Supporting Information S1). The J-aggregates
were then spin-cast onto the patterned ITO substrate, resulting
in a J-aggregate/PVA film with a thickness of 15−25 nm.
Scattering measurements of single hybrid nanostructures
were taken using a hyperspectral transmission dark-field
microscope.
Plasmonic dimers have two distinct dipole LSP modes in the
longitudinal and transverse directions. Light scattered by each
LSP mode can be collected independently, depending on the
angle of the linear polarizer in the collection path. The
geometries of the Au dimers were chosen so that the
longitudinal plasmon resonance overlaps with the J-aggregate
exciton peak at 693 nm (1.79 eV). Individual nanodisk
diameters of 60, 70, 85, 100, and 115 nm were used, with a
fixed gap size of 15 nm to ensure the creation of an intense hot
spot in each dimer gap. Scanning electron micrographs and
longitudinal scattering spectra of the bare dimers confirm the
nanostructure dimensions and spectral overlap of each dimer
with the J-aggregate exciton peak (Figure 1). The longitudinal
LSPR is red-shifted with respect to the uncoupled nanodisk
plasmon resonance due to hybridization between the nano-
disks,
25,39
and is accompanied by a large near-field enhance-
ment in the dimer gap.
40
The transverse LSP mode gives rise to
a near-field enhancement weaker by an order of magnitude and
a weaker hybridization between the nanodisks resulting in a
higher resonance energy that, in the case of the smaller dimers,
does not overlap with the J-aggregate exciton.
When the J-aggregate/PVA layer is added, the longitudinal
LSP resonance of each dimer is strongly modified (cf. Figure
2a). The single scattering peak splits into two separate peaks,
separated by a peak minimum at the exciton wavelength (693
nm) revealing a strong coherent coupling between the
longitudinal LSP of the dimer and the exciton. In contrast,
when the transverse LSP of the dimer is excited, the resonance
peak for each structure is notably blue-shifted. While the
spectral position of the smaller dimers has been detuned from
the J-aggregate exciton (cf. green spectra in Figure 2e,f), the
larger dimers still have a large degree of spectral overlap (cf.
black spectra in Figure 2e,f). However, no peak splitting is
observed with this polarization for any of the dimers in the
series, indicating a much weaker coupling between the
transverse LSPR and the J-aggregate excitons.
We used the finite-difference time-domain (FDTD) method
to calculate the optical properties of the hybrid plexcitonic
nanostructures. The scattering profiles for all hybrid dimers
were calculated for both longitudinal and transverse polar-
izations. Calculated spectra (Figure 2b,e) are in very good
agreement with the experimental spectra (Figure 2a,d).
Specifically, the calculated longitudinally polarized spectra
exhibit a strong dip at 693 nm and two distinct plexciton
resonances: a higher energy mode on the blue side of the
exciton which will be referred to as the upper branch (UB) and
a lower energy mode on the red side referred to as the lower
branch (LB). In contrast, the transverse polarized spectra show
a very weak dip at 693 nm (not resolved experimentally).
Figure 2c,d displays the calculated near-field enhancement
distributions |E/Eo|2for the longitudinal and transverse
polarizations, respectively. The largest near-field enhancement
for the longitudinally polarized dimer occurs inside the dimer
gap, where the maximum enhancement is ∼250 for the largest
dimer in the series (Figure 2c). The transverse near-field maps,
magnified by a factor of 10 for clear visualization, illustrate the
absence of any near-field enhancement inside the dimer gap
(Figure 2d). The maximum transverse near-field enhancement
occurs outside the gap and is no larger than 25 for the largest
dimer, that is, an order of magnitude smaller than the largest
longitudinal mode gap enhancement. This suggests that strong
near-field enhancements in the center of the dimers are
essential for the plexciton formation seen in the longitudinally
polarized spectra (Figure 2a,b).
