Simple Approach for Designing Plexcitonic Nanostructures Daniel E

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Semiclassical Plexcitonics: Simple Approach for Designing Plexcitonic Nanostructures Daniel E. Gomez,́ *,†,‡ Harald Giessen,§ and Timothy J. Davis†,‡

† CSIRO, Materials Science and Engineering, Private Bag 33, Clayton, Victoria 3168, Australia ‡ Melbourne Centre for Nanofabrication, Australian National Fabrication Facility, Clayton, Victoria 3168, Australia § 4th Physics Institute, University of Stuttgart, Pfaﬀenwaldring 57, 70569 Stuttgart, Germany

*S Supporting Information

ABSTRACT: We present a classical description of the interaction between localized surface plasmon resonances and excitons which can occur in molecular or solid state systems. Our approach consists of adopting a semianalytical description of the surface plasmon resonances in metal nanoparticles and a semiclassical description of the electronic transitions related to the excitonic material. We consider three plasmon-exciton coupling conﬁgurations, namely a (or a set of) metal nanoparticle(s) uniformly coated with an excitonic material, a set of metal nanoparticles placed in the vicinity of a sub-wavelength-sized “patch” containing the active material, and the limiting case of a single point dipole coupled to a metal nanoparticle. Our key result is the derivation of the conditions required to achieve strong plasmon−exciton coupling as evidenced by polaritonic splitting. We apply our results to describe recent experimental studies on these hybrid systems. Our study provides a simple, yet rigorous prescription to both analyze and design systems that exhibit strong light−matter interactions as mediated by localized surface plasmon resonances (i.e., particle plasmons).

urface plasmon resonances in metallic nanoparticles have interacts strongly with an excitonic material. Aside from this S attracted a significant amount of research due to the sub- simple requirement, here we investigate what are the specific wavelength confinement of light that is possible with these material requirements needed when the plasmonic structures collective excitations. When a surface plasmon field interacts consist of single or coupled metallic nanoparticles which with electronic excitations such as excitons, two interaction interact with an excitonic material in the form of (a) a uniform regimes are possible, one of which (the strong coupling regime) coating around the plasmonic elements, (b) a nanostructured results in the formation of plasmon−exciton hybrid states or “patch”, and (c) a single emitter positioned in the near-field of plexcitons.1 These hybrid states are characterized by avoided the plasmonic nanostructures, as depicted in the diagram of crossings in dispersion diagrams of the coupled system that are Figure 1. To this end, we develop a semianalytical model based manifest in scattering or reflectivity spectra as spectral doublets. on the Electrostatic Eigenmode Method (EEM)34 that is To date, plexcitons have been experimentally achieved in many employed for describing the surface plasmon resonance in − configurations,1 31 including thin metal films with thin metal nanoparticles and a semiclassical description of the excitonic layers,2,9,12,18,19,28 monolayer coatings on nano- electronic transitions related to the excitonic material. Our particles,1,16,23,24 and homogeneous thin films covering nano- results provide a guide that is useful in designing plexcitonic particles.29 systems. Plexcitons are Bosonic quasi-particles half exciton, half In the EEM one solves Maxwell’s equations for metal plasmons which possess the lightest to-date reported effective nanoparticles assuming that these are much smaller than the masses, a feat that could make possible the observation of wavelength of light. Within this approximation, the optical Bose−Einstein condensation at room temperature.27 Plexcitons properties of particles are described in terms of eigenmodes, are also promising candidates for demonstrating polariton which are self-sustained surface charge oscillations that occur at 35 lasing at the nanoscale with highly reduced thresholds as the surface of the particles. According to this approximation, compared to conventional lasers, and unlike conventional the optical properties of coupled nanoparticles can be thought as originating from linear superpositions of the eigenmodes of polariton devices that have required the use of micron-sized 36 optical cavities,32,33 plexciton states can readily occur in single the noninteracting nanoparticles. This permits a description metal nanoparticles which are inherently sub-wavelength sized. In order to create structures that support plexciton states, the Received: June 27, 2014 obvious requirement is that these structures should be Revised: September 14, 2014 composed of a surface plasmon supporting element that Published: September 17, 2014

