1. Introduction

Surface plasmons polaritons (SPPs) are collective charge oscillations coupled to light that propagate along a metal-dielectric interface. They can be excited on a metal by grating coupling, the momentum mismatch between SPPs and free-space light being bridged by Bragg vectors inherent in the periodic nanostructures [1, 2]. Localized surface plasmon polaritons (LSPPs), on the other hand, are non propagating charge excitations in metal nanoparticles much smaller than the incident wavelength. The resonance wavelength of the LSPPs depends on the size, shape, and dielectric function of the nanoparticle as well as the dielectric environment [3]. The intense, localized electromagnetic fields associated to SPPs and LSPPs can be used to manipulate and enhance light-matter interactions at subwavelength scales [4, 5]. 2D plasmonic crystals [6] revealed as promising plasmonic components for thin-film photovoltaics [7], light emitting devices [8, 9] optical switches [10], label-free sensors [11–13] and negative index metamaterials [14].

The investigation of how LSPPs and SPPs interact proves to be highly interesting, as structures combining both phenomena could offer extreme light enhancement/manipulation properties. A dipole-surface interaction manifested by measuring the shift of the LSPP resonance when randomly arranged silver nanoparticles were placed near a silver film [15]. In such a structure, the SPP excited on the silver film was shown to further enhance the dipole - dipole interaction between individual nanoparticles [16]. Multiple resonance modes were reported in the extinction spectra of a hybrid structure combining a two-dimensional gold nanoparti-cle array and a thin gold film, resulting from the coupling between LSPPs and SSPs [17]. More recently, theoretical/experimental studies have predicted/demonstrated that strong coupling between LSPPs and SPPs occurs when their resonance frequencies are approximately equal [18, 19].

Besides the early elegant experiments of Drexhage [20], it has been shown recently [21–26] that the radiative lifetime of an exciton can be modified by the interaction with plasmons (mainly LSPPs). Notably, we have been able recently to synthesize gold core -silica shell nanoparticles grafted with dye molecules [26]. The control of the thickness of the silica shell allowed us to tune the distance between the metal core and the dye molecules. Assemblies of small number (1 to 7) of these core-shell (CS) particles, considered as multimers, were also produced. We have shown a strong enhancement of the decay rates at the LSPP resonance, dominated by the non-radiative energy tranfer from the active medium to the metal. The decay rates decreased as the detuning between the long wavelength emission and the LSPP resonance increases.

In this paper, we extend these studies by numerically investigating and experimentally demonstrating how the LSPP - SPP interaction of a structure combining a gold core - silica shell (CS) nanoparticle (NP) hexagonal close-packed (hcp) array sandwiched between two gold films can strongly enhance (70 – 100 times), on a broadband range (565 nm to 640 nm), the spontaneous emission rate of quantum emitters (rhodamine isothiocyanate, RITC) grafted in the silica shell of the NP.

2. Results and discussion

2.1. Properties of the metallic nano-structures: UV-visible reflection spectra

For metallic spheres with a diameter smaller than the light wavelength, the LSPP resonances are given by ${\omega }_l={\omega }_p\sqrt{l/[l+(l+1){\epsilon }_D]}$ for each angular momentum l, where ω_p is the bulk metal plasmon frequency and ε_D the dielectric constant of the dielectric medium. The optical spectra of NPs are modified by the presence of other particles in the neighborood [27] or different substrates [16]. On a metallic - dielectric interface, SPPs are bound states since their dispersion relation