To further investigate the dependence of the coupling
behavior on the polarization-dependent near-field enhancement
in the dimer gap, a spectrum was collected from each individual
nanostructure as the polarization angle was varied by 5°
increments. The linear polarizer in the collection path of the
microscope was rotated, and a spectrum was collected at each
angle from 0°to 90°, corresponding to the longitudinal
(horizontal arrow) and transverse (vertical arrow) polarizations,
respectively (Figure 3). The results for the 70 nm nanodisk
dimer,showninFigure3ain15°increments, show a
progressive emergence of the two plexcitonic peaks as the
polarization is rotated from transverse (90°) to longitudinal
(0°). Results from FDTD calculations show an identical trend
(Figure 3b). As the polarization angle decreases (polarization
changes from transverse to longitudinal), the UB plexciton
shifts to longer wavelengths, and the LB mode appears
gradually on the red side of the exciton transition (693 nm/
1.79 eV). The intensity of the LB peak increases as the
polarization angle approaches 0°, corresponding to the
maximum coupling. Each individual polarized spectrum was
Figure 1. Bare gold nanodisk dimers. (a) SEM images of five gold
dimers with diameters increasing from top to bottom (diameters are
60, 70, 85, 100, and 115 nm). The interparticle gap is fixed at 15 nm.
The scale bars correspond to 100 nm. (b) Longitudinally polarized
scattering spectra measured for the five bare dimers. The exciton
absorption peak from the J-aggregate complex is shown as reference
(gray line).
Nano Letters Letter
dx.doi.org/10.1021/nl4014887 |Nano Lett. XXXX, XXX, XXX−XXXB

Figure 2. Size dependence of hybrid nanodisk dimers. Scattering spectra of plexcitonic gold dimer−J-aggregate nanostructures with nanodisks
ranging from 60 to 115 nm in diameter recorded for (a) longitudinal and (e) transverse polarizations. Corresponding calculated spectra are shown
for (b) longitudinal and (f) transverse polarizations. The exciton transition (693 nm/1.79 eV) of the J-aggregate is indicated by the light blue vertical
line. Near-field enhancement maps |E/E0|2calculated at the exciton energy are displayed in the center panels for both (c) longitudinal and (d)
transverse polarizations. The near-field intensities calculated for the transverse excitation have been multiplied by a factor of 10.
Figure 3. Polarization dependence of plexcitonic properties on a single plasmonic dimer with individual disk diameters of 70 nm and a 15 nm gap.
(a) Polarized scattering spectra of plexcitonic dimer with detected polarization angles of 0°,15°,30°,45°,60°,75°, and 90°. (b) Scattering spectra
calculated for the same polarization angles. (c) Calculated near-field enhancement |E/E0|2corresponding to increasing polarization angles.
Polarization directions are shown with the white arrows. (d) Shift of the UB mode as a function of the polarization angle (green dots). (e) Relative
scattering intensity of the LB mode as a function of the polarization angle (green dots). Both quantities are compared to the polarization dependence
of the near-field intensity calculated in the dimer gap (blue line).
Nano Letters Letter
dx.doi.org/10.1021/nl4014887 |Nano Lett. XXXX, XXX, XXX−XXXC

normalized to the maximum scattering amplitude of the UB, so
that the relative amplitudes of the LB could be compared (cf.
Figure 3a). Identical measurements were performed on dimers
with 85 and 100 nm disk diameters, which exhibit the same
polarization dependence (Supporting Information S2). The
polarization dependence of the UB shift (Figure 3d) and the
LB intensity (Figure 3e) are found to correlate very well with
the calculated near-field enhancement. The polarization
dependence of the UB shift and LB intensity is most
pronounced around 40−50°, where the near-field intensity
varies most strongly and weakest around 0°and 90°, where the
intensity of the near-field levels out. These similarities provide
strong evidence that the plexcitonic coupling is dependent on
the strength of the near-field enhancement inside the dimer
gap.
Discussion. Hybridization diagrams are useful for visualiz-
ing the interaction between the modes in complex systems. For
longitudinal polarization, the coupling of the individual
nanodisk LSPRs leads to the formation of a bright bonding
and a dark antibonding dipolar dimer LSPR mode.