2 fωo εe()ωε=−∞ 22 ωω−+Γo i ω (2)

where ε∞ is a parameter describing the permittivity at ω Γ wavelengths above the resonance frequency o. is the line width of the transition, f is its reduced oscillator strength, and the permittivity of the metal is described by a Drude model: ε ω εD − ω2 ω2 ωΓ ( )= ∞ P/( + i m). Using eq 1 with the Drude model for ε(ω) near a plasmon ω resonance m [as done in ref 35; see Supporting Information ε ω ≈ ω section, eq S3], eq 2 is combined for e, assuming that o, which leads to 2 2 D ωP 2ωP ε∞ −+2 3 (/2)ωω −+Γmmi ωm ωm ⎛ ⎞ 1 + γ ⎛ ⎞ ⎜ pm ⎟ fωo = ⎜ ⎟⎜ε − ⎟ 12(/2)− γ ⎝ ∞ ωω−+Γi ⎠ ⎝ pm ⎠ o (3) Figure 1. Configuration of plasmon−exciton coupling. g is the where the value of the plasmon resonance ω is obtained as Γ m coupling strength, m is a rate representing the losses in the plasmon [see section S2, eq S5]: mode m and Γ the losses in the excitonic system. ε(ω) is the ε ω ⎛ ⎞ permittivity of the metal, e( ) the permittivity of the excitonic 1 + γ ω 2 system, and ε that of the surrounding dielectric medium. Here, we ⎜ pm ⎟ D P b ε()ωm = ⎜ ⎟εε∞∞≈− consider the cases where the nanoparticles are homogeneously coated 1 − γ ω2 ⎝ pm ⎠ m (4) with the “excitonic” material or when they interact with “patches” of emitters and single emitters, as depicted in this figure. To simplify notation, we introduce the following complex ω̃ ω − Γ ω̃ ω − Γ frequencies o = o i /2 and m = m i m/2. It is straightforward to show that the equation for the resonance of the optical properties of complex arrays of nanoparticles by frequency of the metal particles in the excitonic medium is using group theoretical analysis.37 In spite of its approximate 1 + γ 3 pm fωωom nature, the EEM can explain several experimental observations, (ωωωω− ̃ )(− ̃ ) = omγ − 1 ω 2 including the effect of the substrate on the resonances of metal pm 4 P (5) 38 39,40 nanoparticles, the optical modes of nanoparticle chains, ω 41 which leads to a quadratic equation whose two roots ± are the optical response of 3D nanostructures, the generation of given by optical chirality,42,43 and the optical excitation of collective dark 44 modes. ωω+ Γ+Γ ⎛ ω̃ − ω̃ ⎞2 omi() m2 ⎜⎟ mo According to the EEM, optical excitation of nanoparticles ω± = + ±+g ⎝ ⎠ results in oscillating charge densities σ at the surface of metal 2 42 nanoparticles which can be decomposed into superpositions of (6) σ the normal modes of the nanoparticles pm where each mode m where we have defined the plasmon−exciton coupling constant γ of particle p is associated with an eigenvalue pm that dictates as the resonance wavelength (a real-valued quantity) of the ⎛ ⎞ 1 + γ 3 surface plasmon mode through the following relationship: 2 ⎜ pm ⎟ ωm fωo g ≡ ⎜ ⎟ × γεωγε−++= pm ⎝ γ − 1 ⎠ 2ω 2 2 Re{(pm 1) (pm ) (1pm )b } 0 (1) pm P (7) ε ω ε with ( ) the (complex) metal permittivity and b the According to eq 6, the condition required for observing two ω ω 2 Γ − permittivity of the surrounding medium. For the case of an distinct (real valued) resonances when o = m is gpm >( m ellipsoid, γ can be related to the depolarization factors.38 This Γ)2/16, which is the “strong coupling condition”, a result pm − very simple relationship can be used to describe the resonances consistent with studies of strong coupling in microcavities.45 47 2 − Γ − Γ 2 1/2 of metal nanoparticles when these interact with uniform and The splitting in this case is given by 2[gpm ( m ) /16] , spatially homogeneous media containing an exciton transition. which in order to result in clearly resolvable spectral doublets In the experiments of Schlather et al.,29 Au nanodisks were must additionally exceed the value of the average line widths (Γ Γ embedded in a PVA matrix doped with J-aggregates of a + m)/4. cyanine dye, and under certain experimental conditions, they The most significant aspect of this result is that this strong observed doublets in the measured scattering spectra of the coupling condition has no dependence on the magnitude of the nanoparticles, a characteristic of the formation of plexciton electric near-field around the nanoparticle. More explicitly, states in this system. resonance splitting in these plasmon−exciton systems does Within the EEM, the observation of spectral doublets in a not depend on the presence of hot spots in the metallic configuration consisting of metal nanoparticles in a uniform nanostructures when these are homogeneously coated with the and infinite medium containing J-aggregates (the excitonic excitonic material. Instead, in this case the coupling strength as material) can be fully accounted for by using eq 1. To this end, written in eq 7 depends on the material properties of the ε ω the permittivity e of the excitonic material is described by excitonic material through f and o and those of the metal

