Strong ExcitonâPlasmon Coupling in Silver Nanowire Nanocavities

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Energy Conversion and Storage; Plasmonics and Optoelectronics

Strong Exciton-Plasmon Coupling in Silver Nanowire Nanocavities Gary Beane, Brendan S. Brown, Paul Johns, Tuphan Devkota, and Gregory V Hartland J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00313 • Publication Date (Web): 16 Mar 2018 Downloaded from http://pubs.acs.org on March 19, 2018

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The Journal of Physical Chemistry Letters

Strong Exciton-Plasmon Coupling in Silver Nanowire Nanocavities Gary Beane,* Brendan S. Brown, Paul Johns, Tuphan Devkota, Gregory V. Hartland† Department of Chemistry and Biochemistry University of Notre Dame Notre Dame, Indiana 46556, United States

Abstract: The interaction between plasmonic and excitonic systems and the formation of hybridized states is an area of intense interest, due to the potential to create exotic lightmatter states. We report herein coupling between the leaky surface plasmon polariton (SPP) modes of single Ag nanowires and excitons of a cyanine dye (TDBC) in an open nanocavity. Silver nanowires were spin-cast onto glass coverslips, and the wavevector of the leaky SPP mode was measured by back focal plane (BFP) microscopy. Performing these measurements at different wavelengths allows the generation of dispersion curves, which show avoided crossings after deposition of a concentrated TDBC-PVA film. The Rabi splitting frequencies (Ω) determined from the dispersion curves vary between nanowires, with a maximum value of Ω = 390 ± 80 meV. The experiments also show an increase in attenuation of the SPP mode in the avoided crossing region. The ability to measure attenuation for the hybrid exciton-SPP states is a powerful aspect of these single nanowire experiments, as this quantity not readily available from ensemble experiments.

* Corresponding author: e-mail: [email protected] † e-mail: [email protected]

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ACS Paragon Plus Environment


R=

390 ± 80 meV

2.6

Energy ( eV )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2.4 2.2 2 1.8 1.6 1.4 0.008

0.01

0.012

0.014

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When dye molecules or quantum dots are placed in photonic or plasmonic cavities, new hybrid states can be formed that are mixtures of the exciton and the plasmonic/photonic states.1 These strongly coupled exciton-polaritons (which we term “exciplons”) offer the potential to investigate exotic phenomena such as entanglement,2 Bose-Einstein condensation,3 as well as the control of spontaneous emission, stimulated emission and energy transfer processes.1 Hybrid exciton-polariton states also find applications in low-threshold lasing,4-7 enhanced exciton conduction,8,9 all-optical switches,10-12 single photon transistors13 and other applications that employ the strong optical non-linearity of these states.14,15 To realize strong coupling in exciplons, the coupling strength needs to exceed the dissipation rates for the uncoupled excitons and plasmons.1 While the dissipation rates are not directly amenable to control, the coupling strength can be manipulated. The coupling strength is proportional to the electric field in the cavity, and the square root of the number density of the excitonic species.1 Experimentally high electric fields can be achieved in cavities with high quality factors (Q) and small mode volumes. For photonic cavities the mode volume scales with λ3, where λ is the wavelength of light, and cannot be further compressed due to the diffraction limit.16 This means that large quality factors - on the order of 106 - are needed for strong coupling.1 In contrast, in plasmonic cavities

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created with metal surfaces or nanoparticles, the modes are strongly confined, so that much smaller Q values can achieve strong coupling.1 Exciplons have been studied for a variety of different type of nanomaterials.16-20 However, it is often difficult to determine the coupling strength in these systems. In photonic cavities,1,21 or for cavities created from propagating surface plasmon polaritons (SPPs) in thin metal films,22 the most direct way of measuring the coupling strength is to record a dispersion curve (typically frequency versus wavevector).1 In strongly coupled systems these curves show an avoided crossing, which directly yields the coupling strength. This is more difficult to achieve for studies of nanomaterials, especially since these measurements should be performed at the single particle level to remove problems from sample heterogeneity. Recently Zheng et al. studied exciton-plasmon coupling for monolayer WSe2 in a cavity formed between Ag nanorods and a SiO2/Si surface.23 In these experiments the n = 3 longitudinal plasmon resonance of the nanorod was tuned through the exciton resonance of the WSe2 monolayer by changing the dielectric constant around the nanorod through coating the sample with Al2O3. The resulting dispersion curve showed an avoided crossing with a Rabi splitting of ca. 50 meV. 23 In this paper we examine coupling between the leaky SPP mode of single Ag nanowires and J-aggregates of the cyanine dye 5,5’,6,6’-tetrachloro-1,1’-diethyl-3,3’-di(4-sulfobutyl)-benzimidacarbocyanine (TDBC). The coupled system is created by simply spin coating a concentrated dye-PVA solution on top of the nanowires. J-aggregates have been used extensively in plasmon coupling experiments because of their large oscillator strengths and narrow linewidths.10,12,24-28 To determine the dispersion curves of the coupled and uncoupled system, we monitored the wavevector of the leaky mode using