We first consider 2D hcp arrays of gold core - silica shell NPs with a core of diameter 60 nm and a shell of radius 40 nm, providing a total diameter D = 140 nm of the CS NP. For the sake of comparison of the optical properties, this 2D array is either deposited on a glass substrate (gl sample) or deposited on a thick gold film (g sample) or sandwiched between a glass substrate and a 30 nm gold curved film (glg sample) or sandwiched between a thick gold film and a 30 nm gold curved film (gg sample). Figure 1(a) shows the reflection spectra of these four combinations simulated by Finite Difference Time Domain (FDTD, see Materials and methods for details). Interestingly, the four spectra exhibit two main resonances at around 510 nm and 650 nm. For the g, glg and gg samples, the high-energy dip is close to and on the long wavelength side with respect to the resonance of the array of spheres in the gl sample. While the high-energy dip is clearly observed for the four samples, the low-energy dip is barely discernible for the gl and glg sample, appears clearly in the case of the g sample and strengthens significantly in the case of the gg sample. The two observed maxima are reminescent of those observed by Freeman et al. [29] for spherical gold particles immobilized on a silanized glass substrate. These authors attributed the first band at 525 nm to surface plasmon localized on individual gold particles (LSPPs) and the second one, shifted to much longer wavelengths (650 nm), to a plasmon resonance of a set of particles resulting in a strong dipole-dipole coupling due to the particles proximity (array plasmon).

 

Fig. 1 Simulated (a) and experimental (b) reflection spectra of a hcp array of CS NPs either sandwiched bewteen a glass substrate and air (gl), a thick gold film and air (g), a glass substrate and a 30 nm gold curved film (glg) or a thick gold film and a 30 nm gold curved film (gg). The considered structures are schematically illustrated in c).

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The case provided by the gg sample is extremely interesting to investigate in details since it appears that sandwiching the array of NPs between two gold films strongly enhance the depth of the low-energy dip with respect to the case where the NP array is surrounded only by a single gold film. For this structure, the evolution of the reflection spectra as a function of the NP shell radius r is shown in Fig. 2(a). The modification of the shell radius induces a modification of the lattice constant a of the NP array and of the distance r between the NP gold cores and the metallic films (the shell acts as a spacer). As best shown in Fig. 2(c), the high-energy dip slightly shifts to lower energies with increasing r. On the contrary, the low-energy dip strongly shifts to higher energies as r is increased from 10 to 30 nm, where the dip wavelength stabilizes while r still increases to reach 50 nm.

 

Fig. 2 Evolution of the reflection spectra of the gg nanostructure as a function of either the shell radius (a) or the core diameter D, increasing from left to right from D = 40 nm to 140 nm by step of 20 nm (b). c) and d) Corresponding resonance wavelengths of the two dips (plasmon resonance modes) observed as a function of the lattice constant of the hcp array. HER (LER) pertains to the High- (Low-) Energy Resonance modes. In d), the (1,0) SPP resonances of the metallic film grating coupled with the metallic spheres is also shown.

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A metallic nanoparticle placed near a metallic substrate will be strongly attracted to it, through the image charges induced in the substrate by its presence [5]. However very usefull in practice, Nordlander et al. have shown how inadequate this simple image model can be in some situations where it is essential to model the surface using the right surface plasmon frequency, in the hybridization picture [30]. Accordingly, hybridization shifts the nanosphere plasmons to higher energy with decreasing nanoparticle separation only if the surface plasmon energy is lower than the nanosphere plasmon energy. Silica coated gold core NPs are known to have a significant quadrupolar resonance mode at around 500 nm for large enough cores [31]. Assuming that such a mode can strongly interact with the gold films surface plasmon could explain the trend shown by the high-energy dip in Figs. 2(a) and 2(c). This assumption is further evidenced by the blue shifting of the high-energy dip observed in Fig. 2(d). Figure 2(b) (Fig. 2(d)) shows the evolution of the reflection spectra (resonance dips) as the gold core diameter is increased from 40 to 60, 80, 100, 120 and 140 nm, from left to right, respectively, while the shell radius is kept constant r = 40 nm. The blue shift of the high-energy dip observed as the core gold diameter is increased simply results from the stronger interaction of this quadrupolar mode (extending more and more in the silica shell as the core radius is increased) with the surface plasmon mode of the film, of lower energy. For a planar wave close to the resonance wavelength λ = 515 nm propagating in the z direction and polarized along x, Fig. 3(a) shows the near-field enhancement maps in the xy equatorial plane for a structure with CS NPs of D = 140 nm total diameter and r = 40 nm shell radius. Besides the dipolar LSPP resonance manifesting in the polarization direction |E_x|², the intensity pattern of the |E_y|² field intensity component clearly exhibits a quadrupolar feature.

