PlasmonicâMolecular Resonance Coupling: Plasmonic Splitting

Article pubs.acs.org/JPCC

Plasmonic−Molecular Resonance Coupling: Plasmonic Splitting versus Energy Transfer Huanjun Chen,† Lei Shao,† Kat Choi Woo,† Jianfang Wang,*,† and Hai-Qing Lin†,‡ †

Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR Beijing Computational Science Research Center, Beijing 100084, China

‡

S Supporting Information *

ABSTRACT: Plasmonic−molecular resonance coupling was systematically studied using quasistatic approximation, Mie theory, and rigorous finite-difference time-domain calculations. The results indicate that the two types of coupling behaviors, plasmonic splitting and energy transfer, which are commonly manifested in experiments as peak splitting and a quenching dip, respectively, can be unified by considering a Au nanocrystal core coated with dye molecules. The dye coating is treated as a dielectric shell with Lorentzian-type absorption. By varying the oscillator strength and molecular transition line width, either plasmonic splitting or a quenching dip can be observed on the scattering spectrum of the dye-coated Au nanocrystal. The effects of the thickness of the dye coating, the spacing between the dye shell and the Au core, the partial dye coating, and the Au core shape on the coupled spectral shape were also ascertained. Our results will be useful for further exploring new phenomena in plasmon-based light−matter interactions as well as for developing highly selective and sensitive detection devices on the basis of plasmonic−molecular resonance coupling. technological applications, a large number of experimental11−17 and theoretical18−22 studies have been devoted to it. On the basis of these studies, many applications have been demonstrated, such as biological sensing23,24 and imaging,16,17 infrared detection,25 and all-optical switches.26 Moreover, studying and understanding the resonance coupling is especially important for plasmon-enhanced spectroscopies because the resonance wavelength of the hybrid system essentially determines the plasmon-derived electric field enhancement.27,28 The occurrence of plasmonic−molecular resonance coupling is evidenced by the optical extinction or scattering spectra of metal nanocrystal−organic dye hybrid nanostructures. In the strong resonance coupling regime, two types of spectral features can typically be observed. The first one is plasmonic splitting, which is manifested as two or more resonance peaks on the optical spectrum, depending on the number of the absorption bands of the dye.12−15 The spectral shape in the case of plasmonic splitting is usually very different from that of the bare metal nanocrystal, and the intensity of the entire spectrum is much lower than that of the bare nanocrystal. Resonance coupling-induced plasmonic splitting has been comprehensively studied in the past several years. The splitting magnitude has been found to be strongly dependent on the overlap between the molecular absorption and the plasmon resonance. When the plasmon resonance energy is systematically varied across the molecular absorption energy, an anticrossing behavior in the energy diagram is usually

1. INTRODUCTION Noble metal nanocrystals have been well-known for their localized surface plasmon resonances, which can induce large electric field enhancements around the nanocrystals upon resonant excitation. Such concentrated electric fields can strongly polarize or efficiently transfer their energy to adjacent organic molecules. Metal nanocrystals can therefore couple with adsorbed molecules electromagnetically and give rise to a number of intriguing phenomena, such as plasmon-enhanced spectroscopy,1,2 plasmon-modulated absorption/emission spectra,2,3 refractive index-induced plasmon shift,4 and plasmonenhanced nonlinear optical processes.5 All of them are the bases for developing and realizing a wide range of technological applications, such as ultrasensitive chemical and biological sensors,6 nanoscale lasers,7 plasmon-assisted photolithography,8 and plasmon-enhanced solar energy harvesting.9 Of particular interest among various plasmon−molecule interactions is plasmonic−molecular resonance coupling, which occurs when the plasmon energy of a metal nanocrystal is degenerated with the absorption energy of adjacent dye molecules.10 Under such a circumstance, the molecules can be remarkably polarized by the plasmon field surrounding the metal nanocrystal to generate a strong electromagnetic field. This electromagnetic field can in turn disturb the electron oscillation in the metal nanocrystal. As a result, the optical responses of both the molecules and metal nanocrystal are strongly modified, leading to distinct spectral changes on the hybrid nanostructure in comparison to the spectra of the separate constituents. Due to the great importance of plasmonic−molecular resonance coupling in both the fundamental understanding of light−matter interactions and practical © 2012 American Chemical Society