23964 dx.doi.org/10.1021/jp506402m | J. Phys. Chem. C 2014, 118, 23963−23969 The Journal of Physical Chemistry C Article

− 2 ω ε ω Figure 2. (a) Plasmon exciton coupling constant g [eq 7] vs particle plasmon resonance frequency m for ∞ = 2.5. In these calculations, P = 9.04 ω 2 ω ω ε eV for Ag and P = 8.62 eV for Au. (b) Evolution of 2g /(f o) vs the localized surface plasmon resonance m with the value of ∞ for Au. (c) g ω ω ε calculated vs m and o for ∞ = 2.5 and f = 0.4. (d) Intrinsic line width of a localized surface plasmon resonance plotted vs particle plasmon ω ε resonance frequency m for ∞ = 2.5. for Au and Ag. ω through the value of the plasma frequency P, the eigenvalue conductors. At the peak value shown in Figure 2a, one would γ γ pm ( pm > 1) which is a shape-dependent parameter, and the therefore expect to obtain the strongest coupling which will ω localized surface plasmon resonance m, which is an implicit manifest as a large spectral splitting. Figure 2c shows how the ε γ function both of the ∞ of the excitonic medium and pm as of coupling constant gpm varies with the localized surface plasmon 2 Γ − Γ 2 ω eq 4 (see also, Figure S1). Clearly, when gpm <( m ) /16, frequency (energy) m for Au and the resonance frequency ω ε the plasmon resonance is only weakly perturbed and one would (energy) o of an excitonic medium described by eq 2 with ∞ expect to observe a red shift in the position of the plasmon = 2.25 and f = 0.4 typical values for thin polymer films doped resonance with an increase in its line width. Equation 7 with J-aggregates.2,29 Similar to the case shown in Figure 2a, the fi − quanti es the plasmon exciton coupling strength for a highest values for gpm are obtained when the localized plasmon ω plasmon mode m characterized by a surface charge distribution resonances m are in the spectral region between 1.5 and 2 eV, σ pm which, through its associated dipole moment, dictates how but these high values also occur when the resonance frequency 36 ω the mode interacts with light. of the excitonic medium o is slightly detuned (blueshifted) Let us now examine in more detail the dependence of gpm on from the plasmon resonance. This is partly due to the fact that ff ω ∝√ω the material properties of the metal. In Figure 2a, we show how eq 7 for gpm has di erent dependencies on o (gpm o) and 2 ω ∝ ω3 1/2 gpm (as normalized to the properties of the excitonic material, m (gpm ( m) ). ω i.e., divided by f o/2) changes as a function of localized surface The predictions of Figure 2b however do not completely plasmon frequency (energy) for Au and Ag in a medium with specify the conditions for strong coupling, since as previously ε γ ∞ = 2.25. In this case, the eigenvalue pm is allowed to vary, stated, in order to achieve this regime, gpm has to exceed the and according to eq 4, there is a one-to-one mapping between losses in the coupled system. the eigenvalue and the localized surface plasmon resonance For Au nanoparticles, the losses can be decomposed into ω γ 48 frequency ( m increases with increasing pm as shown in Figure three contributions: intrinsic bulk damping mechanisms, S1 of the Supporting Information). This situation therefore surface scattering, and radiative losses. The first mechanism is corresponds to the case of having a fixed excitonic medium and due to electron inelastic scattering by phonons, impurities, and metal nanoparticles of different shapes or different resonance defects and is generally a process described by the dielectric frequencies. Figure 2a shows clearly that Ag exhibits the permittivity of the metal which contributes to the surface strongest coupling strength across the entire spectrum. plasmon line width as indicated in Figure 2d. The contribution 2 48,49 Γ ν Additionally, gpm seems to peak for either metal at a particular of surface scattering to the line width is given by s = A F/ 2 ν frequency: 1.83 eV for Au and 2.58 eV for Ag. g decreases Leff, with A as a constant of the order of unity, F the Fermi ω ff strongly when m approaches either the interband transitions velocity, and Leff the e ective path length of the electrons. of the metals or the near-infrared. Figure 2b shows that the Radiative damping on the other hand is approximately given 2 48,49 Γ ℏκ κ (normalized) value of gpm also decreases with increasing the by r =2 V, with as a phenomenological constant and V value of ε∞ of eq 2, indicating that strong coupling can be more the volume of the nanoparticle. The net effect of the easily observed for excitonic materials with a low background appearance of Leff and V in these two expressions is that the permittivity, which is typically the case for organic semi- contribution of these two damping mechanisms to the total