 

Fig. 3 Near field intensity patterns in the xy-plane (a) or xz-plane (b, c) for a plane wave either at the resonance wavelength λ = 515 nm of the high-energy dip (a, b) or at the resonance wavelength λ = 636 nm of the low-energy dip (c) propagating along z and polarized along x in the gg structure. Notice the quadripolar feature exhibited by the |E_y|² field intensity component in a. d) Near field intensity patterns (insets) in the xz-plane for the two modes exhibited in the reflection spectrum of a hypothetical gg structure where the surrounding gold layers are both flat.

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The trends shown by the low-energy dip are in contradistinction with the previous case and result from strong dipole-dipole interactions between either the CS NPs themselves (hybridization of dipolar LSPPs leading to array plasmons) or the CS NPS and the gold film (hybridization between dipolar array plasmons and SPPs of the gold film). As such, the coupling strength between these plasmon modes strongly increases as i) the distance between the gold cores and from the gold cores to the film decrease (Figs. 2(a) and 2(c)) and ii) the core diameter increases at shell radius constant (Figs. 2(b) and 2(d)) as a result of the increased field enhancement overlap area. Last but not least, Fig. 2(d) shows an amazingly perfect matching of the low-energy resonances with the (1,0) SPP resonances due to the presence of a periodic array of metallic spheres close to the metallic film, according to Eqs. (1)–(2). As a result of the strong coupling between LSPPs and SPPs, the quality factor of the low-energy resonance for a structure composed of CS NPs with core diameters of 140 nm can be as large as 36.

Figure 3 further exemplifies the variations in the near-field intensity patterns between the high-energy (Fig. 3(b)) and low-energy (Fig. 3(c)) modes. In both cases, a x-polarized planar wave close to the resonance wavelength (λ = 515 nm for the high-energy dip (Fig. 3(b)), λ = 636 nm for the low-energy dip (Fig. 3(c)) is propagating in the z direction. In the xz plane of a gg structure with CS NPs of D = 140 nm total diameter and r = 40 nm shell radius, the field intensity enhancement is clearly one order of magnitude larger for the Low-Energy Resonance (LER) mode (c) than the High-Energy Resonance (HER) mode (b). Indeed, while the HER near-field intensity barely reaches a level of 0.2, which is the order of magnitude of the incident light intensity (Fig. 3(b)), the LER near-field intensity reaches a level of 3, which is thus 10 times larger than the incident light intensity (in Fig. 3(c), the incident light intensity is colored in black). Furthermore, while both the |E_x|² and |E_y|² field intensity components exhibit a strong dipolar feature along x for the low-energy resonance, the |E_y|² field intensity component of the high-energy resonance vanishes in the xz plane, favoring the appearance of a quadrupolar feature in the xy plane (Fig. 3(a)).

It is interesting at this level to differentiate the effect of the surface corrugation in the top gold film of the gg structure on the nature of the 2 modes exhibited as compared to a similar but hypothetical gg structure with bottom and top smooth gold films. Figure 3(d) shows the reflection spectrum of such a structure. Clearly, it exhibits two resonances as well, only slightly blue shifted with respect to the real gg structure (Fig. 1). The insets show the near-field intensity patterns corresponding to the HER and LER modes. Once more, the field intensity enhancement is one order of magnitude larger for the Low-Energy Resonance (LER) mode than for the High-Energy Resonance (HER) mode. The LER intensity pattern clearly exhibits the coupling between adjacent spheres, due to the formation of the array-plasmon. This interaction between adjacent spheres, which was also slightly observed in the real gg structure for the HER intensity pattern, as a result of the metal surface corrugation, is missing in the HER intensity pattern of the hypothetical flat structure.