Received: April 13, 2012 Revised: June 5, 2012 Published: June 6, 2012 14088

dx.doi.org/10.1021/jp303560s | J. Phys. Chem. C 2012, 116, 14088−14095

The Journal of Physical Chemistry C

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observed.12,15 In addition, the plasmonic splitting also varies with the spacing between the dye molecules and metal nanocrystal surface, the number of the adsorbed dye molecules, the molecular volume-normalized molecular absorptivity, and the external stimuli, such as the illumination laser, solution pH, and existent metal ions.13,14 Recent studies utilizing ultrafast time-domain techniques to probe the dynamics of the plasmonic splitting have indicated the existence of an exotic transient behavior in the coupled system in the first 80 ps after its excitation.29 Moreover, the plasmonic splitting is the plasmonic analogue of Rabi splitting usually observed in quantum mechanical systems. From this point of view, the plasmonic splitting occurs due to the exchange of photons between the plasmonic field and the dye molecules in the strong coupling regime. Such a mechanism can overcome decoherence effects and give rise to new coherent hybrid light− matter states. Therefore, the plasmonic splitting provides a classical system for investigating Rabi splitting and developing its related applications. For example, two recent studies have shown that resonance coupling-induced Rabi splitting can reach as high as 700 meV.30,31 Such a large splitting can be utilized to modify the chemical reaction landscape of a photochromic dye.31 On the other hand, a few studies have also shown another type of spectral feature induced by the strong resonance coupling, which is known as plasmonic energy transfer.16,17 The plasmonic energy transfer is characterized by a quantized quenching dip or overall quenching of the plasmonic scattering spectrum of an uncoated metal nanocrystal.16,17,32 The quenching position is in accordance with the molecular absorption band. Except the quenching dip, the overall spectral shape is not changed after the adsorption of dye molecules. Although the plasmonic energy transfer has not been studied as intensively as the plasmonic splitting, it has been shown to have great potential in ultrasensitive biological sensing and in vivo molecular imaging.16,17,32 Despite the great efforts, as mentioned above, made on the studies of plasmonic−molecular resonance coupling, the respective conditions for the plasmonic splitting and energy transfer to occur have still remained elusive. Answering this question needs comprehensive scrutiny of the effects of the molecular properties, such as the absorption strength, transition line width, and packing density, on the resonance coupling behaviors. This is a formidable task for experimental studies. In addition, as far as we know, the behaviors of the electron oscillations associated with the plasmonic splitting and energy transfer have not been studied. Understanding these questions will be important for further exploring the optical responses of inorganic−organic hybrid nanostructures as well as for α3 =

designing plasmonic devices with various functionalities. In this work, we use systematic theoretical calculations and numerical simulations to scrutinize plasmonic−molecular resonance coupling and reveal the conditions for the plasmonic splitting and energy transfer. The hybrid nanostructure of an elongated Au nanocrystal core coated with a concentric dye molecule shell is considered. The choice of an elongated Au nanocrystal is because of its larger local electric field enhancement and smaller plasmon damping in comparison with its spherical counterpart. Both factors are beneficial for achieving strong plasmonic−molecular resonance coupling. The adsorbed dye molecules are modeled as a coating shell with its dielectric function described by the Lorentz model. Although there have been several reports on plasmonic− molecular resonance coupling using this theoretical model,14,15,18,21 all of them have focused on plasmonic splitting. Our study represents the first try on unifying these two coupling phenomena with the same theoretical model. Our theoretical calculations on the core−shell nanostructure with a prolate spheroid shape using classical electrodynamics under quasistatic approximation indicate that the plasmonic splitting and energy transfer phenomena observed in different experiments can be unified. The plasmonic splitting occurs when both the oscillator strength and line width of the molecular transition of the dye are large. The plasmonic energy transfer characterized by a quenching dip takes place when both the oscillator strength and the molecular transition line width are small, and that characterized by overall quenching of the plasmon resonance can be observed when the oscillator strength is small and the line width is large. Numerical simulations on the core−shell nanostructure with a rod shape using the finite-difference time-domain (FDTD) method reveal the respective electron oscillations associated with the plasmonic splitting and energy transfer. Moreover, the effects of the thickness of the dye shell, partial dye coating, and the spacing between the dye shell and the Au nanocrystal surface on the resonance coupling are elucidated.

