Strong Exciton–Plasmon Coupling in Silver Nanowire Nanocavities

Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 1676−1681

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

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S Supporting Information *

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 because this quantity is not readily available from ensemble experiments.

W

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 because 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 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 line widths.10,12,24−28 To determine the dispersion curves of the coupled and uncoupled system, we monitored the wavevector of the leaky mode using 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

hen 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 transistors,13 and other applications that employ the strong optical nonlinearity 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 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 © 2018 American Chemical Society

Received: January 30, 2018 Accepted: March 16, 2018 Published: March 16, 2018 1676

DOI: 10.1021/acs.jpclett.8b00313 J. Phys. Chem. Lett. 2018, 9, 1676−1681

Letter

The Journal of Physical Chemistry Letters

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 panel 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.

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 1a shows transmission electron microscopy (TEM) images of the silver nanowires used in our experiments. The wires have a five-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 1b 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 1c. 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 measurements. Figure 1d shows a diagram of the BFP experiments. The outer circle in the Fourier image is determined by the numerical aperture of the objective (k/k0 = 1.35 for our system), and the inner circle is determined by the condition for total internal reflection (k/k0 = 1). For a nanowire orientated along the y axis, momentum matching between photons in the substrate and the SPP occurs when (kx/k0, ky/k0) = (kSPP Tan(φ)/k0, kSPP/k0) (see Figure 1d), which creates a line in the image.38

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 1e 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 Figure 1e 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. Figure 2a,b shows 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 PVAcoated silver nanowires (NWs with a polymer coating but no dye) from finite element simulations (see below). The experimental data show avoided crossings at frequencies that are close to the exciton resonance of the TDBC J-aggregate (horizontal dashed lines in Figure 2a,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 Figure 1d justifies this approach. Figure 2c shows the experimental fwhm (Δk/k0) of the SPP wavevector in the BFP images for the bare NWs (blue circles, average of six different NWs) and for the dye-coated NW in Figure 2b (black 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. To determine the coupling strength between the leaky mode and the dye excitons, a coupled oscillator model was used to 1677

DOI: 10.1021/acs.jpclett.8b00313 J. Phys. Chem. Lett. 2018, 9, 1676−1681

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The Journal of Physical Chemistry Letters

The red lines in Figure 2a,b show fits to the experimental date using eq 3, where the simulated dispersion curve for PVAcoated NWs was used for Epl(k). In this analysis Epl(k) and E0 were fixed and g was adjusted to fit the lower branch of the 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

Figure 2. (a,b) Dispersion curves for two different TDBC−PVAcoated 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 oscillator model fit to the data. (c) fwhm of the SPP wavevector (Δk/k0) from the BFP measurements for bare NWs (blue circles) and for the dyecoated NW in panel b (black markers and line). The shaded area represents the estimated error.

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) Real (black) and imaginary (red) parts (ϵ′, ϵ″) of the complex dielectric constant of the TDBC−PVA film.33 (c) Real (β) and (d) imaginary (2α/k0) 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 Figure 2. The open green symbols in panel c are the experimental results for the NW in Figure 2b.

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 equation43 ⎡ Epl(k) − i Γpl(k) ⎤⎡ α ⎤ g ⎡α ⎤ ⎢ ⎥⎢ ⎥ = E ⎢ ⎥ ⎣ β⎦ ⎢⎣ g E0 − i Γ0 ⎥⎦⎣ β ⎦

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 Figure 2a,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 line width in the BFP images in the avoided crossing region (Figure 2c) 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 eq 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 Figure 2c. To more quantitatively understand both the coupling and the dissipation rates, finite element simulations were performed for the dye−NW system.