Having numerically investigated in depth the origin and evolution of the resonance modes of a gg structure, we now turn to the experimental investigation of a particular gg structure, namely the case of a gg structure with CS NPs having a 60 nm gold core diameter and 40 nm silica shell radius sandwiched between a 100 μm gold thick flat film deposited on top of a glass substrate and a 30 nm gold thick curved film deposited on top of the CS NPs. Numerically, the quality factor of the low-energy resonance for this structure is 14.

A TEM picture of the synthesized CS colloids exhibiting a small dispersity in size and shape is shown in Fig. 4(a). The arrangement of these particles in the gg sample is shown in the AFM picture of Fig. 4(b). While the CS particles are not perfectly hexagonally closed packed on the subtrate, the geometry of the overall structure is good enough to observe a very nice matching between the predicted (Fig. 1(a)) and experimentally obtained (Fig. 1(b)) reflection spectra. The positions of the 2 dips exhibited in the simulated and experimental reflection spectra agree very well, with the second dip being broadened and weakened in the experimental case, resulting in a Q factor smaller than predicted. For the sake of comparison, the glg and g structures have also been engineered and optically characterized. Their reflection spectra are shown in Fig. 1(b). As compared to the predictions (Fig. 1(a)), the high energy peak observed in the experimental spectrum of the glg (g) structure is slightly blue (red) shifted. Furthermore, contrarily to the case of the gg structure, the experimental spectra of the glg and g structures do not exhibit the low-energy peak. In all cases, the CS particles are not perfectly hexagonally closed-packed in either the experimental g, glg or gg structure. As a probable consequence, the low energy peak disappears in the spectra of the glg and g structures and is slightly broadened and weakened in the case of the gg structure, pointing to the robustness of this feature in the latter structure.

 

Fig. 4 TEM picture of the active CS NPs (a) and AFM picture of their arrangement in a hcp array in the gg nanostructure.

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2.2. Properties of the active medium: emission spectra of the emitters in the nanostructures

We have measured the decay rate enhancement g_t of nanoemitters embedded in the g, gl, glg and gg nanostructures by performing spectrally and temporally resolved measurements, simultaneously, owing to the use of a streak camera. Figure 5 shows the intensity plots for RITC emitters in the gl (Fig. 5(a)) and gg (Fig. 5(b)) nanostructures. By projecting the intensity on the time axis, one obtains the decay times profiles as a function of wavelength. Figure 5 clearly reveals that the decay profiles are about 6 to 22 times shorter as a function of wavelength for the RITC emitters embedded in the gg (Fig. 5(b)) as compared to the gl structure (Fig. 5(a)). To quantify these observations, we determined the spontaneous emission decay times as a function of wavelength. Firstly, we divided the intensity plots in 20 parts on the wavelength range and built the 20 corresponding decay profiles. Figure 6 shows 3 such decay profiles (taken respectively at λ = 564 nm, 594 nm and 634 nm) for the 4 different types of samples investigated in this study. Secondly, since the profiles clearly exhibited a non exponential behavior, we fitted them with a stretch exponential function I(t,λ) = I₀(λ)exp(−(t/τ_K(λ))^β(λ)), i.e., introducing a relaxation time τ_K (λ) and a stretching parameter 0 < β < = 1 [26]. The decay times (mean relaxation times) were then obtained from the relation $〈\tau (\lambda )〉=\frac{{\tau }_K(\lambda )}{\beta (\lambda )}\mathrm{\Gamma }\left(\frac{1}{\beta (\lambda )}\right)$, where Γ is the gamma function. Finally, we normalized the decay times by dividing them with the lifetime τ₀ = 3 ns of RITC in an ethanol solution [26].