2. EXPERIMENTAL SECTION Quasistatic Approximation. The scattering spectrum of the Au prolate spheroid core−dye shell nanostructure was calculated under quasistatic approximation. The three principal semiaxes of the spheroid core were set as a = b < c. In our calculations, we only considered the excitation along the longitudinal axis of the nanostructure. The thickness of the dye shell was varied. The polarizability of the core−shell nanostructure is given by33

V {(εdye − εbg)[εdye + (εAu − εdye)(L3(1) − fL3(2))] + fεdye(εAu − εdye)} [εdye + (εAu − εdye)(L3(1) − fL3(2))][εbg + (εdye − εbg)L3(2)] + fL3(2)εdye(εAu − εdye)

In eq 1, V is the volume of the entire core−shell nanostructure; εAu and εdye are the dielectric functions of the Au core and the dye shell, respectively; εbg = 1.7780 is the dielectric constant of the surrounding water background; f is the fraction of the total particle volume occupied by the inner spheroid; and L(1) 3 and (2) L3 are the geometrical factors of the inner and outer spheroids. The geometrical factors are determined according to

L3(k) =

ak bk ck 2

∫0

∞

dq (ck2

+ q)Fk(q)

(1)

k = 1, 2 (2)

where ak, bk, and ck are the three principal semiaxes of the core (k = 1) and the overall core−shell nanostructure (k = 2). Fk(q) is given by Fk(q) = 14089

(q + ak2)(q + bk2)(q + ck2)

(3)



Article

During the calculations, an electromagnetic pulse in the wavelength range from 500 to 950 nm was launched into a box containing the target nanostructure to simulate a propagating plane wave interacting with the nanostructure. The nanostructure and its surrounding medium were divided into 0.5 nm meshes. The refractive index of the surrounding medium was taken to be 1.3334. Mie Theory. Mie theory was utilized to calculate the scattering spectrum of the Au sphere core−dye shell nanostructure. Specifically, Mie theory and its extension to core−multishell nanostructures on the basis of the recursion algorithm was utilized.33,35 An individual nanostructure was modeled as a Au sphere core−dye shell structure embedded in water. The refractive index of the dye shell was set according to the Lorentzian dielectric function of the dye. The summation coefficients for calculating the scattering cross section can be obtained from the expressions below

The scattering cross section of the nanostructure can then be obtained from Csca =

k4 |α3|2 6π

(4) 1/2

where k = [(2π(εbg) )/λ] is the wavevector. Finite-Difference Time-Domain (FDTD) Simulations. The FDTD simulations were performed using FDTD Solutions 6.0, which was developed by Lumerical Solutions, Inc. The Au nanorod core was modeled as a cylinder capped with a hemisphere at each end. A concentric dye shell of 5 nm thickness was coated around the Au nanorod. The Lorentzian dielectric function of the dye and the measured dielectric function34 of gold were employed for the core and shell, respectively. For the nanostructure with a spacer layer, a dielectric layer with a given refractive index was inserted between the Au nanorod core and the dye shell. The thickness of the spacer layer was increased gradually from 0 to 20 nm. Tn1 = −

Tnw = −

m1χn (m1ρ1)ψn′(ρ1) − χn′(m1ρ1)ψn(ρ1)

(5)

mwψn(mwρw )[ψn′(ρw ) + Tnw − 1χn′(ρw )] − ψn′(mwρw )[ψn(ρw ) + Tnw − 1χn (ρw )] mwχn (mwρw )[ψn′(ρw ) + Tnw − 1χn′(ρw )] − χn′(mwρw )[ψn(ρw ) + Tnw − 1χn (ρw )]

an = −

(6)

mr ψn(mr ρr )[ψn′(ρr ) + Tnr − 1χn′(ρr )] − ψn′(mr ρr )[ψn(ρr ) + Tnr − 1χn (ρr )] mr ξn(mr ρr )[ψn′(ρr ) + Tnr − 1χn′(ρr )] − ξn′(mr ρr )[ψn(ρr ) + Tnr − 1χn (ρr )]

Sn1 = −

Snw = −

m1ψn(m1ρ1)ψn′(ρ1) − ψn′(m1ρ1)ψn(ρ1)

(7)

ψn(m1ρ1)ψn′(ρ1) − m1ψn′(m1ρ1)ψn(ρ1) χn (m1ρ1)ψn′(ρ1) − m1χn′(m1ρ1)ψn(ρ1)

(8)

