Fano resonances in complex plasmonic super-nanoclusters: The effect of environmental modifications on the LSPR sensitivity

Abstract

In this study, gold nanodisk clusters in heptamer orientations as clusters were used to design a super-heptamer consisting of one central and six peripheral heptamers. We examined the position and movement of the plasmon and Fano resonances by sketching the spectral response of the superstructure for various nanodisk dimensions. The quality of the interference between the superradiant and subradiant plasmon resonance modes of the nanodisk clusters was found to depend strongly on the structural configuration and the refractive index of the environmental medium. We replaced the central heptamer with a nanodisk and probed the position of the Fano resonance by geometrically altering the nanodisk structure. Finally, the effect of the dielectric environment on the plasmon response of both of the studied structures was examined numerically and theoretically. The localized surface plasmon resonance sensitivity of the finite plasmonic structures to the presence of liquid substances was investigated and shown by plotting the linear figure of merit. The finite-difference time-domain method was used as a numerical tool to investigate the plasmon response of the structure.

Graphical abstract

Keywords

gold nanodisk / spectral response / Fano resonance / localized surface plasmon resonance (LSPR) / figure of merit (FoM)

1 Introduction

Localized surface plasmon resonances (LSPRs) in nanoscale noble metal structures have been broadly investigated in most recent publications on the topic [1–5]. The plasmonic resonances can be spectrally tuned by controlling the structural and compositional properties of the metallic configurations and embedded medium [6–10]. Recent works have extensively studied mostly simple and composite metallic nanoclusters, such as dimers [11–14], trimers [15–17], quadrumers [18], heptamers [19–22], tetramers [23], and oligomers [24], where the nanoclusters are commonly presented in two- and three-dimensional regimes to exploit the manipulation of novel blueprints. Each of the nanocluster types above exhibits particular unique collective plasmon and Fano resonance modes that arise from constructive interaction and coupling between the plasmon modes of adjacent metallic nanoparticles inside the cluster aggregate. Collective and coherent plasmon resonance modes can be excited at different optical powers (in eV) that depend strongly on the corresponding plasmon resonance fluctuations in individual nanoparticles. These close and intense interactions of plasmon modes can be analyzed using plasmon hybridization theory [25–28]. Using this theory, we can characterize the multicomponent plasmon modes in complex nanostructures and nanoclusters. For instance, Prodan et al. [25] and Fan et al. [20] proved that a plasmonic heptamer in a symmetric molecular (benzene) regime can be tailored to support strong magnetic plasmon resonance and Fano resonance originating from the constructive interference of hybridized bright (superradiant) and dark (subradiant) plasmon resonance modes. The spectral response of these particle clusters depends strongly on the coherence of the interfering resonance modes; consequently, minor derangements differences in the physical and chemical properties of clusters and the surrounding medium, such as the shape of the utilized nanoparticles, symmetry cancellation, and substance modifications, directly and dramatically affect the plasmon response of the proposed configuration. Spheres [30], disks [31], shells [32], pyramids [33], core-shells [34], and ellipsoids [35] have been employed extensively as subwavelength nanoparticles in designing various orientations of sef-assembled clusters and associated particle networks to support plasmon and Fano resonances efficiently. On the other hand, remarkable efforts have been made recently to develop the concept of Fano resonance, and it is shown that Fano resonance can be employed to design practical and applicable plasmonic Fano switches [36], nanoantennas [37], LSPR sensors [38], and (de)multiplexers [39].

In this work, we examine the plasmonic properties and spectral response of a super-heptamer composed of one central and six identical peripheral heptamers that are separated by an identical gap of D_{7h}. The distances of the nanoparticles in a cluster from each other and from those in each of the adjacent heptamers are equal. The design of the proposed heptamers is based on gold nanodisks with experimentally calculated Johnson–Christy constants [40, 41] that are situated 12 nm (D_{7h} = 12 nm) from nearby particles. This work also describes the effect of the medium material and the sizes of the nanoparticles on the scattering spectra and plasmon response, especially for the LSPR sensing approaches. It is shown that the examined heptamer assembly is highly sensitive to chemical and structural alterations that directly influence the Fano resonance wavelength position. Therefore, we measured the effect of controlled symmetry cancellation in the superstructure by replacing the central heptamer with a large nanodisk. Additionally, the effect of modifications in the medium material on the scattering intensity was evaluated numerically for both of the proposed nanostructures. The Fano resonance shift and minimum depth were compared with those of other analogous nanostructures, and the corresponding figure of merit (FoM) for the LSPR response was calculated and demonstrated using a diagram. The proposed superstructures open new paths to the design of enhanced high-sensitivity devices such as biosensors, surface-enhanced Raman spectroscopy (SERS) devices, and efficient Fano switches. The finite-difference time-domain (FDTD) method [42, 43] was considered as a numerical model to extract and evaluate the optical properties of the examined structures.

