1. Introduction

Plasmon-enhanced near-field interactions have been intensively studied with versatile metallic nanostructures such as dimers [1–5], core–shells [6–9], colloidal nanocrystals [10], and cavities [11–15]. The plasmon energy has proved promising for use in enhancing the photoluminescence [16], electroluminescence [17], and optoelectronic efficiency of the quantum dots or materials near the metallic nanostructure [18–20]. It has been widely used in solar cells [21–24], catalysis [25–28], and optical sensors [29–32]. However, the optical near-field that is confined within 10 nm requires stringent form factors and spatial arrangement of these nanostructures. It relies on complex and precise nano-fabrication process that has hindered future scale-up commercialization.

To overcome this barrier resulting from the near-field optical effect and to produce large-area plasmonic devices, a fullerene film was utilized as an active spacer to enable long-distance coupling between gold nano-islands and a gold film, as illustrated in Fig. 1(a). Fullerene is a kind of carbon allotrope with delocalized electrons. The unique molecule structure brings many interesting optical characteristics, such as photoluminescence [33, 34], second [35] or high-order [36] harmonic generation, and nonlinear optical response [37, 38]. It can be excited by incident visible light at the plasmonic resonance of the gold nano-islands [39, 40]. The resonant energy can then be propagated further out of the near-field range of the plasmon coupling. Three different configurations are used in this paper to discuss the coupling effect and characteristic of resonance. The sample without gold film in Fig. 1(b) shows localized surface plasmon resonance of the gold nano-islands. The gold film acts as a plasmon mirror producing image charges (Fig. 1(c) and 1(d)) [15, 41–43], which is intended to couple with the upper gold islands. It is thickened to a certain extent in order to effectively shield off the effect of the substrate. Consequently, the image charges become almost complete and identical to the real nano-islands. This process would then provide a large coupling effect. Such a plasmonic resonance could be used in the design of a device display or in a color filter that shows omnidirectional saturated colors.

 

Fig. 1 (a) Schematic diagram of the plasmon fullerene cavity, which is composed of a single layer dispersed gold islands, coupling with the gold substrate through a fullerene film. There are three different configurations discussed in this paper: (b) without gold film, (c) with a thin gold film, and (d) with a thick gold film, which can totally shield off the substrate effect.

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2. Results and discussion

The fullerene powder was purchased from SIGMA-ALDRICH and used e-beam evaporation to deposit the fullerene on substrate. Then, we deposited gold islands on top of the fullerene film. Without applying extra heat on the substrate, the evaporated Au molecules have limited mobility on the substrate and thus aggregate into islands rather than a uniform film [44] (Fig. 2(a)). The thickness of all films is measured by analyzing the side-view images taken with transmission electron microscopy (Fig. 2(b)) and the composition of the films are determined under energy dispersive spectroscopy (Fig. 7 in the Appendix). The size and interval of these gold nano-islands are ~12 and ~43 nm, respectively. From the observation by scanning electron microscopy and atomic force microscopy in Fig. 8 (Appendix), these nano-islands are dispersed on the top of the fullerene film. The deposited C60 molecules are arranged amorphously in the film, as shown in Fig. 2(c). The Raman spectrum (Fig. 9 in the Appendix) confirms that the fullerene molecules remain intact following e-beam evaporation. The central peak at 1470 cm⁻¹ and the side peaks at 1425 and 1565 cm⁻¹, which can be clearly observed, indicate that the pristine properties of the molecules are of high symmetry and have weak intermolecular interactions [45].

 

Fig. 2 (a) Formation mechanism of gold islands on top of fullerene film. (b) Scanning transmission electron microscopy image in a dark field. (c) Transmission electron microscopy image of fullerene.