ψn(mwρw )[ψn′(ρw ) + Snw − 1χn′(ρw )] − mwψn′(mwρw )[ψn(ρw ) + Snw − 1χn (ρw )] χn (mwρw )[ψn′(ρw ) + Snw − 1χ ′n (ρw )] − mwχn′(mwρw )[ψn(ρw ) + Snw − 1χn (ρw )]

bn = −

(9)

ψn(mr ρr )[ψn′(ρr ) + Snr − 1χn′(ρr )] − mr ψn′(mr ρr )[ψn(ρr ) + Snr − 1χn (ρr )] ξn(mr ρr )[ψn′ + Snr − 1χn′(ρr )] − mr ξn′(mr ρr )[ψn(ρr ) + Snr − 1χn (ρr )]

(10)

wavenumber is kw = (2πnw)/λ. The Riccati−Bessel functions are defined as

In the above equations, the parameter w denotes the layer index of the core−shell nanostructure, with w = 1 representing the core and w = 2 standing for the shell; the parameter r is the outmost layer index, which is 2 in our calculations; and the parameter mw = nw+1/nw represents the refractive index ratio between the w + 1 shell and the w shell. The prime denotes the derivation of the function. In each layer, the corresponding 14090

ψn(ρw ) = ρw jn (ρw )

(11)

χn (ρw ) = ρw yn (ρw )

(12)


The Journal of Physical Chemistry C ξn(ρw ) = ρw hn(1)(ρw )

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where the high-frequency component of the dielectric function is εbg; ω0 is the frequency of the molecular transition of the dye; γ is the line width of the molecular transition; and s is the oscillator strength. In our study, εbg is set as 1.7780 since most of the experimental measurements are conducted in water.12−15 ω0 is set to be equal to the longitudinal plasmon energy of the Au core to ensure that the plasmonic and molecular resonances are in the strong coupling regime.10−22 s and γ are varied within the ranges from 0 to 6 and 0.0001 to 0.25 eV, respectively. These values cover those of common dyes, which are in the ranges of s = 0.001−0.1 and γ = 0.03−0.24 eV according to their absorption spectra and molar absorptivities.13,16,37 Single-particle measurements are highly favored in experimental studies because they can avoid the extrinsic factors on the plasmonic−molecular resonance coupling behavior, such as the inhomogeneous size distribution of metal nanocrystals, the background absorption from excess dye molecules, and the aggregation of metal nanocrystals.14,16,17,32 Single-particle measurements can usually capture only scattering spectra. We therefore in our study focused on the scattering spectrum of the Au core−dye shell nanostructure. Figure 1A and Figure S1 (Supporting Information) show the imaginary and real parts of the dielectric functions of the dye shell with different oscillator strengths and linewidths. Figure 1B shows the corresponding scattering spectra of the core−shell nanostructure. In the calculations, the thickness of the dye shell is set at 1 nm according to the sizes of common dyes used in experiments.14 The unshelled Au spheroid core exhibits a plasmon resonance at 674 nm. The core−shell hybrid nanostructure exhibits notably different scattering spectra. When the dye shell has a small oscillator strength of s = 0.003 and a narrow molecular transition line width of γ = 0.005 eV, a quenching dip is clearly observed at the same spectral location as the molecular absorption on the scattering spectrum (Figure 1B, cyan) of the hybrid nanostructure. The dip indicates the occurrence of the plasmonic energy transfer. Increasing the oscillator strength to s = 0.02 and broadening the line width to γ = 0.025 eV makes the dip become less sharp and deep (Figure 1B, pink). When s and γ are further increased, overall quenching of the plasmon resonance, which is the other type of the plasmonic energy transfer, is seen (Figure 1B, red). If s is set to an even larger value of 0.5, the scattering peak red shifts to 710 nm, and a small bump appears around 660 nm (Figure 1B, blue). This is an indication of the transition from the plasmonic energy transfer to splitting, with the splitting characterized by a pair of scattering peaks. To reveal the plasmonic splitting more clearly, we simultaneously enlarge s to 5 and γ to 0.2 eV. Under this situation, two scattering peaks with comparable intensities are clearly present on the scattering spectrum (Figure 1B, green). One is centered at 760 nm, and the other is located at 628 nm. This is a typical spectral feature of the plasmonic splitting. These calculations suggest that the plasmonic splitting and energy transfer observed on Au nanocrystals coated with dye molecules can be unified by modeling molecular absorption with a Lorentzian dielectric function under quasistatic approximation. The pivotal parameters that determine whether the plasmonic splitting or energy transfer occurs are the oscillator strength and molecular transition line width of the dye. To see clearly how the plasmonic splitting and energy transfer evolve with the oscillator strength and line width of the molecular transition, we calculated the resonance coupling energy diagrams of the Au spheroid core−dye shell