23965 dx.doi.org/10.1021/jp506402m | J. Phys. Chem. C 2014, 118, 23963−23969 The Journal of Physical Chemistry C Article Γ surface plasmon line width m depends on the geometry of the indicate modes such as the dipole-like, quadrupole-like mode, ffi ̃ nanoparticles, setting thus the dashed lines shown in Figure 2c etc.). The coe cients am are the excitation amplitudes for the as the lower limits to the total surface plasmon mode line coupled system, which according to the EEM can be written in “ ” width. terms of the uncoupled excitation amplitudes am of its Armed with a description of the plasmonic contribution to constituents. am for a metallic nanoparticle is approximately 35 ≈ ω ⃗· ⃗ ω the coupling strength g and to the losses in the coupled given by am f m( )pm E, where f m( ) is a frequency and systems, our attention is now focused on the excitonic materials shape dependent function describing the spectral properties of and their material properties, as described by eq 2, which are the plasmon resonance (more details in section S4), p⃗is the − m required to achieve strong plasmon exciton coupling. To this dipole moment of the m-th surface plasmon mode, and E⃗is the fi end, we proceed rst by drawing an example from the literature total electric field incident of the particle. For a single plasmon and consider in Figure 3 the attainable coupling strengths gpm mode interacting with a single emitter, the total electric field for an excitonic medium described with eq 2, namely: DPDC that drives the localized surface plasmon mode consists of the (2,2′-dimethyl-8-phenyl-5,6,5′,6′-dibenzothiacarbocyanine fi ⃗ fi 29 ε ω applied eld Eo plus the eld originating from the single chloride) J-aggregates, for which ∞ = 2.5, f = 0.4, o = 1.79 ̃ ⃗ fi ℏΓ emitter: asEs. In this case, the excitation amplitude is modi ed eV, and = 52 meV. ̃ to am and is given by (more details in section S4)

= ω · ⃗ + ⃗ afm̃ m () pEaEm⃗ (oss̃ ) =+ωω ⟨· ⃗ ⟩ =+ afm m () pEaafm⃗ ss̃ m m () Gams s̃ (8)

Similarly, the excitation amplitude of the single emitter is also expressed as50,51