2 Results and discussion

Figure 1(a) shows a three-dimensional schematic diagram of the proposed configuration based on gold nanodisk heptamers, the orientation of which resembles a super-heptamer. Note that two adjacent nanoparticles supply strong resonance coupling between nearby clusters within the structure. It is well known that because of the inherent symmetry of heptamer structures, the frequency of coupled plasmon modes for two adjacent particles in a symmetric regime can be written as [34]

\begin{array}{}\text{(1)}& {\omega }_l^2=\frac{{\omega }_B^2}{2}\left(1-{\displaystyle \frac{1}{2l+1}}\sqrt{1+4l(l+1)r^{2l+1}}\right),\end{array}

where l is the energy level corresponding to a bonding mode, and r is the radius of the gold nanodisk. Using an electric dipole source located to the left of the super-heptamer, we excited surface plasmon resonances (SPRs) through the arrays of nanoparticles. In terms of the Fano resonance, two fundamental modes are involved: interference of the superradiant mode (bonding bright mode), which corresponds to the in-phase oscillations of the dipolar plasmons of all the nanoparticles, and on the other hand, subradiant (antibonding dark mode) modes that are related to the plasmon dipolar moment of the central components (here, the central heptamer), which oscillates in the direction opposite to the nearby particles’ moments [29]. Here, we used a heptamer of nanodisks for each of the central and peripheral particles. It is well understood that in the nonretarded limit, the subradiant mode cannot be coupled to the superradiant mode efficiently, and on the other side, in the retarded limit, an interaction between the dark and bright modes occurs that contains a Fano resonance in the bright continuum at the energy level of the bright mode [29, 44]. Employing the FDTD method as a numerical tool, we demonstrated the effect of changes in the nanodisk size on the scattering cross-section diagram for the proposed super-heptamer under illumination by an incident dipole source. Gold particles are deposited on a glass substrate (default substrate) with a permittivity of \epsilon\sim 2.1, and the gap sizes between all of the nanoparticles in the seven heptamers is set to 12 nm; this distance will remain fixed during geometrical alterations in all of the other regimes discussed later. To show the effect of geometrical modifications on the Fano resonance behavior, we increased the radii of all of the nanodisks (central and peripheral) from 55 nm to 90 nm simultaneously, while the distance between them remained unchanged. Figure 1(b) demonstrates the scattering cross-section transition from the quasi-static limit to the completely retarded limit, which affects the Fano resonance minimum dramatically. This figure shows the spectral response of the smallest super-heptamer (nanodisks with radii of 55 nm); we detected a plasmon resonance extreme representing superradiant bonding at λ \sim 1045 nm and a Fano minimum mode at λ \sim 1190 nm. When the radii of the nanodisks was increased to 75 nm, a Fano minimum appeared at λ \sim 1280 nm, which shows a strong red-shift of the subradiant modes compared to the superradiant ones because of the existence of quadrupole and higher-order poles (multipoles) in the subradiant modes. As we expected, increasing the size of the heptamer arrays directly enhances the intensity of the interacting plasmon resonance modes, and this regime directly causes dramatic red-shifts in the position of the subradiant dark mode compared to that of the superradiant bright mode. For the heptamers composed of nanodisks with radii of 90 nm, the Fano resonance minimum appears at λ \sim 1325 nm; it is narrower than those in the previous regimes and is completely red-shifted to the edge of the NIR region. However, the Fano depth is reduced, and this conditionis not favorable. This behavior is attributed to the high ratio of damping or internal absorption of the incident electromagnetic field by Au nanodisks with large radii. Accordingly, finding suitable nanoparticle dimensions on the basis of their spectral response can help us to design an efficient subwavelength structure. Thus, in the remainder of the paper, we will consider radii smaller than 90 nm (e.g., 85 nm) to prevent an undesirable amount of light absorption and to provide deep, narrow Fano resonance minima that exhibit the desired red-shift. The inset snapshots in Fig. 1(b) (i–iii) demonstrate two-dimensional (x-y) simulation images of robust SPR excitation and coupling between clusters and particles. A comparison with a simple nanoparticle heptamer cluster reveals that in the proposed complex heptamer-based structure, the quality of the Fano minimum has switched to strong Fano resonance from the Fano-like regime. This capability is attributed to constructive and weak interference of the sub- and superradiant dipolar plasmon resonance mode extremes for the super-heptamer.