(13)

where jn and yn are the spherical Bessel functions; h(1) n is the Hankel function of the first kind; and ρw = kwRw, with Rw being the radius of each layer. After the coefficients an and bn are calculated, the scattering cross section of the core−shell nanostructure can be obtained as Csca =

2π k2

∞

∑ (2n + 1)(|an|2 + |bn|2 ) n=1

(14)

where k is the wavenumber in water. In practical calculations, a truncation of n is applied according to the following criteria36 nmax = ρr + 4.05ρr1/3 + 2

(15)

3. RESULTS AND DISCUSSION The core−shell nanostructure considered in our quasistatic calculations consists of a Au prolate spheroid coated with a layer of adsorbed dye molecules (Figure 1B, inset). The use of a

Figure 1. Calculated scattering spectra of the Au spheroid core−dye shell nanostructure under quasistatic approximation. (A) Imaginary parts of the dielectric functions of the dye shell with varying oscillator strengths and linewidths. (B) Corresponding scattering spectra. The dye shell thickness is set at 1 nm. The wavelength ranges in (A) and (B) are set to be different to show clearly all the spectral features.

prolate spheroid shape is because there are analytic solutions to Maxwell’s equations for such a geometry. The three principal semiaxes of the Au spheroid core are set at a = b = 10 nm and c = 30 nm. The Au core is uniformly coated with a concentric dye shell of thickness t. The entire core−shell nanostructure is embedded in a homogeneous nonabsorbing medium having a dielectric constant of εbg. Previous studies have shown that such a system is a very good approximation in modeling the absorption and scattering properties of core−shell nanostructures.14,18,21 The dielectric function of the dye shell is described using a homogeneously broadened one-oscillator Lorentzian model as ε = εbg −

sω02 ω 2 − ω02 + i2ωγ

(16) 14091



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Figure 2. Calculated energy diagrams of the plasmonic−molecular resonance coupling of the Au spheroid core−dye shell nanostructure. (A) Energy diagram when γ is kept at 0.2 eV while s is increased from 0 to 6. (B) Energy diagram when γ is kept at 0.005 eV while s is increased from 0 to 0.01. (C) Energy diagram when s is kept at 5 while γ is increased from 0 to 0.25 eV. (D) Energy diagram when s is kept at 0.03 while γ is increased from 0 to 0.05 eV. (E) Energy diagram with varying dye shell thicknesses. s and γ are kept at 5 and 0.2 eV, respectively. (F) Energy diagram with varying dye shell thicknesses. s and γ are kept at 0.003 and 0.005 eV, respectively.

of both of them requires γ to be large. Because the line width usually characterizes the damping magnitude of an oscillation, coating a dye layer with very large damping will smear out the characteristics of the plasmon resonance of a metal nanocrystal core owing to the rapid dissipation of the oscillation. The plasmonic splitting and quenching dip-featured energy transfer will therefore become a broad resonance peak for very large γ, just as if the plasmon resonance is weakened by a broad background. In the above quasistatic calculations, the thickness of the dye shell is 1 nm. In experiments, dyes with different molecular sizes are used.11,14,15 In addition, dye molecules often form aggregates on metal nanocrystals.12−15,19,29 The sizes of dye aggregates can be up to a few nanometers. Therefore, the thickness of the dye shell is also a parameter that can affect plasmonic−molecular resonance coupling. Figure 2E gives the energy diagram of the plasmonic splitting with varying thicknesses, t, of the dye shell. As t is increased, the splitting magnitude of the two peaks gets larger, indicating that thicker dye shells cause stronger resonance coupling between the dye layer and the Au core. In addition, the intensity of the blue branch overwhelms that of the red branch when t is above 2 nm. This phenomenon is consistent with that found in a recent theoretical study on plasmonic−molecular resonance coupling.21 In the case of the plasmonic energy transfer, the quenching dip is always present irrespective of the change in t. With increasing t, the quenching dip gets wider (Figure 2F), also indicating that thicker dye shells lead to larger coupling strengths. These results reveal that the thickness of the dye layer only affects the magnitude of plasmonic−molecular resonance coupling, with the other main features nearly unchanged. To further verify this point, we conducted the calculations on the Au spheroid core−dye shell nanostructure with a shell thickness of 5 nm and varying s and γ. The overall