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back focal plane (BFP) microscopy.29-33 Analysis of the data using the coupled oscillator model34 gives Rabi splittings on the order of 300 meV. Finite element calculations were also used to simulate the response of the system. In these simulations the dielectric constants of the nanowires and the dye-PVA film were taken from the literature.35,36 The calculated dispersion curves show a complicated structure in the avoided crossing region, which is attributed to the form of the dielectric constant for the dye layer. Analysis of the full-width-at-half maximum (FWHM) of the BFP images shows that there is an increase in attenuation of the leaky SPP mode in the avoided crossing region. This effect is also reproduced by the simulations. Figure 1(a) shows transmission electron microscopy (TEM) images of the silver nanowires used in our experiments. The wires have a 5-fold twinned structure, which gives rise to the line that runs down the length of the nanowires in the TEM image.37 The average width of the nanowires is 170 ± 40 nm (see Figure S3 in the Supporting Information), and the typical lengths are tens of microns. Figure 1(b) shows a real space scattered light image of a “bare” NW on glass (as deposited NW without the dye-PVA film). In this image the SPP modes are launched by focusing a laser at an end of the NW, where the break in symmetry relaxes the momentum matching restrictions for coupling between photons and SPPs.38-41 The leaky SPP mode can be identified by the two lines that run down the length of the NW in the image.29,31,33,42 A BFP (Fourier space) image is presented in Figure 1(c). The line in the BFP image corresponds to the wavevector of the leaky mode.29,31,33,42 Note that it is possible that the bound SPP mode is also excited in our experiments.38 This mode can also potentially couple to the dye excitons, however, it does not contribute to the BFP

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measurements. Figure 1(d) shows a diagram of the BFP experiments. The outer circle in the Fourier image is determined by the numerical aperture of the objective (𝑘 𝑘" = 1.35 for our system), and the inner circle is determined by the condition for total internal reflection (𝑘 𝑘" = 1). For a nanowire orientated along the y-axis, momentum matching between photons in the substrate and the SPP occurs when

𝑘( 𝑘" , 𝑘* 𝑘" =

𝑘+,, Tan(𝜑) 𝑘" , 𝑘+,, 𝑘" (see Figure 1(d)), which creates a line in the image.38

a)

10 nm

c)

b)

5 m 200 nm

e)

d)

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Energy ( eV )

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2.4 2.2 2 1.8 1.6 1.4

0.008 0.01 0.012 0.014 0.016

k ( nm-1 )

Figure 1: (a) Transmission Electron Microscopy micrograph of representative silver NWs used in the experiments. (b) Real space image recorded by focusing a laser at one end of a NW. (c) Corresponding Fourier space image of the NW in (b). (d) Illustration of the connection between the SPP wavevector kSPP and the features in the BFP image. (e) Dispersion curve for bare silver NWs determined by BFP imaging (black circles). The red line is the calculated dispersion curve for a 170 nm wide NW, and the dashed lines are the air and glass light lines.

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Recording BFP images as a function of laser frequency allows us to generate a dispersion curve for the leaky mode. This is shown in Figure 1(e) for the bare NWs. The solid black markers are the average of six different nanowires, and the gray shaded region represents a 95% confidence interval. Finite element simulations of the frequency versus wavevector for bare NWs are shown as the red line, and are in good agreement with the experimental data. The dashed lines in Fig. 1(e) show the light lines for photons in air and glass. It is observed that the leaky mode for the bare NWs is very close to the light line for air, particularly at low frequency. Figures 2(a) and 2(b) show dispersion curves obtained from two different NWs coated with the TDBC-PVA film. The open black markers represent the wavevectors determined from the BFP images, and the gray region is the estimated error. The solid blue lines show the calculated dispersion curve for PVA-coated silver nanowires (NWs with a polymer coating but no dye) from finite element simulations (see below). The experimental data shows avoided crossings at frequencies that are close to the exciton resonance of the TDBC J-aggregate (horizontal dashed lines in Figs. 2(a) and 2(b)). Note that it was not possible to reliably measure dispersion curves for NWs with just PVA, due to inhomogeneities in the thickness of the PVA layer.