 

Fig. 5 Time and spectrally resolved (experimental) spontaneous emission intensities of rhodamine isothiocyanate (RITC) molecules in the gl (a) and gg (b) nanostructures. Normalized spontaneous emission rates of RITC emitters embedded in the gl, g, glg and gg nanostructures experimentally obtained (c) and comparison between simulated (dash-dot: radiative part, dot: non radiative part and solid blue line: total rate) and experimental (solid balck line) rates for RITC emitters in the gg nanostructure (d).

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Fig. 6 Decay profiles as a function of wavelength for RITC emitters embedded in the gl (a), g (b), glg (c) and gg (d) nanostructures. The solid lines are stretched exponentials fits of the various decay profiles convoluted with the instrumental response function of the setup.

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The normalized spontaneous emission rates (formally defined as the reciprocals of the normalized decay times) $g_t(\lambda )=\frac{{\tau }_0}{\tau (\lambda )}$ for the RITC emitters in all types of samples are shown in Fig. 5(c). In the gl nanostructure, g_t (λ) shows a trend similar to the one oberved for the bare CS NPs dispersed in an ethanol solution [26], with a maximum enhancement at the NP LSPP resonance, followed by a 1/λ decay law as the detuning between the long wavelength emission and the LSPP (high-energy dip in Fig. 1) increases. This trend is modified and the long wavelength decay of g_t (λ) is more and more attenuated as g, glg and gg samples are sequentially considered. In the latter case, the total decay rate enhancement g_t (λ) remarkably reaches a quasi-plateau value of about 90, i.e. the decay rate of the RITC emitters is enhanced by 2 orders of magnitude when embedded in the gg nanostructure as compared to their dispersion in an ethanol solution, on a broadband (essentially flat above 580 nm) range extending from 560 to 640 nm.

Obviously, the total decay rate enhancement g_t (λ) is the sum of a radiative part g_r(λ) and a non-radiative part g_nr(λ), allowing for the energy-transfer from the emitter to the metal. In the case of CS NPs dispersed in an ethanol solution, we have shown, owing to simulations [26], that the non-radiative part was always dominant, with a major contribution located at the LSPP resonance. On the contrary, the radiative part was shown to be slightly red-shifted with respect to this LSPP resonance, in agreement with the existing litterature [32].

In order to determine the non-radiative contribution in our experimentally determined total decay rate enhancements of RITC emitters embedded in the gg nanostructure, we calculated the (normalized) spontaneous emission rate g(λ) in the following way. We placed a broadband point current source polarized along the x direction and 30 nm away from a gold core (position of the emitters in the CS NPs) in the structure. The radiated power P_r(λ) into the far field and the power dissipated in the metal P_nr(λ) were calculated. The radiative g_r(λ) = Pr(λ)/P₀(λ), non-radiative g_nr(λ) = P_nr(λ)/P₀(λ) factors as well their sum, g(λ), were then obtained by normalization with respect to the radiated power P₀(λ) of the same point current source in air.

Figure 5(d) (solid lines) shows the experimental and simulated total enhancement rates as a function of wavelength. The comparison between the experimental and simulated results shows an excellent agreement, with a very slowly decaying function of wavelength prior to reach a quasi-plateau. The contributions of the radiative and non-radiative parts are also shown and the non-radiative decay proves to be dominant, as was the case for CS NPs dispersed in solution [26]. However, in contradistinction with the latter case, both radiative and non-radiative rates of the RITC emitters in the gg sample do extend at a high level through the whole range of wavelengths. Furthermore, the relative contribution of the radiative part in the total rate enhancement slightly increases (g_r ↑ and g_nr ↓) in the long wavelength range, at λ = 630 nm, as a consequence of the array-plasmon resonance (low-energy dip) exhibited by the gg structure (Fig. 1).