nanostructure by systematically varying s or γ while keeping the other parameters unchanged. We first looked at the plasmonic splitting (Figure 2A), where γ is kept at 0.2 eV. At small s, only one peak is present on the scattering spectrum. With increasing s, the dominant scattering peak gradually red-shifts and becomes weaker. When s is larger than 4, another peak appears in the shorter-wavelength region, indicating the occurrence of the plasmonic splitting. On the other hand, if γ is kept at 0.005 eV and s is varied from 0 to 0.01, a quenching dip at the spectral position corresponding to the absorption peak of the dye appears on the relatively broad plasmonic scattering background and becomes deeper (Figure 2B). During this process, the width of the plasmon band remains almost unchanged. These spectral features are the characteristics of the plasmonic energy transfer. The above two energy diagrams show that the plasmonic splitting and energy transfer can take place only when the oscillator strength of the dye is increased to a certain point within the particular ranges. This is because higher oscillator strengths result in greater polarization of the dye and therefore the larger polarization-induced electric field felt by the Au core. As a result, the coupling between the dye molecules and the Au spheroid core will become stronger and give rise to the observed plasmonic splitting or energy transfer. We then looked at the effect of the molecular transition line width, γ, on the resonance coupling-induced plasmonic splitting. Upon the gradual increase in γ, the two split peaks merge together to become a single broad peak (Figure 2C). A similar behavior is also seen in the case of the plasmonic energy transfer (Figure 2D). The quenching dip becomes shallower as γ is increased. It finally disappears, and the resonance coupling changes into the regime of overall quenching of the plasmon resonance. These two energy diagrams show that there exist respective upper limits of γ for the plasmonic splitting and the quenching dip-featured energy transfer although the occurrence 14092



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Figure 3. FDTD simulations of the plasmonic−molecular resonance coupling in the Au nanorod core−dye shell nanostructure. (A) Representative scattering spectrum for the plasmonic splitting. s and γ are 1 and 0.2 eV, respectively. (B) Representative scattering spectrum for the plasmonic energy transfer. s and γ are 0.001 and 0.005 eV, respectively. (C) Charge distribution contours on the central cross section of the core−shell nanostructure. The number in each contour corresponds to the spectral position labeled in (A) and (B). (D) Scattering spectra of the nanostructure with the dye shell gradually cut away from the middle of the nanostructure. (E) Scattering spectra of the nanostructure with the dye shell gradually cut away symmetrically from the two ends of the nanostructure. The uncut nanostructure in (D) and (E) exhibits the plasmonic splitting behavior, with s and γ being the same as those in (A).

arise from the use of the nanorod geometry in the FDTD simulations. Similar results from the quasistatic calculations and FDTD simulations verify the effectiveness of the FDTD method in simulating plasmonic−molecular resonance coupling, which will be helpful in the investigation of plasmonic− molecular resonance coupling involving arbitrarily shaped metal nanostructures. Figure 3A shows a representative scattering spectrum obtained from the FDTD simulations for the plasmonic splitting. The two split peaks are located at 836 and 692 nm, respectively. Their charge distributions are displayed in Figure 3C. For both of the peaks, charges are seen to be distributed around the outer surfaces of both the Au nanorod core and the concentric dye shell, suggesting that the dye shell is coupled strongly with the Au core through electromagnetic interaction. These charge distributions therefore reveal that the plasmonic splitting is caused by the hybridization between the dye shell and the Au core. The occurrence of the plasmonic splitting requires relatively large values of s and γ. Large γ values induce quick relaxation of the dye shell, and large s values ensure strong polarization of the dye shell. The electromagnetic energy will not be stored in the dye shell but dissipated via light scattering. As a result, the two hybridization-induced modes can be clearly observed in the scattering spectrum of the nanostructure. Figure 3B shows a representative scattering spectrum for the quenching dip-featured plasmonic energy transfer. There are three major features on the scattering spectrum: two shoulders and one quenching dip. The charges associated with the two shoulders are mainly distributed on the surface of the Au core (Figure 3C). There are almost no charges on the outer dye shell surface. This suggests that the two shoulders are of the plasmonic nature of the Au core. In contrast, at the quenching dip, the charges are distributed not only on the surface of the Au nanorod core but also on the outer dye shell surface. This is clear evidence of the energy transfer from the Au core to the dye shell. The occurrence of the quenching dip-featured plasmonic energy transfer requires s and γ values to be small,