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The coupling effect and resonant characteristics of the configurations shown in Fig. 1 were measured on a UV–Vis–NIR spectrometer. The characteristics of these configurations were shown to be different from the plasmonic films without nano-islands, which are discussed in Appendix V. The reflection spectra shown in Fig. 3(a)–3(c), correspond to three configurations of the nano-islands: AuI/C60/Si, AuI/C60/AuTF/Si, and AuI/C60/Au, where AuI, C60, AuTF, and Au represent the island-like gold film, fullerene film, thin gold film of 15 nm in thickness, and thick gold film, respectively. The fullerene thickness we used ranged from 28 to 84 nm in order to investigate the electromagnetic field coupling distance between the upper and lower gold films. In Fig. 3(a), the structure of AuI/C60/Si shows the broadest bandwidth in the visible regime. Localized surface plasmons are excited in these gold nano-islands but are suppressed by the fullerene films. The interference and absorption resulting from the fullerene films dominate the profiles of the spectra, and these gold islands only dissipate the light energy. One more continuous gold film was deposited between the fullerene layer and the silicon substrate in order to build the structure of AuI/C60/AuTF/Si; the effect of surface plasmon resonance becomes prominent in comparison with the previous structures. The gold films hold promising applicability to the excitation of surface plasmons by the evanescent fields [46]. They are intended to interact with the optical near-field around the gold islands to yield plasmonic coupling systems. Compared with the spectral curves in Fig. 3(a), those in Fig. 3(b) exhibit more obvious peaks and dips, along with narrower bandwidths.

 

Fig. 3 (a) Reflection spectra of the structure with a single layer of gold nano-islands and fullerene film on a silicon substrate. The thickness of fullerene ranges from 28 to 84 nm. (b & c) Structures with another 15 nm (b) and 100 nm (c) gold film, respectively, between the fullerene film and silicon substrate. (d) Resonant wavelength shifting corresponding to different incident light angles. Black, blue, and green traces are results for the C60/AuTF/Si, AuI/C60/AuTF/Si, and AuI/C60/Au structures, respectively. The thickness of the fullerene films is 56 nm.

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In order to shield off the influence of the substrate entirely, the thickness of the gold film is increased to 100 nm to construct the AuI/C60/Au configuration. The effect of the plasmonic mirror strengthened with the increase in thickness of the gold film, such that the thick gold film produces a completely imaginary structure that behaves identically to the real nano-islands. The completely plasmonic mirror effect results in a strong interaction between the real and imaginary structures. Therefore, the AuI/C60/Au configurations possess an optical filtering effect (e.g., deeper dip and narrower bandwidth in the spectra of Fig. 3(c)) that is more obvious than that of configurations with the AuI/C60/AuTF/Si form. The structure with a thick gold film (AuI/C60/Au configuration) is particularly a plasmon fullerene cavity. Plasmon fullerene cavities display the property of hybridization-mode resonance [47–50] for which the curves in the spectra ascend to a peak and then rapidly descend to a dip. Almost all resonant energy is trapped in the plasmonic structures at the resonant wavelength; the wavelength can be tuned by the thickness of the fullerene film, since the wavelength red shifts as the fullerene thickness increases. We note that the gold nano-islands, fullerene, and gold film are considered a coupling system. The dominant effect is the interaction between the gold islands and gold film, which are connected by the fullerene spacer. It is not enough to interpret the results via optical interference considering the permittivity of the materials and phase shifts (Fig. 13 in the Appendix).

The omnidirectional properties of three different structures, C60/AuTF/Si (black diamonds), AuI/C60/AuTF/Si (blue square), and plasmon fullerene cavity (green triangle), are shown in Fig. 3(d). The reflection spectra obtained with different incident angles are shown in Fig. 14 of the Appendix. For the C60/AuTF/Si structure, which lacks gold islands, the resonant wavelength is shifted to a maximum of 8.67% by tilting the incident angle from 15° to 45°, and the interference is destroyed when the incident angle is made larger than 45°. However, the resonant wavelength shifts for the structure with gold islands decrease to below 5% at 60° incident angle and are independent of the thickness of the underlying gold film. The whole profile begins to be significantly distorted until the incident angle is varied up to 75°. Comparison of the two structures with gold islands shows that the AuI/C60/AuTF/Si structures possesses one more interface between the gold thin film and silicon substrate yielding plasmon resonance. Therefore, AuI/C60/AuTF/Si performs slightly better than the cavities do in terms of omnidirectional performance. Despite slightly more spectrum shifting, the plasmon fullerene cavity for every incident angle exhibits much higher contrast and narrower bandwidth than the other structures do. The photographs shown in Fig. 6 are captured at normal and oblique directions of our samples of three different structures; the colors of the samples remain unchanged as the tilt angle of observation becomes more than 75°.