This is why finite element

simulations were used to the determine the dispersion curves for the uncoupled nanowires. The good agreement between the measured and calculated dispersion curves for the bare wires in Fig. 1(d) justifies this approach. Figure 2(c) shows the experimental FWHM (Δ𝑘 𝑘" ) of the SPP wavevector in the BFP images for the bare NWs (blue circles, average of 6 different NWs), and for the dye-coated NW in Fig. 2(b) (black

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circles and lines). The dye-coated NW shows a significant increase in the FWHM in the avoided crossing region, which implies increased attenuation of the leaky SPP mode.

a) Energy ( eV )

2.6 2.4

R=

260 ± 50 meV

2.2 2 1.8 1.6 1.4 0.008

0.01

0.012 -1

k ( nm

b) Energy ( eV )

2.6 2.4

R=

)

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390 ± 80 meV

1.4 0.008

k ( nm

0.014

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0.08 0.04 0 1.4

1.6

1.8

2

2.2

2.4

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Energy ( eV ) Figure 2: (a) and (b) Dispersion curves for 2 different TDBC-PVA coated Ag NWs (open black markers), the gray area is the estimated error. The blue line is the calculated dispersion curve for PVA-coated NWs (without dye), and the red solid line is a coupled

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oscillator model fit to the data. (c) FWHM of the SPP wavevector (Δ𝑘 𝑘" ) from the BFP measurements for bare NWs (blue circles), and for the dye-coated NW in (b) (black markers and line). The shaded area represents the estimated error.

In order to determine the coupling strength between the leaky mode and the dye excitons, a coupled oscillator model was used to analyze the experimental dispersion curves in Figure 2.1,34 The coupled oscillator model assumes that the NW and the Jaggregate system can be represented by the following equation:43 𝐸56 (𝑘) − 𝑖𝛤56 (𝑘) 𝑔

𝛼 𝛼 𝑔 = 𝐸 𝛽 , 𝐸" − 𝑖𝛤" 𝛽

(1)

where 𝐸56 (𝑘) and 𝐸" are the frequencies of the NW SPP and the J-aggregate excitons respectively, 𝛤56 (𝑘) and 𝛤" denote the corresponding dissipation rates, 𝑔 is the coupling strength, and the eigenvalue E is the energy of the coupled system. The eigenvector coefficients α and β satisfy 𝛼

=

+ 𝛽

=

= 1. The eigenvalues are obtained from the

secular equation A

A

𝐸" − i 𝛤" − 𝐸 = 𝑔=

𝐸56 (k) − i 𝛤56 (k) − 𝐸 =

=

(2)

When the dissipation rates of the SPP and exciton are small compared to their energies, the eigenvalues of the coupled system can be approximated by A

A

=

C

𝐸± (k) = (𝐸56 (k) + 𝐸" ) ± 𝑔= + 𝛿 = ,

(3)

where 𝛿 = 𝐸56 𝑘 − 𝐸" is the detuning and the Rabi splitting is Ω = 2𝑔. The red lines in Figs. 2(a) and (b) show fits to the experimental date using Eqn. (3), where the simulated dispersion curve for PVA coated NWs was used for 𝐸56 (𝑘). In this analysis 𝐸56 (k) and 𝐸" were fixed and g was adjusted to fit the lower branch of the

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experimental dispersion curve. The upper branch was not used in the analysis, as it does not follow the form expected from the coupled oscillator model (see Figure 2). This is attributed to a combination of effects that distort the upper branch, including the complicated structure of the avoided crossing in this system (see Figure 3 below), and the possible presence of higher order leaky SPP modes at higher frequencies (see the Supporting Information, Figure S8). The Rabi frequencies extracted from the fitting procedure are Ω = 260 ± 50 meV and 390 ± 80 meV for the NWs in Fig. 2(a) and 2(b), respectively, which are 15 – 20% of the exciton frequency. The difference between the Rabi frequencies for the two NWs is attributed to inhomogeneity in the dye coating for the system. The increase in the linewidth in the BFP images in the avoided crossing region (Fig. 2(c)) shows that the leaky SPP mode suffers increased attenuation when it is coupled to excitons from the dye layer. This type of information is difficult to obtain from conventional ensemble studies of dye layers over thin metal films,1 which average over a range of different environments and, thus, are subject to inhomogeneous broadening. Our single nanowire experiments avoid these effects. Note that the coupled oscillator model of Eqn. (1) predicts that the damping of the coupled system should essentially be an average of the dissipation rates for the plasmon and exciton.1 Thus, because the propagation lengths of TDBC excitons are shorter than those of Ag SPPs,44,45 an increase in attenuation is expected for the coupled exciton-plasmon system, consistent with the observations in Fig. 2(c). In order to more quantitatively understand both the coupling and the dissipation rates, finite element simulations were performed for the dyeNW system.