40
In Figure
4a, we show how the bright dipolar LSPR mode of the dimer
interacts with the exciton transition dipole of the J-aggregate
complex (Jex), leading to the formation of the two plexcitonic
UB and LB modes. For a symmetry broken dimer, the dark
LSPR mode could also couple to the J-aggregate
37,41
but due to
large energy detuning between the exciton and the dark LSPR
mode of the dimer, we rule out the possibility of the exciton
coupling to the higher order plasmon modes.
The interaction between the bonding dimer LSPR and the
excitons of the J-aggregate results in hybridized plexciton states
which exhibit typical anticrossing behavior. The energies of the
UB and LB plexciton states are calculated using a coupled
harmonic oscillator model,
42
ω
ωω
ωω
ℏ=
ℏ+ℏ
±ℏΩ+ℏ−ℏ
E() 2
1
2()( )
plexiton
UB,LB p
p0
R2p0
2
where ℏω0and ℏωpare the uncoupled exciton and dimer LSPR
energies, respectively. The coupling energy, ℏΩR, also called
Rabi splitting, is given by the spatial overlap of the excitonic
transition dipole moment μ0(r) and the induced surface
plasmon electric field Ep(r): ℏΩR=∫μ0(r)·Ep(r)dV. Previous
works have reported splitting energies ranging from few
millielectron volts to several hundreds of millielectron
volts.
7,8,10,13,16,28,43−46
By extracting the LSPR energy from
the scattering spectra of the bare nanodisk dimers and the
measured UB and LB modes as shown in Figure 4b, the Rabi
splitting is found to be approximately 230 meV which is in
good agreement with the highest values previously reported.
Moreover, for several hybrid dimer nanostructures (cf. Figures
3a and 4b) we were able to observe even larger coupling
leading to giant Rabi splitting energies of ∼400 meV
comparable to the largest values previously reported in
literature (Supporting Information S3). Energy transfer (i.e.,
Fano resonance and Rabi splitting) and plasmonic splitting
have been shown to occur in different coupling regimes defined
by the relative resonance linewidths (γLSPR and γ0) and by the
oscillator strength, f, of the excitonic resonance. Plasmonic
splitting is observed with large oscillator strengths ( f> 2) and
large molecular resonance linewidths (γ0> 200 meV).
47
In our
case f= 0.4 and γ0= 52 meV are indicative of an energy
transfer. Moreover, the transition from Fano resonance to Rabi
splitting has also been theoretically investigated.
27
It has been
shown that Rabi splitting occurs when ℏΩR>(γLSPR −γ0)/2.
Our hybrid system satisfies this criterion, as (γLSPR −γ0)/2 ≈
160 meV.
The large Rabi splitting energies in these hybrid nanostruc-
tures arise from alignment of the J-aggregate transition dipole
moment with the polarized near-field inside the dimer
junction.
11
When the J-aggregate complex is moved away
from the center of the gap, the plexcitonic coupling becomes
strongly suppressed (Supporting Information S4). If the J-
aggregate transition dipole is moved only 30 nm away from the
gap center, the near-field is substantially weaker, and no
measurable Rabi splitting can be detected.
The position of the J-aggregate complex relative to the dimer
junction is vital to obtain large plexcitonic coupling energies. In
order to obtain better control of the J-aggregate size and
location, an alternate hybrid dimer geometry was fabricated.
Instead of being cast from a PVA solution, the J-aggregates
were allowed to self-assemble on the surface of the metallic
disks from a solution of dye monomers.
8
In this case, J-
aggregates cover the entire surface of the metallic disk,
48
including the surface near the dimer gap. Adsorption of dye
molecules on the metal nanodisk surface occurs through a
combination of van der Waals forces and electrostatic attraction
between the Au and the positively charged nitrogen atoms on
the benzothiazole rings.
8
The UB and LB energies were
extracted from the measured longitudinal scattering spectra
(Supporting Information S5) and overlaid with the calculated
dispersion curve and the first data set (Figure 4b). The Rabi
splitting energies of this second set (stars) are smaller than the
Figure 4. (a) Hybridization energy diagram of the plexcitonic dimer.