= ω · ⃗ + ⃗ afs̃ s () pEaEs⃗ (omm̃ ) =+ωω ⟨· ⃗ ⟩ =+ afs s () pEaafs⃗ mm̃ s s () Gasm m̃ (9) − ⃗ Figure 3. Plasmon exciton coupling constant gpm calculated for with ps as the induced dipole moment on the dielectric sphere DPDC J-aggregates plotted vs localized plasmon resonance frequency ffi ω and Gsm as the sphere-to-metal coupling coe cient. It is worth m for Au and Ag. Also shown (dotted and dashed lines) are the lower noting here that both E⃗and E⃗are the electric fields produced limits to the line width of the surface plasmon resonance. The gray s m by the eigen-modes of the dielectric sphere (a three-fold lines correspond to the calculated coupling constant with the 50,51 minimum values of f that would still result in strong coupling. degenerate dipolar mode ) and the m-th surface plasmon eigenmode of the metallic nanoparticles, and that furthermore ⟨···⟩ denotes a spatial average of these fields in either the metal Figure 3 clearly shows that, for both Ag and Au nanoparticles nanoparticle or the dielectric sphere (more details in section D uniformly coated with DPDC, gpm is always larger than the of the Supporting Information). Γ Γ average line widths ( + m)/4 (discontinuous lines in Figure These two linear equations can be combined as follows: 3) and thus the observation of a strong plasmon−exciton is very likely in this case, in agreement with the results of ⎛ ⎞−1 29 29 ⎛ ⎞ 1 −fG ⎛ ⎞ Schlather et al. For the case presented by Schlather et al., am̃ m ms am ⎜ ⎟ = ⎜ ⎟ ⎜ ⎟ our model predicts a splitting of 590 meV which is larger than ⎝ ⎠ ⎜ ⎟ ⎝ a ⎠ as̃ ⎝−fGsm 1 ⎠ s the one experimentally measured (230−400 meV). Our s ff ⎛ ⎞ estimate ignores radiative damping, the e ect of which is to 1 fG ⎛a ⎞ decrease this value. By artificially decreasing the value of f and 1 ⎜ m ms⎟⎜ m⎟ = ⎜ ⎟⎝ ⎠ evaluating eq 7 (only f and ω describe the J-aggregates in this Δ ⎝ fG 1 ⎠ as o s sm (10) equation), our simple model predicts that in order to realize strong coupling to localized surface plasmon resonances, the where we have introduced the (implicitly defined) coupling minimum value of the reduced oscillator strength required for − coefficients G and G , dimensionless quantities that quantify Au in the 1.5 to 2 eV spectral region is f ≳ 5 × 10 2 and for Ag ms sm − the nanoparticle-to-sphere coupling and which only depend on this is f ≳ 5 × 10 3 (see gray lines in Figure 3; in the the relative orientations and separation distances between these Supporting Information, we give details on how these f values 35 Δ translate into absorption cross sections). One question that objects and not on the frequencies. In this equation, is the determinant of the coupling matrix which for this simple case is naturally arises: is it possible to improve the coupling by Δ − ω ω nanostructuring both the plasmonic and excitonic elements? given by =1 f m( ) fs( ) GmsGsm. We consider this in the following section. The scattering spectrum of this simple coupled system is | ̃ |2 ∝ |Δ|2 36 A single dipole emitter/absorber can be modeled as a proportional to ai 1/ , meaning that the resonances of ω polarizable dielectric sphere with a complex dielectric function this coupled system occur for frequencies which satisfy 1 = ε ω ω ω e( ) given by that of eq 2. f m( ) fs( ) GmsGsm. In order to obtain closed analytical forms For a single or set of coupled metal nanoparticles proximal to that predict the values of these frequencies, we employ the this excitonic material, the surface plasmon excitations can be following approximate forms of f(ω) for both the single emitter 36 σ Σ ̃ σ written as = mam m, where the index m indicates the and the metallic nanoparticle, which have been derived in the surface plasmon mode (i.e., for a spherical particle, m can Supporting Information [eqs S11 and S12]:

23966 dx.doi.org/10.1021/jp506402m | J. Phys. Chem. C 2014, 118, 23963−23969 The Journal of Physical Chemistry C Article

fω /2 f ()ω ≈− o s fωo Γ ωω−−o +i 62εb

2 3 2 2γpm ω ε f ()ω ≈− m b m γ − 2 ω 2 ωω− ̃ (1)pm P m (11) With these, the resonance condition leads to the following quadratic equation for the resonance frequencies of the coupled system: ⎛ ⎞ fω Γ (ωωωω− ̃ )⎜ −−o +ig⎟ = 2 mo⎝ ⎠ pm 62εb (12) where we have deﬁned the plasmon−exciton coupling constant as