The two curves in Fig. 4(a) show the resonant wavelengths corresponding to the peak and dip reflection amounts of the plasmon fullerene cavity in Fig. 3(c). Note that the unapparent peaks are extracted by the assistance of the polynomial curve-fitting at its local change. We found that these curves are distinct from those of the plasmonic film without nano-islands. For the plasmonic film, the wavelengths corresponding to either a peak or dip reflection are both linearly dependent on the thickness of the fullerene spacer, as shown in Fig. 11(b). For the plasmon fullerene cavity, the wavelength of the peak is also proportional to the fullerene thickness, but the relation between the wavelength of the dip and the fullerene thickness is evidently nonlinear. These relations are attributed to the planar mode (peak) and couple mode (dip) of plasmon resonance. The plasmonic phase shift caused by the evanescent fields at the interface of the gold films and the optical path in the fullerene film contribute to the planar mode, the same as for the plasmonic film. The theoretical results for the planar mode must be linear (Fig. 12 in the Appendix). The couple mode is caused by the long-distance coupling effect between the gold islands and the gold film, which is mediated by the fullerene layer. Fullerene propagates the plasmons produced by the nano-islands through a long distance in order for them to couple with the plasmons of the imaginary nano-islands. Under the influence of the planar and couple modes, the spectra of the plasmonic cavity show a hybridized resonance. The particular spectra of the plasmon fullerene cavity are caused by the continuum state (planar mode) and discrete state (couple mode). The asymmetric profiles in the spectra lead to the considerably bright and saturated color of the samples.

 

Fig. 4 (a) Constructive and destructive wavelengths corresponding to the different thicknesses of C60 films of the plasmon fullerene cavity. (b & c) The displayed spectra were obtained by spectroscopic ellipsometry, Ψ and Δ spectra, respectively. (d) Resonant wavelengths corresponding to different thicknesses of the fullerene films. Red squares are the experimental results obtained by spectroscopic ellipsometry. The dotted line shows the fitting result for the circuit model. The cutoff thickness is 92 nm.

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The plasmonic near-field in many studies exhibits coupling effects at a very narrow gap, and the spacers used in these studies are much thinner than our fullerene films, e.g., a monolayer of amine-terminated alkane thiols [11, 12] or few layers of two-dimension materials [13]. The narrow gap makes the plasmon fields merging together and produces resonance. For the fullerene, the π-bonding electrons between carbon atoms are delocalized over the whole of the molecules because of the fullerene’s particular molecular structure, and the external stimulus can easily interact with or propagate through the C60 molecules. Therefore, the plasmonic near-field produced by the gold islands on the top surface penetrates and extends through a long distance (up to tens of nanometers), eventually coupling with the lower gold film.

Besides this, the shifting of the resonant wavelength via tuning of the spacer thickness is another significant difference. These resonant phenomena can be modeled as the resonance of an RLC electric circuit. This model is a time-harmonic, quasistatic electric approach to approximate the electric field in the vicinity of the sphere, which is developed by Engheta’s [51], Yang’s [52], and Baumberg’s [42] groups. For the conventional plasmon cavity, the dominant shifting effect is caused by the variation of the capacitance for the ultrathin spacer, which decreases with increasing thickness, resulting in blue shifting of the resonance. On the contrary, our experiments reveal a red-shifting trend. In our configurations, the fullerene films can be considered as a kinetic inductor ($L_{C60}$) and a resistor ($R_{C60}$) in series because of the delocalized π-bonding of the fullerene. The impedance ($Z_{tot}$) could be expressed as:

We assumed that the inductance and resistance of fullerene are both linear in relation to its thickness in our circuit model. The resonant wavelength (λs) can be approximated as

Figure 5 exhibits the simulation results of the fullerene plasmon cavity by finite element method (FEM). We substitute the refractive indices of the fullerene film measured by ellipsometry (Fig. 10) and the gold film from the measurement of Lemarchand’s group [53]. The black dashed line in Fig. 5(a) is the simulated spectrum of the structure with 56-nm thick fullerene film. This simulation has a large difference from our experimental spectrum (yellow line in Fig. 3(c)) because the fullerene-gold interaction is not considered. Due to the delocalized electrons in the fullerene film, the Lorentz-Drude model [54] is adopted to modify the permittivity of the fullerene film. The effective permittivity,${\overline{\epsilon }}_{C60}$, that describes the interaction of fullerene and gold for propagating plasmons is, therefore,

 

Fig. 5 Simulation of the plasmon fullerene cavity by finite element method. (a) Reflection spectra of original ($f=0$) and modified ($f=0.14$) fullerene film in cavity. (b)(c) Evanescent field of the cavity structure with the original and modified fullerene at the resonant wavelength

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For the simulation without considering the interaction, the field is confined at the interface between the gold nanoparticle and the fullerene film. However, the evanescent field is extended by the modified fullerene films, and this property agrees with the analysis of the circuit model. Both of them prove that the fullerene layer plays a critical role in the plasmonic cavity and plasmonic inductor, connecting the gold nano-islands with the gold film even when the separation distance is higher than the optical near-field. Therefore, the fullerene retains characteristics of both planar and couple modes in the cavity, resulting in hybridized resonance and providing a simpler route for fabricating and controlling the plasmonic cavity. Sample photographs taken from two different angles are shown in Fig. 6. The colors, which were caused by the asymmetric profiles of their spectra, are omnidirectional, bright, and saturated. The rapid change from the highest reflection to the lowest in the visible range contributes to the high color contrast of these devices.

 

Fig. 6 Wide variety of colors obtained by depositing gold-fullerene nanostructure on silicon wafers. The arrangement from the top to bottom follows the thickness of gold film of 0, 15, and 100 nm, and the arrangement from the right to left corresponds to the different thickness of fullerene film. (a) Top View. (b) Oblique view.

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3. Conclusions

In this study, we successfully used electron beam evaporation, which is a low-temperature and large-area process, to fabricate plasmonic films and cavities composed of a layer of dispersed gold nano-islands on top of a fullerene film stack on top of a gold film. The plasmon fullerene cavities showed high contrast of optical filtration due to their hybridized resonance. The spectra are asymmetric and show the plasmonic planar and couple modes simultaneously. The fullerene films exhibited bright colors in the plasmonic design used here. The circuit model and the simulations of finite element method were utilized to prove that the delocalized electrons in the fullerene layer result in the behavior of the C60 molecules as plasmonic inductors, coupling the gold nano-islands and the gold film together in the cavity even though the islands and film are separated by a range of greater than the optical near-field. The reflection spectra are insensitive to the angle of the incident light. We observed only a 5% shift of the resonant wavelength when the viewing angle reached 60°. With these advantages, fullerene films have potential use in many optical applications, such as reflectors, color filters, and optical sensors for detecting a spectrum shift or for directly responding with a visible color change.

Appendix

I. Energy dispersive spectroscopy (EDS)

The energy dispersive spectroscopy, provided in TEM, confirms the compositions of our structure. Fig. 7 shows the EDS spectra of gold nano-island and fullerene film, as marked by the red circle in each inset, respectively. It indicates that the gold nano-islands are dispersed on the top of the fullerene film.

 

Fig. 7 Energy dispersive spectroscopy, provided in TEM, shows the composition in our configuration. (a) gold nano-islands (b) fullerene film.