trends seen on the coupling energy diagrams are similar to those of the nanostructure with a 1 nm dye shell. At fixed γ values, the plasmonic splitting and the quenching dip-featured energy transfer occur when the oscillator strength s is increased above certain threshold values (Figure S2A and B, Supporting Information). At fixed s values, the plasmonic splitting and the quenching dip-featured energy transfer are blurred out when γ is increased above certain threshold values (Figure S2C and D, Supporting Information). The threshold values of s for the appearance and those of γ for the disappearance of the plasmonic splitting and the quenching dip-featured energy transfer vary with the dye shell thickness. This variation can generally be ascribed to the strengthening of the resonance coupling by thick dye shells. Fully understanding plasmonic−molecular resonance coupling requires knowledge of the electron oscillation dynamics associated with the plasmonic splitting or energy transfer. However, the theoretical calculations based on quasistatic approximation can only provide the far-field response of the core−shell nanostructure. In this regard, we performed FDTD simulations and determined the charge distributions associated with the different coupling behaviors to reveal the underlying physics. For the FDTD simulations, due to the limit of the computational resource on the mesh size, we chose the core− shell nanostructure with a 5 nm dye shell. In addition, the Au core was modeled as a cylinder capped with a hemisphere at each end. Such a geometry is closer than a prolate spheroid to Au nanorods that are colloidally grown and employed in resonance coupling experiments.12−14 The overall length of the Au nanorod core is 60 nm, and its diameter is 20 nm, with its aspect ratio being equal to that of the Au prolate spheroid used in the quasistatic calculations. The Au nanorod is coated with a concentric dye layer. Comparison of the scattering spectra from the quasistatic calculations and the FDTD simulations with the same sets of s and γ values reveals that the obtained results are similar to each other, except that the FDTD-simulated peaks are red-shifted and show slight increases in intensity (Figure S3, Supporting Information). The red shifts and intensity increases 14093



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blue shift value when the spacer is very thick is determined by the refractive index of the spacer since the reference point for the plasmon shift is the longitudinal plasmon wavelength of the uncoated Au nanorod immersed in water. We finally conducted the calculations of the plasmonic− molecular resonance coupling in the Au sphere core−dye shell nanostructure on the basis of Mie theory since spherical Au nanoparticles were also utilized in many studies of plasmonic− molecular resonance coupling, including both the plasmonic splitting and energy transfer.15−17,19,22 Mie theory is a wellknown analytic solution to light scattering on spherical particles. The diameter of the Au nanosphere core and the thickness of the dye shell are set at 60 and 1 nm, respectively. The imaginary and real parts of the dielectric functions used in the calculations are plotted in Figure 4A and Figure S5