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In the finite element simulations the system is modeled as an infinitely long NW with a 25 nm thick layer of 1.5 %wt. TBDC-PVA. The geometry used in the simulations is shown in Figure 3(a) and described in full in the Supporting Information. The complex dielectric constant for the NWs was taken from Johnson and Christy,35 and that of the dye-PVA film from Gentile et. al.36 The real (𝜖′) and imaginary (𝜖′′) parts of the complex dielectric constant for the TDBC-PVA film are plotted versus frequency in Fig. 3(b). Note that the dielectric function for TDBC contains two oscillators, which have resonance frequencies at 2.03 eV and 2.10 eV. The lower energy oscillator has a smaller oscillator strength, and appears as a shoulder in the (𝜖 H , 𝜖′′) data in Fig. 3(b). The finite element simulations were performed in COMSOL Multiphysics (v. 5.3) using a twodimensional mode analysis calculation. This analysis yields the complex wavevector for the SPP mode 𝑘+,, = 𝛽 + 𝑖𝛼 , where 𝛽 and 𝛼 are the propagation and attenuation constants, respectively. Note that the FWHM in the Fourier image is related to the SPP attenuation constant by Δ𝑘 = 2𝛼. In turn, 𝛼 and Δ𝑘 are related to the SPP propagation length 𝐿+,, by 𝐿+,, = 1 2𝛼 = 1 Δ𝑘.36 a)

b) 16 12 r

8 4 0 -4 -8 1.4 1.6 1.8

2.8 2.6 2.4 2.2 2 1.8 1.6 1.4 0.007

d)

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k ( nm-1 )

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Energy ( eV )

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Figure 3: (a) Plot of the norm of the electric field for the leaky mode from finite element simulations for a 170 nm wide NW at an excitation frequency of 1.73 eV. (b) The real (black) and imaginary (red) parts (𝜖 H , 𝜖′′) of the complex dielectric constant of the TDBCPVA film.33 (c) Real (𝛽) and (d) imaginary (2𝛼 𝑘" ) parts of the leaky SPP mode wavevector for a NW coated by PVA but with no dye (blue curve), and for a TDBC-PVA coated NW (red circles and line), determined by the finite element simulations. Panel (c) is plotted as frequency versus wavevector for comparison to the experimental dispersion curves in Fig. 2. The open green symbols in panel (c) are the experimental results for the NW in Fig. 2(b).

Figure 3(c) shows the simulated dispersion curve for the leaky SPP mode for NWs coated by PVA and TDBC-PVA films. The curve for the dye coated NWs shows a complicated behavior in the avoided crossing region.

In particular, the simulations

appear to show two avoided crossings at frequencies of approximately 2.05 and 2.28 eV. A possible explanation for this effect is the multiple exciton transitions of the dye layer. However, the frequencies of the oscillators in the TDBC dielectric constant determined in Ref. [36], which was used in our simulations, do not match the frequencies of the features in Fig. 3(c).

Furthermore, finite element simulations with a single oscillator can

reproduce the features in Figure 3(c) (see Figures S6 and S7 of the Supporting Information). These simulations show that the oscillator strength and the width of the exciton resonance are the main parameters for determining whether a single or double feature is observed in the calculated dispersion curves. Dispersion curves with multiple avoided crossings have also been observed in simulations and experiments for a dye film

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on a silver surface by Pockrand and co-workers.46,47 In that work the two features were attributed to coupling to “transverse” and “longitudinal” exciton resonances of the dye layer. These resonances occur near frequencies where 𝜖′ for the dye crosses zero – see Figure 3 and Figures S6 and S7 of the Supporting Information. Thus, the multiple avoided crossings for the simulations in Figure 3 are a consequence of the form of the dielectric function for the dye. The open green markers in Fig. 3(c) are the experimental data for the NW in Fig. 2(b). Similar to the coupled oscillator model results, the experiments and simulations are in reasonable agreement at low frequencies, that is, for the lower branch of the dispersion curve. At high frequencies the experiments do not resolve the second avoided crossing. This could be because the experiments are affected by higher order leaky modes at higher laser frequencies – see Figure S8 of the Supporting Information. These modes suffer a size dependent cut off, and would only affect the BFP images for nanowires with diameters greater than 170 nm. We do not know the width of the NWs in the BFP images, thus, it is possible that these higher order leaky modes contribute to the experiments. Figure 3(d) shows a plot of the normalized attenuation constant 2𝛼 𝑘" for the TBDC-PVA coated and PVA coated NWs obtained from the finite element simulations (2𝛼 𝑘" is plotted instead of 𝛼 𝑘" to allow direct comparison to the Δ𝑘 𝑘" data in Figure 2(c)). Similar to the experimental data in Fig. 2(c) the attenuation increases in the avoided crossing region.