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II. Scanning electron microscopy and atomic force microscopy

The gold nano-islands are dispersed on the top of the fullerene film. Scanning electron microscopy (SEM) and atomic force microscopy (AFM) provide the observed top view. The averaged size and intervals of these gold nano-islands are 12 nm and 37 nm, respectively. The measurement is close to the results of TEM measurement, 12 nm and ~43 nm. The AFM profile, Fig. 8(b), indicates that the height of the nano-islands is 10 nm, which is also consistent with the TEM result.

 

Fig. 8 The measurement of gold nano-islands from the top view. (a) Image taken scanning electron microscopy (SEM). (b) Image taken with atomic forece microscopy (AFM)

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III. Raman spectroscopy

The Raman spectrum excited by green light (532 nm) confirms that the fullerene films remain intact after the e-beam evaporation, shown in Fig. 9. The peak at 1470 cm⁻¹ and those on both sides (1425 and 1565 cm⁻¹) are evident, that is, the molecules have their pristine properties of high symmetry and weak intermolecular interactions. This result is consistent with our observation in the TEM image.

 

Fig. 9 Raman shift spectrum of the fullerene film on gold shows the quality of fullerene deposited by electron-beam evaporation. The main peak is at 1470 cm⁻¹.

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IV. Refractive index of fullerene

For the measurement of refractive index of fullerene layer, we deposited the fullerene film on the silicon substrate and measured with spectroscopic ellipsometry. We fit the data by the B-spline curve to get the fullerene’s refractive index, as shown in Fig. 10.

 

Fig. 10 Real and imaginary of refractive indices of fullerene films measured by the variable angle spectroscopic ellipsometry.

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V. Planar mode of plasmon resonance

Figure 11(a) shows the reflection spectra of plasmonic fullerene films with different thicknesses on the silicon substrate, which are recorded by a UV–Vis–NIR spectrometer. The dotted lines are specified as spectra of the bare silicon substrate and that of the film with a 40 nm thick fullerene film on the top surface (C60/Si film). The reflection spectrum of the C60/Si film mainly depended on the absorption of the materials, and optical interference was absent. Optical interference occurs when the spacer thickness is larger than a quarter of the ratio of the wavelength of incident light to the refractive index (λ/4n). However, we observed optical interference when the sample contained a 15 nm thick gold film (AuTF) sandwiched between the fullerene layer and the silicon substrate. In this case, the interference dominates the spectrum profile even though the fullerene thickness is still less than λ/4n. The structure of the C60/AuTF/Si film is called a plasmonic fullerene film; its spectrum is shown by solid lines in blue, green, yellow, and black in Fig. 11(a). These solid lines correspond to fullerene thicknesses of 25, 40, 55, and 80 nm, respectively. Comparison of both structures with a 40 nm thick fullerene film, namely, the C60/Si and plasmonic fullerene film, shows that the reflection intensity of the plasmonic fullerene film is almost suppressed at short wavelengths (400–550 nm) and approaches zero at 507 nm. However, the reflection intensity also increases with the wavelength and even exceeds the intensity of the pure silicon substrate in the long-wavelength region. These effects could be attributed to the surface plasmon resonance that was excited by the gold thin film. The other solid lines (blue, yellow, and black) show the spectra of the other plasmonic fullerene films with different fullerene thicknesses (25, 55, and 80 nm, respectively). The phenomenon of interference can be clearly observed, except for the 25 nm thick sample. The wavelengths corresponding to the peak and dip in Fig. 11(a) are displayed in Fig. 11(b). The relation between the wavelength and fullerene thickness is linear. This kind of plasmon resonance is called a plasmonic planar mode, which is caused by the combination of the plasmonic phase shift at the interface and the optical path in the fullerene film.

 

Fig. 11 (a) Two dotted lines are the spectra of the silicon and the fullerene films on the silicon substrate. Solid lines are the results for the fullerene plasmonic films; black, red, blue, and green lines correspond to the films with about 25, 40, 55, and 80 nm thicknesses, respectively, deposited on the 15 nm Au films. (b) Resonant wavelengths corresponding to the different C60 thick films.