Next, we studied the results of modifications in the shape of the super-heptamer components on the spectral response of this configuration. Figure 2(a) illustrates the modified version of the structure in which the central heptamer was replaced by a large nanodisk (360 nm in radius), and the dimensions of the peripheral heptamers, which are composed of nanodisks with radii of 85 nm, remain unchanged. This geometrical alteration will help us to provide the required asymmetry for Fano resonance formation along the scattering spectra simply. Figure 2(b) shows a two-dimensional (x-y) snapshot of SPR excitation and coupling between nearby particles and heptamers. Because of the outstanding and inherent symmetry of the structure, the position of the employed particles, the angle of the incident light, and the configuration rotation do not significantly affect the scattering efficiency, and these results are depicted in Fig. 2(c) for incident light with different angles and polarizations (φ) of 0^∘, 45^∘, or 90^∘. Owing to this initial symmetry in the structural components of the large heptamer, therefore, we investigated the optical response of the structure to different polarizations as a major parameter merely to draw the scattering efficiency profile numerically. In this regime, the position of the Fano resonance is blue-shifted (λ \sim 1370 nm); the polarization direction does not significantly affect the Fano resonance shifting and quality, and causes minor variations in the amplitude of the scattering spectra. The detected minima along the diagram indicate the subradiant dark mode. Considering the position of the superradiant bright mode (λ \sim 1110 nm), we would be able to calculate and draw the charge density distribution within and between the Au nanodisks. Accordingly, because of the constructive interference of radiated plasmon resonance modes that originate in the symmetry of the proposed superstructure, the charge density distribution directions in all of the nanoparticles are the same; this situation resembles the in-phase mode. The charge density distribution plot for the super-heptamer at the subradiant dark mode (at λ \sim 1415 nm) shows that this mode supports charge oscillations within the structure in different directions (out-of-phase mode) caused by interference of radiated dark and bright plasmon resonance modes [Fig. 2(a)]. To provide a comprehensive study, we modified the geometries of the structure to supply the asymmetry required to enhance the quality of the Fano dip. This situation helps us to examine the optical response of the structure during the transition from the symmetric to the antisymmetric regime.

To this end, we reduced the size of the central nanodisk to break the symmetry of the superstructure while keeping the radii of the disks in the peripheral heptamers fixed at 85 nm. Technically, reducing the size of the central nanodisk disrupts the structure by decreasing the size of the gap between nearby particle units; this affects the performance of the structure dramatically by changing the quality of the Fano resonance and the resonance hybridization strength. Figure 3(a) shows the results of a numerical calculation using the FDTD method that demonstrates the effect of decreasing the central disk radius on the scattering efficiency and the position of the Fano resonance minimum. Obviously, this reduction directly blue-shifts the Fano dip. In this regime, we observed highly pronounced Fano minima due to the presence of peripheral heptamers, which cancel the dipole moment of the nanoparticle clusters (bright mode), while the central nanodisk provides the subradiant dark mode. In the proposed structure, the antibonding mode remains subradiant, and a robust Fano resonance dip is induced by all of the structural modifications; this dip cannot be observed in analogous structures such as octamers in both homo and hetero regimes. To prove this claim, we reduced the size of the central nanodisk from 340 nm to 200 nm. Changing the structure from the homo-regime to the hetero-regime does not affect the presence of the Faro minimum, but blue-shifts its position and broadens it. In addition, the dipole moment is completely coupled to the incident light because it remains equal to the moments of the surrounding heptamers. To provide a comprehensive investigation, we altered the size of the nanodisks in the peripheral heptamers while keeping the size of the central nanodisk unchanged at 360 nm. Figure 3(b) numerically demonstrates the effect of these variations on the existence and position of the Fano resonance. Subtle increments in the size of the surrounding nanodisks directly red-shift the Fano resonance; further, the curve becomes narrower, and a superradiant bright mode appears with these increments. In this case, for nanodisks with radii of R = 105 nm, the Fano dip appeared at λ \sim 1345 nm. This narrow Fano minimum helps us to provide highly precise and sensitive nanostructures, which allow for a more rigorous evaluation of extremely minor movements of resonances that are induced by modifications in the local dielectric properties that appear in the NIR spectra.

In terms of the practical exploitation of Fano resonance, plasmonic Fano switches, demultiplexers, and LSPR sensors [45-47] based on this aspect of optical physics have been reported. Most previous works have examined the effect of environmental modifications on the spectral response of the simple heptamers, oligomers, octamers, and so on that were discussed in the previous section. It is well understood that to evaluate the efficiency of the LSPR sensing of a finite plasmonic nanostructure, the FoM must be determined and drawn [48, 49]. Sherry et al. [49] verified that the FoM for a given finite plasmonic subwavelength structure can be quantified by calculating the ratio of the plasmon energy deviation (\mathrm{\Delta }E, in eV) to the change in the medium’s refractive index (n) divided by the cross-sectional peak width. In addition, Hao et al. [50] proved that the plasmon resonance energy for the antisymmetric Fano resonances can be determined by finding the midpoint across the energy of the first maximum and minimum through the spectral curve, which provides the energy width.