(b) Dispersion curves of the hybrid plexcitonic states extracted from
experimental data (stars and diamonds) and calculated from the
equation in the text (blue and red lines). Experimental points come
from two sets of samples: a thin J-aggregate layer formed at the surface
of the gold dimers (stars) (Supporting Information S5), and J-
aggregates formed in the PVA covering the dimers (diamonds). The
black and green dashed lines represent the uncoupled exciton and
surface plasmon energies, respectively.
Nano Letters Letter
dx.doi.org/10.1021/nl4014887 |Nano Lett. XXXX, XXX, XXX−XXXD

first set (diamonds) and more closely follow the theoretical
plexciton dispersion curves. This observation can be explained
by considering the position of the J-aggregates on the metal
surface. In the self-assembly method, only a small fraction of
the J-aggregates form in the nanodisk region that experiences
strong near-fields, that is, inside the dimer gap. Most of the J-
aggregate complexes form on the Au surfaces outside of the
dimer gap region and do not contribute to plexcitonic coupling.
While not all Au dimers showed strong coupling with J-
aggregates formed in solution (J-aggregates did not always
successfully align inside the dimer gaps), the coupling energies
measured for these structures (diamonds, Figure 4b) were
overall larger than that obtained when the J-aggregates self-
assembled directly at the nanodisk surface (stars, Figure 4b),
due to greater interaction with the intense near-field.
Moreover, the high quality of the J-aggregates allows us to
perform a direct and rigorous comparison of the coupling
intensities for different gap sizes. For hybrid dimers with gap
sizes exceeding 25 nm, the plexcitonic coupling was found to be
too weak to induce significant Rabi splitting. Dimers with gap
sizes of 30 and 60 nm showed no peak splitting with either J-
aggregates formed on the surface or in solution (Supporting
Information S6). In both cases, only weak coupling was evident,
as determined by the LSPR shift.
49
The reason for the weak
coupling for these larger gap dimers is the reduced near-field in
the junction, the near-field intensity being three times smaller
than that of the 15 nm gap dimer.
In conclusion, we have reported a rigorous investigation of
plexcitonic interactions between localized surface plasmon
resonances in individual hybrid metallic nanodisk dimers and J-
aggregate excitons. We have shown spatially resolved field-
enhanced coherent coupling between two discrete optical
excitations, leading to a plexciton-induced transparency (i.e.,
almost complete suppression of far-field scattering) in the
visible range. Careful geometrical design allowed a near-field
enhanced plexcitonic coupling, giving rise to giant Rabi
splitting. Further engineering of these hybrid nanostructures,
by introducing symmetry breaking for instance, can lead to
comparably larger near-field enhancements and introduce the
possibility of coupling excitons to higher order dark LSP
modes. The quantitative investigation of plexciton formation
we reported here with an unprecedented control in the single
particle regime opens up a new way to promising nanoscale
applications at optical frequencies.
Methods. Fabrication Process. The plasmonic dimers were
created using planar fabrication on an ITO-coated SiO2wafer.
Arrays of nanodisk dimers, spaced with a pitch of 10 μm, were
patterned by electron beam lithography using a ∼70 nm thick
poly(methyl methacrylate) positive resist (PMMA, 950 wt).
Electron beam evaporation was used to deposit a 2 nm Ti
adhesion layer followed by a 35 nm Au layer, where the layer
thicknesses were monitored via quartz crystal microbalance.
The excess metal and resist were removed by liftoffin NMP (1-
methyl-2-pyrrolidone) at 65 °C for two hours to reveal the
nanostructures. Plasma cleaning (O2, 50 W, 100 mTorr) was
performed for one minute to remove traces of residual resist
around the nanostructures after liftoff, as well as after scanning
electron microscope (SEM) imaging (FEI Quanta 650) to
remove carbon contamination from the electron beam.