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VI. Theory of planar mode

The plasmonic planar mode is caused by the plasmonic phase shift at the metal–dielectric interface and its optical path. A free-standing membrane composed of an ideal dielectric–metal structure in the air was derived. The refractive index of the dielectric–metal is constant and real (n_d), and the index of the metal (iν_m) could be described by the simplified Drude model. The equation that was derived is shown as below.

(A1)$$d=\frac{\lambda }{2\pi n_d}\left(\mu \pi +{\tan }^{-1}\left(\frac{n_1\left({\nu }_m{}^2+1\right)}{{\nu }_m\left(n_1{}^2-1\right)}\tanh \left({\eta }_m\right)\right)\right)$$

where ${\eta }_m=2\pi {\nu }_m{d}_m/\lambda$, d_m is the thickness of the metal, λ is the wavelength of incident light, and μ is the modal number. If the modal number is an integer (μ = 0, 1, 2, etc.), then the metal–dielectric film shows almost zero reflection. On the other hand, if the modal number is a half-integer (μ = 1/2, 3/2, 5/2, etc.), then the film shows a maximum reflection. These modal values respectively correspond to the dip and peak in the spectrum of plasmonic planar mode. Figure 12 shows the results for the dielectric–metal structure at its different modal numbers, which was composed of the ideal Au and C60 films with the real part of the refractive index ($n_d=2.25$). The solid and dotted lines are approximately linear in the visible-light region.

 

Fig. 12 Relationship between the spacer thickness and resonant wavelength of the planar mode that was estimated from Eq. (A1).

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VII. Interference properties of the plasmonic fullerene cavity

The spectra in Fig. 13 show the contribution of the plasmonic phase shift at the metal–dielectric interface and its optical path in the plasmonic fullerene cavities. We can see that the curved line of the spectra is different from our experimental spectra of plasmonic fullerene cavities, shown in Fig. 3(c). This difference is especially noticeable when considering fullerene thicknesses from 42 to 70 nm, for which the coupling strength is quite high. The coupling effect assisted by C60 molecules acting as a plasmonic inductor should be considered. The optical near-field produced by the island-like gold on the top surface penetrate and extend through a long distance (up to tens of nanometers) in order to couple with the lower gold film. Therefore, the gold nano-islands, fullerene, and gold film are considered as a coupling system. The dominant effect of this system is the interaction between the gold islands and gold film, which are connected by the fullerene spacer. It is not enough to interpret the results via optical interference concerning the permittivity of the materials and phase shifts.

 

Fig. 13 Spectra of plasmonic fullerene cavities, which is caused by the plasmonic phase shift at the metal–dielectric interface and its optical path.

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VIII. Omnidirectional properties

The sample stage in the UV–Vis–NIR spectrometer was rotated to measure the spectra with different incident (viewing) light angles (ranging from 15° to 75°). Figure 14 shows the spectra of the reflection coefficient in relation to the wavelength for the three different structures: C60/AuTF/Si, AuI/C60/AuTF/Si, and the plasmon fullerene cavity, for which the thickness of all fullerene films are 56 nm. Although the interference effect of the C60/AuTF/Si structure is evident, as shown in Fig. 11(a), this feature does not remain when the incident angle is changed. The wavelength of the interference shifts to a maximum of 8.67% when the incident angle varies from 15° to 45°; the effect is almost destroyed when the angle is larger than 60°. However, the gold nano-islands on top of the fullerene in the other structures have a large influence and depress the distortion of this effect until the angle reaches 75°. Comparison of the two structures with gold nano-islands reveals that the structure with a gold thin film has one substantial interface between the gold thin film and the silicon substrate over which to yield plasmon resonance. Therefore, AuI/C60/AuTF/Si structure has slightly better omnidirectional performance than that of the cavities. Apart from this, the coupling effect and the color contrast in the plasmonic cavities are much better for every rotational angle. Overall, the cavities still possess many advantages in many optical applications.