3. Conclusion

In summary, we provided in this paper a new engineering approach to investigate the interaction of localized (LSPP) and propagating (SPP) surface plamon polariton resonances. The samples consist in hexagonal close packed arrays of gold core - silica shell NPs sandwiched either between two gold films (gg structure) or in contact with a single gold film (glg and g structures). For the sizes of the CS NPs investigated in this paper, the reflection spectra of the gg samples obtained either numerically or experimentally exhibit two dips. They have been assigned to resonances resulting from hybridization of either the NP LSPPs (high-energy resonance) or the array plasmons (low-energy resonance) with the SPPs of the surrounding gold films. In the case of the glg and g samples, the low-energy dip vanishes in the experimental reflection spectra, probably as a consequence of slight disorder. The robustness of the optical properties exhibited by the gg structure against disorder makes it an ideal candidate for further investigations. The measured and simulated decay rates of the CS NPs arranged in the gg structure exhibit a broadband quasi-constant enhancement as a function of wavelength, i.e. show a trend dissimilar to the results obtained either in the gl structure or in the case of emitters embedded in the same CS NPs simply dispersed in ethanol [26]. Furthermore, the relative contribution of the radiative part in the total rate enhancement of emitters in the gg structure increases (g_r ↑ and g_nr ↓) at the array-plasmon resonance. We believe that the designed gg structure will be of potential interest as a plasmonic nanostructure for efficient charge transfer from excitons to metallic electrodes in Dye Sensitized Solar Cells (DSSCs).

4. Materials and methods

The gold core - silica shell particles (core size 60 ± 5 nm, shell thickness 30 ± 3 nm) were synthesized according to the procedures published by Brown et al. [33] and Graf et al. [34]. An ethoxy-silano rhodamine B [35] was grafted on the silica surface. A second protective silica shell of 10 nm diameter was then grown by dropwise addition of an ethanolic solution of TEOS [36], leading to a CS particle of 140 nm total diameter. The optical cavities were obtained by deposition, owing to the Langmuir-Blodgett technique, [37] of a mono-layer of active mono-disperse CS particles arranged in a hexagonal closed packed (hcp) structure between a bottom glass substrate covered with a 30 nm thick gold layer and a 30 nm thick top gold layer (herein named gg).

Atomic Force Microscopy images were recorded by a commercial Icon AFM (Brucker). A standard silicon cantilever (≈ 40 N/m, 300 Khz) was employed for the tapping AFM mode. TEM observations were performed with a Hitachi H-600 microscope operating at 75 kV. The reflection spectra have been recorded with a UV-vis-NIR CRAIC microspectrophotometer (20/20 PV) used in reflection mode. The spontaneous emission properties of the various samples were recorded with a spectral- and time- resolved setup consisting of a streak camera (HAMA-MATSU Streak Scope C10627) pre-fitted with a spectrograph (Princeton Instruments) with a 150 gr/mm choice of the grating. The excitation light was the frequency doubled output of the λ = 1030 nm wavelength, 10 MHz repetition rate, 300 fs line width pulses delivered by a diode-pumped Ytterbium femtosecond oscillator from Amplitude systems (t-Pulse 200). The beam was collimated to a 3 mW, 5 mm diameter spot to excite the particles in the samples prior to focus the 530 nm long-pass filtered emission intensity on the entrance slit of the spectrograph.

The various experimental situations have been simulated by solving Maxwell equations using the three-dimensional finite-difference time-domain (FDTD method) [38], as implemented in the freely available MEEP software package [39]. The dielectric permittivity of gold was specified by using the Drude-Lorentz model with parameters determined by Vial et al. [40], based on the best fits, following a FDTD approach, to the relative permittivity of gold as tabulated by Johnson and Christy [41]. By Fourier-transforming the response to a short, broadband, spatially extended gaussian pulse in the far field of the passive structures and normalizing with the response in vacuum for the same excitation conditions, a single simulation yielded the reflexion spectra over a wide spectrum of frequencies. Similarly, in order to compute the emission properties g_r(λ) and g_nr(λ) for the active nanostructures, we performed Fourier-transforms of the response to a short, broadband, point dipole (electric current) gaussian pulse polarized along the x-axis. We then normalized this response with the one obtained in vacuum for the same excitation conditions.