J-aggregates were formed from monomers of a cyanine dye
(Supporting Information S1) by adding 5 μL aliquots of
monomers in ethanol (3 μg/mL) to 3 mL of a 5 mg/mL
polyvinyl alcohol (PVA) solution. UV−vis spectroscopy was
used to monitor J-aggregate formation, which is indicated by a
narrowing and red shift of the monomer absorption peak from
599 to 693 nm. The J-aggregates were then spin-cast from
solution at 3000 rpm onto the patterned ITO substrate,
resulting in a J-aggregate/PVA film with a thickness of 15−25
nm, as determined by AFM measurements.
Hyperspectral Dark-Field Spectroscopy. Scattering meas-
urements were taken using a hyperspectral transmission dark-
field microscope from Cytoviva HSI. In this configuration,
scattered light is collected over the entire sample surface area,
and each pixel of the image produced contains a complete
spectral profile. Unpolarized white light was focused onto the
sample through a high NA condenser lens at an angle varying
between 66°and 72°(corresponding to NA 1.2−1.4).
Scattered light from the nanostructures was collected by a
40×objective (NA 0.6) and passed through a 360°rotating
linear polarizer before entrance into a spectrograph and CCD
camera.
Finite-Difference Time-Domain Simulations. We used the
finite-difference time-domain (Lumerical Solutions) method to
calculate the optical properties of the hybrid plexcitonic
nanostructures. Geometrical parameters have been extracted
from SEM images of individual dimers in Figure 1. The dimers
were coated with a continuous layer of PVA and J-aggregates
and supported by an ITO-coated SiO2substrate. The bulk
dielectric function tabulated by Johnson and Christy was used
for Au,
50
and the dielectric function from Palik was used for
SiO2.
51
The J-aggregate complex was modeled as a dispersive
medium with dimensions set from approximated values
obtained through dynamic light scattering measurements (not
shown) of the J-aggregates in a PVA solution. In order to
account for the J-aggregate exciton, the dielectric permittivity of
the J-aggregate/PVA mixture has been described by the Lorentz
model as
ε
ωε
ω
ωω γω
=+
−−
∞
f
i
() ()
J0
2
0
22
0
where ε∞= 2.5 is the high-frequency component of the J-
aggregate/PVA matrix dielectric function, f= 0.4 is the reduced
oscillator strength, ℏω0= 1.79 eV is the exciton transition
energy, and γ0= 52 meV is the exciton line width.
■ASSOCIATED CONTENT
*
SSupporting Information
S1: J-aggregate formation and UV−vis spectroscopy; S2:
polarization-dependent plexcitonic coupling for nanodisk
dimers (disk diameters D= 100 nm, D= 85 nm); S3: Rabi
splitting energy comparison with highest reported literature
values; S4: probing of near-field mediated plexcitonic coupling
locality; S5: coupling between individual dimers and self-
assembled J-aggregate monolayers; S6: weak plexcitonic
coupling in large gap (g= 30 nm, g= 60 nm) nanodisk
dimers. This material is available free of charge via the Internet
at http://pubs.acs.org.
■AUTHOR INFORMATION
Corresponding Author
*E-mail: halas@rice.edu.
Author Contributions
A.E.S. and N.L. contributed equally to this work. A.E.S. carried
out the fabrication of the nanostructures, optical measurements,
and data analysis. N.L. performed the theoretical study,
Nano Letters Letter
dx.doi.org/10.1021/nl4014887 |Nano Lett. XXXX, XXX, XXX−XXXE

numerical simulations, and data analysis. A.S.U. optimized the
experimental data analysis process. N.J.H. and P.N. designed
the project. All of the authors discussed the results and wrote
the paper.
Notes
The authors declare no competing financial interest.
■ACKNOWLEDGMENTS
The authors wish to thank M. W. Knight, N. S. King, J. B.
Lassiter, Z. Fang, H. Sobhani, and N. T. Fofang for their insight
and input. This research was supported by the Robert A. Welch
Foundation under grants C-1220 and C-1222, the Office of
Naval Research under grant N00014-10-1-0989, the DoD
NSSEFF (N00244-09-1-0067), and the U.S. Army Research
Laboratory and Office under contract/grant number
WF911NF-12-1-0407.
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