Next, we numerically plotted the scattering spectra for both of the studied superstructures immersed in the following media: CH₃COCH₃ (acetone), n = 1.351; C₄H₁₀O (butanol), n = 1.399; and BK7 matching liquid (similar to Cargille immersion oil type B, which is measured in the Cargille laboratory), n = 1.516. In all of the simulations of the supercluster, the proposed structures are deposited on a quartz substrate and thoroughly immersed in one of the above liquids. Figure 4(a) shows the scattering cross-section diagram for the superstructure with a central heptamer composed of gold nanodisks that is surrounded by six peripheral heptamers. All the employed gold nanodisks have radii of 85 nm; obviously, increasing the refractive index of the medium directly red-shifts the Fano minimum robustly and provides a deep Fano minimum at λ \sim 1385 nm for the medium with a refractive index of n = 1.516. Figure 4(b) shows the same scattering spectra diagram for a super-heptamer composed of a central nanodisk 360 nm in radius with six peripheral heptamers with the radii of 80nm. The radii of the nanodisks are chosen to provide a desirable Fano resonance minimum (this situation leads to the formation of an isotropic Fano resonance). As we expected, because of the unique shape of the proposed configuration, which was discussed above, the Fano minimum was red-shifted with increasing refractive index of the surrounding medium. This shift in the Fano resonance is remarkably greater than that in the previous regime and provides a deeper and narrower Fano dip at λ \sim 1560 nm. To determine the sensitivity of LSPR sensing for both of these superstructures, we divided the slope of the linear regression by the Fano line width of 0.067 eV (0.061 eV), which yielded FoM values of 13.6 (14.2) [Figs. 4(c) and 4(d), respectively] for the entirely heptamer-based superstructure (central disk superstructure). Compared to the LSPR sensitivity of analogous nanostructures, the LSPR sensitivity of the examined configurations of the proposed super-heptamers is noticeable and highly interesting. These finite super-heptamers yield precise LSPR sensing capability by centering on the Fano resonance position and minimum depth. The proposed clusters of heptamers can be fabricated lithographically with smaller gaps between the ensembles of nanodisks to provide more accuracy in sensing applications. The sensitivity of the proposed nanostructure is clearly superior to that of structures reported in previous works. For instance, Lassiter et al. [12] has shown that an octamer cluster composed of Au nanodisks in symmetric and asymmetric orientations can provide remarkable Fano dips along the scattering spectral profile with a maximum FoM of 5.7. Moreover, Liu et al. [51] has verified that coupled dipole–quadrupole nanoantennas yield an FoM of 3.8. Therefore, the proposed nanostructure offers strong sensitivity for various sensing and SERS applications.

3 Conclusions

In this work, we examined different novel shapes of plasmonic nanoclusters that can be used to design subwavelength configurations for various optical applications from sensing to switching. Gold nanodisk heptamer clusters are the key components of the examined configurations. When a heptamer-based structure consisting of seven heptamers was illuminated by an electric dipole source, pronounced Fano resonances were induced, as shown by the scattering cross-section profile of the structure, and we showed that the position and width of the Fano minimum are highly sensitive to differences in the structure and local medium. Then, we replaced the central heptamer of the superstructure with a large gold nanodisk and studied the effect of this substitution on the coupling strength of the subradiant dark and superradiant bright modes and also the position and quality of the Fano resonance. In this regime, we altered the geometrical sizes of the central and peripheral nanodisks to enhance the Fano resonance depth and performance. In addition, we verified that reducing the size of the central nanodisk blue-shifts the Fano minimum; this situation resembles a symmetry-breaking regime. In contrast, increasing the size of the peripheral nanodisks red-shifts the Fano minimum to the edge of the NIR region because of the tendency to offset the asymmetry. Ultimately, using various dielectric substances with different refractive indices as environmental variables, we probed the LSPR sensitivity for both of the examined superstructures on the basis of the corresponding calculated FoM. We quantified the FoM of the entirely heptamer-based superstructure as 13.6, and that of the superstructure with a central nanodisk instead of a heptamer as 14.2. These results proved that the proposed structures have strong potential for use in designing ultrasensitive LSPR sensing devices and nanostructures with high sensitivity and accuracy.

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