The simulations show two features, corresponding to the

longitudinal and transverse exciton modes of the dye layer (using the language of Ref.

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[43]). As was the case for the dispersion curves, the higher energy Δ𝑘 𝑘" feature is not clearly defined in the experimental data. The minimum in the calculated attenuation is reminiscent of electromagnetically induced transparency,21,48 which is an effect that occurs when a weakly damped mode is coupled to a lossy mode. However, this explanation does not seem likely for our system, as both the SPP and the dye exciton are lossy. Specifically, the quality factors for the propagating SPP mode and the exciton resonance are given by 𝑄+,, = 𝜔 2𝛼𝑣N and 𝑄O(P = 𝜔 Γ, respectively, where 𝑣N is the group velocity of the SPP mode and Γ is the linewidth of the exciton resonance.38 For the uncoupled system we have 𝑄+,, ≈ 27 and 𝑄O(P ≈ 40, showing that both modes are moderately lossy. The last point addressed in this paper is the question of whether the coupled exciton-SPP states are in the strong coupling regime. Strong coupling occurs when the Rabi frequency is much faster than the dissipation rates for the uncoupled systems, that is, Ω 2𝛼𝑣N , Ω Γ ≫ 1. The strongest coupled NW has a Rabi frequency of Ω = 390 ± 80 meV. For this nanowire we have Ω 2𝛼𝑣N ≈ 5 and Ω Γ ≈ 7, which is consistent with strong coupling

Conclusion Exciton-plasmon coupling has been investigated for silver nanowires coupled to a cyanine dye TDBC. In our experiments BFP imaging was used to record dispersion curves for the leaky SPP modes of single silver nanowires. These curves show an avoided crossing when the nanowires are coated with a layer of TDBC-PVA. The maximum Rabi frequencies observed for the NW-TDBC system is Ω = 390 ± 80 meV,

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which indicates strong coupling. The BFP images also show an increase in the SPP attenuation in the avoided crossing region. This effect is reproduced by finite element simulations, and is also expected from the coupled oscillator model for exaction-SPP coupling. The ability to measure attenuation is an important attribute of the single nanowire BFP experiments, and provides unique information about these hybrid systems.

Experimental Methods: The samples for the optical experiments were prepared by spin-casting dilute silver nanowire dispersions from water onto a flamed coverslip at 5000 rpm for 1 minute. TDBC-PVA films (from a 1.5% wt. TDBC and 1.5% wt. PVA solution) were then spincast onto the nanowires under the same settings.

The thickness of the film was

characterized using ellipsometry (V-VASE ® Variable Angle Ellipsometer), and was found to be 25±8 nm. The wavevectors for single silver nanowires were directly extracted from Back Focal Plane (BFP) images. In these experiments a laser was focused at the end of the nanowire with a high NA objective to excite the leaky SPP mode. Scattered light from the leaky mode was collected through the same objective and sent to a camera to form either a real-space image or a Fourier space (BFP) image.

A wide bandwidth super-

continuum laser source (Fianium SC450) was used for these experiments. Wavelengths in the range of 480 – 890 nm were selected with an acousto-optic tunable filter (Fianium AOTF-DUAL) before the microscope. Acknowledgements: This work was supported by the United States National Science Foundation (CHE-1502848), and the Office of Naval Research (Award No.: N00014-12-

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1-1030). The authors would like to thank Prof. Masaru Kuno for use of the supercontinuum light source.

ORCID IDs: Gary Beane: 0000-0001-5312-0477 Brendan S. Brown: 0000-0002-6421-9330 Tuphan Devkota: 0000-0002-0572-5874 Paul Johns: 0000-0002-1134-7566  Gregory V. Hartland: 0000-0002-8650-6891

Supplemental Information: The Supplemental Information for this paper includes schematics of the optical setup, transmission electron microscopy images of the silver nanowires used, ellipsometry measurements of the PVA film, a more detailed description of the finite element simulations, and additional simulations of the coupled nanowireTDBC system.

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References: (1) (2) (3) (4) (5) (6) (7) (8) (9)

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Strong ExcitonâPlasmon Coupling in Silver Nanowire Nanocavities

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