2 3 2γpm ω fω 2 = m ××o ε 2 gpm 2 2 bmssmGG (1)γpm − ωP 2 fω =×g o ×ε 2GG P 2 bmssm (13) Figure 4. (A) Plasmonic contribution to the coupling constant of eq which we have conveniently written as a product of three ω 13 plotted as a function of localized surface plasmon resonance m in a factors: the first one depends on the properties of the metal ε × ω medium with b = 2.25. The inset shows the value of (gP ((f o)/ γ fi 1/2 nanoparticle(s) through the eigenvalue pm ( xed by the shape 2)) . (B) Calculated scattering spectra of the isolated rod and the and geometrical properties of the particle(s)), the resonance coupled system for ε =2.25, Au and assuming that the parameters of ω fi γ b frequency of the plasmon mode m which is xed by both pm DPDC describe the dielectric sphere. Inset: Diagram of a coupled ε and the dielectric constant of the surrounding medium ( b), system consisting of a nanorod of 20 nm in diameter and 48 nm in ω length separated by 2 nm from a dielectric sphere of 5 nm radius. The and P the bulk plasma frequency of the metal. The second colors indicate the relative surface charge densities. Gsm and Gms are the term depends solely on the properties of the single emitter, ffi namely the magnitude of its oscillator strength f and resonance geometrical coupling coe cients discussed in the text. ω fi frequency o. The last term depends on the near- elds around the particle and emitter in addition to the their relative bigger than those obtained in Figure 2a. Furthermore, unlike orientations. Thus, unlike the case of a homogeneous and infinite the case shown in that figure, the plasmonic contribution to the coating around the metal nanoparticles, the magnitude of the coupling strength is predicted to increase with decreasing coupling strength depends critically on the placement of this emitter frequency of the localized surface plasmon resonance. The 2 ω in relation to the electric near-field produced by the localized second contribution to gpm of eq 13 is simply f o/2, stating that surface plasmon resonance (implicit in GmsGsm). Again, in this excitonic materials with a high value of f are required for case, the strong coupling condition also reads (at resonance) achieving strong coupling. In the inset of Figure 4a we show 2 Γ − Γ 2 × ω 1/2 gpm >( m) /16 in agreement with our previous derivation. how the value of [gp ((f o)/2)] evolves vs the localized This simple derivation can be easily extended to account for the plasmon frequency for Au and Ag nanoparticles, along with the ω case where the excitonic material is not uniformly distributed intrinsic plasmon line width (dashed lines) for the case of o = around the metal nanoparticle nor in the form of a single 1.79 eV (like the DPDC J-aggregates29) but with f =4× 10−3 emitter but, instead, is distributed in a specific shape or “patch” for the case of Au nanoparticles, whereas for Ag f =4× 10−4. × with a dimension comparable to the nanoparticle. Under the These correspond to the minimum values for which [gp ω 1/2 assumption that this patch contains N nonmutually interacting ((f o)/2)] remains above the intrinsic plasmon line width dipoles, f is simply scaled by this number density, and trivially (dashed lines in inset of Figure 4a). 2 one substitutes f for Nf in the expression shown above for gpm, However, one also needs to account for the last term of eq ⃗ fi bearing in mind that Es represents the collective electric eld 13, which involves the product of the geometrical coupling ε2 35−37,41 produced by the patch acting on the metal nanoparticle. The factors bGmsGsm. In order to assess the order of 2 resulting expression for gpm correctly predicts the scaling of the magnitude of these geometrical coupling constants, one must coupling strength with the number of oscillators (N)as evaluate these quantities for a specific case. As an example, we calculated by more complex approaches.45,46 show in Figure 4b a single metal nanorod (diameter = 20 nm, With these derivations, we can now address the important length = 48 nm, dimensions chosen to represent a chemically question as to how, in the most general instance, one could synthesized Au nanorod) separated by 2 nm from a dielectric design a plasmon−exciton coupled system that exhibits strong sphere of radius of 5 nm (size chosen to approximate a typical coupling. To this end, we consider each of the three terms colloidal QD). The geometry is chosen in such a way that the contributing to the coupling constant of eq 13. In Figure 4a we dielectric sphere is positioned very close to the points of show how the plasmonic contribution evolves as a function of maximum electric near-field created by the longitudinal localized surface plasmon resonance frequency. The most plasmon resonance of the rod, this with the aim of increasing fi salient feature of this graph is that, for both Au and Ag, the the values of GmsGsm. For this con guration a numerical magnitude of this contribution is almost an order of magnitude evaluation of the geometric coupling constants (using