(1)

where Epl(k) and E0 are the frequencies of the NW SPP and the J-aggregate excitons, respectively, Γpl(k) and Γ0 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|2 + |β|2 = 1. The eigenvalues are obtained from the secular equation ⎛ ⎞⎛ ⎞ 1 1 2 ⎜E (k ) − i Γ (k ) − E ⎟⎜E − i Γ − E ⎟ = g pl 0 0 ⎝ pl ⎠ ⎝ ⎠ 2 2

(2)

When the dissipation rates of the SPP and exciton are small compared with their energies, the eigenvalues of the coupled system can be approximated by E±(k) =

1 (Epl(k) + E0) ± 2

g2 +

1 2 δ 4

(3)

where δ = Epl(k) − E0 is the detuning and the Rabi splitting is Ω = 2g. 1678

DOI: 10.1021/acs.jpclett.8b00313 J. Phys. Chem. Lett. 2018, 9, 1676−1681

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plotted instead of α/k0 to allow direct comparison to the Δk/k0 data in Figure 2c). Similar to the experimental data in Figure 2c 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 43). As was the case for the dispersion curves, the higher energy Δk/k0 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 QSPP = ω/2αvg and Qexc = ω/Γ, respectively, where vg is the group velocity of the SPP mode and Γ is the line width of the exciton resonance.38 For the uncoupled system we have QSPP ≈ 27 and Qexc ≈ 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/2αvg, Ω/Γ ≫ 1. The strongest coupled NW has a Rabi frequency of Ω = 390 ± 80 meV. For this nanowire we have Ω/2αvg ≈ 5 and Ω/Γ ≈ 7, which is consistent with strong coupling In conclusion, Exciton−plasmon coupling has been investigated for silver nanowires coupled to the 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 frequency observed for the NW−TDBC system is Ω = 390 ± 80 meV, 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.

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 3a and described in full in the Supporting Information. The complex dielectric constant for the NWs was taken from Johnson and Christy35 and that of the dye− PVA was taken 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 Figure 3b. Note that the dielectric function for TDBC contains two oscillators, which have resonance frequencies at 2.03 and 2.10 eV. The lower energy oscillator has a smaller oscillator strength and appears as a shoulder in the (ϵ′, ϵ″) data in Figure 3b. The finite element simulations were performed in COMSOL Multiphysics (v. 5.3) using a 2D mode analysis calculation. This analysis yields the complex wavevector for the SPP mode kSPP = 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 LSPP by LSPP = 1/2α = 1/Δk.36 Figure 3c 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 Figure 3c. Furthermore, finite element simulations with a single oscillator can reproduce the features in Figure 3c (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 on a silver surface by Pockrand and coworkers.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 Figure 3c are the experimental data for the NW in Figure 2b. 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 cutoff and would only affect the BFP images for nanowires with diameters >170 nm. We do not know the width of the NWs in the BFP images, and thus it is possible that these higher order leaky modes contribute to the experiments. Figure 3d shows a plot of the normalized attenuation constant 2α/k0 for the TBDC−PVA-coated and PVA-coated NWs obtained from the finite element simulations (2α/k0 is

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EXPERIMENTAL METHODS The samples for the optical experiments were prepared by spincasting dilute silver nanowire dispersions from water onto a flamed coverslip at 5000 rpm for 1 min. TDBC−PVA films (from a 1.5% wt. TDBC and 1.5% wt. PVA solution) were then spin-cast onto the nanowires under the same settings. The thickness of the film was characterized using ellipsometry (VVASE variable angle ellipsometer) and was found to be 25 ± 8 nm. The wavevectors for single silver nanowires were directly extracted from 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 supercontinuum laser source (Fianium SC450) was used for these experiments. Wavelengths in the range of 480−890 nm were selected with an acoustooptic tunable filter (Fianium AOTF-DUAL) before the microscope. 1679

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.8b00313. Schematics of the optical setup, TEM 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 nanowire−TDBC system. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*G.B.: E-mail: [email protected]. *G.V.H.: E-mail: [email protected]. ORCID

Gary Beane: 0000-0001-5312-0477 Paul Johns: 0000-0002-1134-7566 Tuphan Devkota: 0000-0002-0572-5874 Gregory V. Hartland: 0000-0002-8650-6891 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the United States National Science Foundation (CHE-1502848) and the Office of Naval Research (award no. N00014-12-1-1030). We thank Prof. Masaru Kuno for use of the supercontinuum light source.

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REFERENCES

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DOI: 10.1021/acs.jpclett.8b00313 J. Phys. Chem. Lett. 2018, 9, 1676−1681

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DOI: 10.1021/acs.jpclett.8b00313 J. Phys. Chem. Lett. 2018, 9, 1676−1681