 

Fig. 14 Reflection spectra of the three different structures obtained at incident angles of 15 to 75 degrees, respectively. (a) C60/AuTF/Si structure, (b) AuI/C60/AuTF/Si structure, and (c) plasmon-fullerene cavity, for which the thickness of all fullerene films are about 56 nm.

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IX. Mirror effect

The mirror effect of gold film is proposed by Nordlander’s [41] and Baumberg’s group [15, 42] to study the interaction between metallic nanoparticles and a plate. It is useful to predict the resonant wavelength. However, for the real cavity structure, the incident light travels back and forth several times in the cavity. Therefore, the amplitude of reflection spectrum would not be identical to the imaginary dimer structure. We simulate the reflection of the dimer and cavity structures, as shown in Fig. 15. The both spectra also have a peak and dip. In comparison with the experimental and analysis in our main text, the first peak at 450-nm wavelength is caused by planar mode, and the other peak at 590-nm wavelength corresponds to the long-distance plasmon resonance. The resonant wavelengths of the dimer and cavity structures are quite close as our above description.

 

Fig. 15 Simulation of reflection of the cavity (black) and dimer (red) structure.

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X. Deviation resulting from neglecting the capacitance of the spacer

In our analysis of the circuit model, we neglected the capacitance effect of the fullerene films because of their large thickness (ranging from 28 to 84 nm), which are over the range of near-field optics. In this section, the deviation resulting from neglecting this effect is estimated. The Taylor expansion was used to expand the expression of the gap capacitance, which was proposed by Baumberg’s group [42], because the thickness (d) is large.

(A2)$$C_g=\frac{\pi {\epsilon }_0{\left(n_g\right)}^{\chi }{r}^2{\theta }_{\max }^2}{d}$$

The parameters ${\theta }_{max}~\pi /5$ and $\chi ~1.14$ are obtained with respect to the angle of the contributing area and a correction parameter of the refractive index (n_g). Comparison of the impedance of this gap capacitance (Z_C) to that of the serial inductance and resistance (Z_LR) was achieved using

(A3)$$\frac{Z_C}{Z_{LR}}=\frac{\lambda \left|2+{\epsilon }_m\right|}{2{\left(n_g\right)}^{\chi }r{A}_L{\theta }_{\max }^2}{\left(\frac{4}{d_{cut}}+{\left(\frac{A_L}{\lambda }\right)}^2\right)}^{-\frac{1}{2}}$$

where $d_{cutoff}=92 nm$ and $A_L=15\sqrt{nm}$. They were estimated from our results in Fig. 4(d) of our main text. The resonant wavelength (λ = 587 nm) of the fullerene plasmonic cavity with a 56 nm thick fullerene film was substituted into Eq. (A2), and this ratio (A3) was this estimated to be 72.5. Hence, the impedance caused by the gap capacitance is much larger than the impedance of the fullerene film. The deviation due to neglect of the capacitance term is only 1.4%. Therefore, the gap capacitance in the circuit model of the plasmon fullerene cavities was justifiably neglected.

XI. Deviation of neglecting the material dispersion in circuit model

The material dispersion should be included in our analysis. We substitute the Drude model into the total impedance function, but the function would become complicated to get the minimum value. Therefore, we analyze the structure with 56 nm thick fullerene film, whose coupling effect is most evident. The resistance could be neglected, and the resonance frequency is corresponding to the zero point of impedance. The resonant frequency is shown as

(A4)$${\omega }_s=\sqrt{\frac{1}{3}\left({\omega }_p^2+{\left(L_{C60}\pi r{\epsilon }_0\right)}^{-1}\right)}$$

The resonant wavelength is 553 nm. Comparison with the experimental result (586 nm) gives the error of only 5.6%. Therefore, the coefficients of ${\text{A}}_{\text{L}}$ and ${\text{d}}_{\text{cutoff}}$ can be assumed constant.

Funding

Ministry of Science and Technology, Taiwan (MOST 106-2221-E-002-132-MY2)

Acknowledgements

We thank “National Taiwan University Nano-Electro-Mechanical-Systems (NEMS) Research Center” for the experimental support.

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