23967 dx.doi.org/10.1021/jp506402m | J. Phys. Chem. C 2014, 118, 23963−23969 The Journal of Physical Chemistry C Article 52 ε2 ≈ ̈ Matlab ) yields bGmsGsm 0.19, which implies a further Wurttemberg Stiftung and ERC (complex plasmonics), Zeiss- decrease in the total value of the coupling constant shown in Stiftung and an ERC Advanced Grant (COMPLEXPLAS). Figure 4a. Other configurations can lead to higher values (such as a nanorod dimer51,53). ■ REFERENCES The key results of this manuscript are the expressions for the (1) Fofang, N. T.; Park, T.-H.; Neumann, O.; Mirin, N. A.; plasmon−exciton coupling strengths given by eqs 7 and 13, Nordlander, P.; Halas, N. J. Plexcitonic Nanoparticles: Plasmon- each expressing the contributions of the plasmonic and Exciton Coupling In Nanoshell-J-Aggregate Complexes. Nano Lett. excitonic material to their interactions in addition to factors 2008, 8, 3481−3487. that arise from the geometry of the coupling. 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Rev. achieved for excitonic materials with reduced oscillators B 2008, 78, 205326. strengths f (eq 2) larger than 4 × 10−3. (12) Symonds, C.; Bonnand, C.; Plenet, J. C.; Brehier, A.; Parashkov, R.; Lauret, J. S.; Deleporte, E.; Bellessa, J. Particularities of Surface ■ ASSOCIATED CONTENT Plasmon-Exciton Strong Coupling with Large Rabi Splitting. New J. Phys. 2008, 10, 065017 (11 pp). *S Supporting Information (13) Vasa, P.; Pomraenke, R.; Schwieger, S.; Mazur, Y. I.; Kunets, V.; Detailed information on some derivations as mentioned in the Srinivasan, P.; Johnson, E.; Kihm, J. E.; Kim, D. S.; Runge, E.; Salamo, text. This material is available free of charge via the Internet at G.; Lienau, C. Coherent Exciton-Surface-Plasmon-Polariton Inter- http://pubs.acs.org. action in Hybrid Metal-Semiconductor Nanostructures. Phys. Rev. Lett. 2008, 101, 116801. ■ AUTHOR INFORMATION (14) Hakala, T. K.; Toppari, J. J.; Kuzyk, A.; Pettersson, M.; Tikkanen, H.; Kunttu, H.; Törma,̈ P. Vacuum Rabi Splitting and Corresponding Author Strong-Coupling Dynamics for Surface-Plasmon Polaritons and *E-mail: [email protected]. Rhodamine 6G Molecules. Phys. Rev. Lett. 2009, 103, 053602. Notes (15) Salomon, A.; Genet, C.; Ebbesen, T. Molecule-Light Complex: fi Dynamics of Hybrid Molecule-Surface Plasmon States. Angew. Chem., The authors declare no competing nancial interest. Int. Ed. 2009, 48, 8748−8751. (16) Yoshida, A.; Uchida, N.; Kometani, N. Synthesis and ■ ACKNOWLEDGMENTS Spectroscopic Studies of Composite Gold Nanorods with a Double- Shell Structure Composed of Spacer and Cyanine Dye J-Aggregate D.E.G. and T.J.D. acknowledge support through a guest − professorship from MPI FKF. This work was performed in Layers. Langmuir 2009, 25, 11802 11807. part at the Melbourne Centre for Nanofabrication (MCN) in (17) Yoshida, A.; Yonezawa, Y.; Kometani, N. Tuning of the Spectroscopic Properties of Composite Nanoparticles by the Insertion the Victorian Node of the Australian National Fabrication of a Spacer Layer: Effect of Exciton−Plasmon Coupling. Langmuir Facility (ANFF). D.E.G. would like to thank the ARC for 2009, 25, 6683−6689. support through a Discovery Project DP110101767. D.E.G. and (18) Gomez,́ D. E.; Vernon, K. C.; Mulvaney, P.; Davis, T. J. Surface T.J.D. acknowledge the ANFF for the MCN Technology Plasmon Mediated Strong Exciton-Photon Coupling in Semiconductor Fellowships. H.G. would like to thank DFG, BMBF, Baden- Nanocrystals. Nano Lett. 2010, 10, 274−278.

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