which gives rise to weak polarization and slow decay in the dye shell. Therefore, the transferred energy will be stored in the dye layer and dissipated mainly through nonradiative decay, leading to the appearance of a quenching dip on the scattering spectrum of the nanostructure. Anisotropic Au nanorods exhibit strong electric field enhancements at their ends due to the large curvature.38,39 Whether and how such anisotropic electric field enhancements affect plasmonic−molecular resonance coupling has rarely been studied. In this regard, we calculated the scattering spectra of the Au nanorod core−dye shell nanostructure with the shell partially removed. We focused on the plasmonic splitting in these calculations because the oscillating charges in the case of the plasmonic splitting are existent on the outer surfaces of both the Au core and the dye shell for the two hybridizationinduced peaks. In addition, the resonance coupling-induced plasmonic splitting has been observed experimentally on Au nanorods.12−14,26 Figure 3D shows the evolution of the scattering spectra when the dye shell is cut away from the middle of the nanostructure. The low-energy mode blue-shifts, and the high-energy one fades out gradually with the reduction in the dye coating. If the dye layer is cut from the ends of the Au nanorod, the low-energy mode disappears, while the highenergy mode becomes dominant (Figure 3E). Reduction of the dye coating in both manners weakens the overall coupling strength, as manifested by the blue/red shifts and simultaneous intensity increases of the low-/high-energy modes. The dependence of the scattering spectrum on the partial dye coating suggests strongly that the high-energy mode is governed by the hybridization between the Au nanorod core and the dye molecules at the side of the nanorod, and the lowenergy mode is contributed mainly by the coupling between the Au core and the dye molecules at the two ends. Because the plasmonic electric field enhancements of metal nanocrystals are located in the near-field region close to the nanocrystal surface, plasmonic−molecular resonance coupling should be very sensitive to the spacing between the dye molecules and the nanocrystal surface. We therefore also carried out FDTD simulations on the Au nanorod core−dye shell nanostructure with a dielectric spacer inserted between the core and the shell. The thickness and refractive index of the spacer layer were varied. As the spacing between the Au core and the dye shell is increased, the low-energy mode in the case of the plasmonic splitting blue-shifts back to the original plasmon wavelength quickly (Figure S4, Supporting Information). This result is qualitatively consistent with our previous experimental results.12 In addition, the blue shift versus the spacer thickness becomes steeper if the spacer layer has a smaller refractive index. In general, the magnitude of the plasmon shift indicates the coupling strength between the Au nanorod core and the dye shell. Insertion of a dielectric spacer will shield the electromagnetic interaction between them. As a result, the coupling strength will be suppressed, leading to the reduction of the plasmon shift. Usually, a spacer layer of a larger refractive index can have a greater shielding effect, giving rise to a steeper blue shift. On the other hand, the longitudinal plasmon mode of the Au nanorod core red-shifts as the refractive index of the surrounding environment is increased. The net plasmon shift of the hybrid nanostructure will therefore depend on the competition between these two factors. Our calculation results show that the blue shift of the plasmon mode versus the spacer thickness becomes steeper if the spacer layer has a smaller refractive index. The asymptotic

Figure 4. Calculations of the plasmonic−molecular resonance coupling in the Au sphere core−dye shell nanostructure on the basis of Mie theory. (A) Imaginary parts of the dielectric functions of the dye shell. (B) Corresponding scattering spectra.

(Supporting Information). The calculated scattering spectra are provided in Figure 4B. When s and γ are large, the scattering spectrum exhibits the plasmonic splitting behavior (cyan). The quenching dip-featured plasmonic energy transfer occurs for small s and γ (pink, red, and green). If s is kept small and γ is sufficiently large, the resonance coupling results in the overall quenching-featured plasmonic energy transfer (blue). The observed overall trend of the resonance coupling in the Au sphere core−dye shell nanostructure is similar to that obtained above in the core−shell nanostructure containing the elongated Au nanocrystals.

4. CONCLUSION In summary, we have systematically studied the plasmonic− molecular resonance coupling between Au nanocrystals and organic dye molecules using quasistatic and Mie-theory calculations. Both spherical and elongated Au nanocrystals are considered. The dye molecules are treated as a dielectric shell that has Lorentzian-type absorption and is coated concentrically around the Au nanocrystal core. The theoretical calculations show that the two types of coupling behaviors, the plasmonic splitting and energy transfer, observed in experiments can be unified. The different coupling behaviors are found to be 14094



Article

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determined by the oscillator strength and molecular transition line width. The charge distributions associated with the two types of coupling behaviors have also been revealed by FDTD calculations. The results show that the two peaks in the case of the plasmonic splitting originate from the hybridization between the plasmon resonance of the Au core and the molecular absorption of the dye shell. The quenching dip in the case of the plasmonic energy transfer arises from the dissipation of the plasmon energy of the Au core by the dye molecules. We have further investigated the effects of the partial dye coating and the spacing between the dye shell and the Au nanocrystal surface on the resonance coupling behavior. We believe that our results will be greatly useful for further exploring the fundamental interactions between localized plasmons and molecular transitions. They will also help in guiding the design of optical and sensing devices on the basis of plasmonic− molecular resonance coupling.

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ASSOCIATED CONTENT

S Supporting Information *

The real parts of the dielectric functions of the dye shell, additional coupling energy diagrams, comparison of the results between the quasistatic calculations and the FDTD simulations, and dependence of the plasmon shift on the spacer thickness. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge support from Hong Kong RGC (GRF Grant, ref. No.: CUHK403211, Project Code: 2130277 and Special Equipment Grant, ref. No.: SEG_CUHK06).

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REFERENCES

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PlasmonicâMolecular Resonance Coupling: Plasmonic Splitting

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