Excitation of Multiple Fano Resonances in Plasmonic Clusters with

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Excitation of Multiple Fano Resonances in Plasmonic Clusters with D Point Group Symmetry 2h

Shao-Ding Liu, Yi-Biao Yang, Zhi-Hui Chen, Wen-Jie Wang, Hong-Ming Fei, Ming-Jiang Zhang, and Yun-Cai Wang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp404575v • Publication Date (Web): 11 Jun 2013 Downloaded from http://pubs.acs.org on June 12, 2013

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The Journal of Physical Chemistry

Excitation of Multiple Fano Resonances in Plasmonic Clusters with D2h Point Group Symmetry Shao-Ding Liu,*, †, ‡ Yi-Biao Yang,†, ‡ Zhi-Hui Chen,†, ‡ Wen-Jie Wang,†, ‡ Hong-Ming Fei,†, ‡ Ming-Jiang Zhang†, ‡ and Yun-Cai Wang†, ‡ †

Key Lab of Advanced Transducers and Intelligent Control System of Ministry of Education,

Taiyuan University of Technology, Taiyuan 030024, P. R. China, and ‡Department of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, P. R. China *Address correspondence to [email protected] ABSTRACT Fano resonances in plasmonic nanostructures exhibit sharp resonance and strong light confinement. These properties are very useful for sensing applications, which rely on plasmon line shape engineering. Fano resonances in plasmonic clusters depend on structure symmetry, and this study provides a general understanding of Fano resonances in clusters with D2h symmetry. We show that because of the excitation of B3u and B2u dark subradiant modes, four kinds of Fano resonances appear in the spectra for hexamers with D2h symmetry. When a central particle is introduced to form a heptamer, it is shown that aside from influence on the resonant behaviors or appearance of an additional Fano resonance for a specific polarization, several hybridized dark subradiant modes are excited for both polarizations, and up to eight kinds of Fano resonances appear in the spectra. Plasmonic clusters with D2h symmetry are suitable for plasmon line shaping, and it is expected that these structures are useful for multi-wavelength sensing applications. This study also reveals that cluster symmetry engineering is a favorable method for generating multiple Fano resonances and tuning spectral features. A similar result is obtained for clusters with other symmetries. Keywords: oligomer cluster; surface plasmon; metallic nanostructure; dark mode; plasmon hybridization ACS Paragon Plus Environment

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1. Introduction Localized surface plasmon resonances (LSPRs) in metallic nanostructures have attracted considerable attention.1,2 The plasmon responses of nanostructures depend on their composition, size, shape, and the dielectric of the surrounding medium.3 Free electrons can be confined to a narrow region, which results in strong near-field enhancement and formation of a “hot spot”. Given these properties, LSPRs have potential use in various applications. For example, LSPRs are very useful for label-free biosensing, where the near-field enhancement must be large and the line width must be narrow to obtain better sensing performance. However, radiative damping significantly increases with increasing particle size, and line width broadening thus occurs, which is a drawback for nearfield enhancement. These disadvantages prevent the further improvement of sensing performance. Fano resonances have been studied for a long while in quantum systems,4 and observed in plasmonic nanostructures several years ago. These phenomena are caused by destructive interference between broad bright modes and narrow dark modes.5-8 For strong interactions and near-degenerate levels, the coupling can lead to plasmon-induced transparency.9 Radiative damping at the spectral positions of Fano resonances is effectively suppressed, resulting in a narrow line width. Incident energy can also be effectively confined around nanostructures, leading to strong near-field enhancement.10 These properties may solve the problems of LSPRs mentioned earlier. Thus, Fano resonances in plasmonic nanostructures have attracted considerable attention in recent years. Traditionally, Fano resonances are generated in nanostructures by symmetry breaking, in which dark modes are excited. Numerous nanostructures can generate Fano resonances, such as ring-disk cavities,11,12 heterodimers,13 nanoshells,14 mismatched nanoparticle dimers,15-19 nanodisks by removal of a wedge,20 and nanoparticles coupled with a substrate.21,22 Multiple Fano resonances are also observed in nanostructures that possess several dark subradiant modes.23-25 Compared with a single Fano resonance, multiple Fano resonances can simultaneously modify the plasmon line at ACS Paragon Plus Environment

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several spectral positions and are very suitable for multi-wavelength sensing.26-28 Many studies have shown that Fano resonances can effectively improve sensing performance.29-34 For example, Hao et al.11,29 reported that the figure of merit (FoM) can be larger than 8 using Fano resonance from a ring-disk cavity. Cetin et al.30 showed that the FoM increases to 72 when a conducting metal layer is introduced. Wu et al.31 demonstrated the identification of molecular monolayers using Fano resonances and showed that biomolecules can even be detected with the naked eye.32 Nanoparticle oligomer clusters are among the most promising structures that can generate Fano resonances.35-39 For a plasmonic heptamer that has the symmetry of point group D6h, hybridizations between the E1u modes of the surrounding and central particles can lead to the formation of dark subradiant bonding and bright superradiant antibonding modes without breaking the structural symmetry.35,36 Spectral overlap and destructive interference between these modes result in the generation of a pronounced Fano resonance. Fano or Fano-like resonances are generated through the same mechanism in plasmonic pentamers,40,41 quadrumers,42-46 and trimers.47-49 Nanoclusters have broad bright resonances, with different dark modes that can be excited by adjusting their geometry; oligomer clusters are also favorable candidates for generating multiple Fano resonances.50-53 Fano resonances generated in plasmonic clusters exhibit strong near-field enhancement because of strong surface plasmon coupling.54-56 Plasmonic clusters are good platforms for biosensing applications.42,57,58 Implementations of biosensing rely on plasmon line shaping, and several studies have demonstrated that the coupling strength and overall dipole moment in symmetric clusters can be modified by adjusting the separation and specific particle size. The spectral positions and modulation depths of Fano resonances in plasmonic clusters can be tuned over a wide range.36,59 Fano resonances can even be generated in all-dielectric clusters.60 Breaking the cluster symmetry is another effective method for plasmon line shaping; this method can significantly influence the generation of Fano resonances, and additional features may ACS Paragon Plus Environment

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appear in the spectra.61-64 Several studies have demonstrated that magnetic plasmon modes can be excited and become involved in the generation of Fano resonances in the following systems: quadrumers with the introduction of small asymmetries,61 symmetric quadrumers under focused cylindrical vector beam excitations,62 and plasmonic clusters by adding dielectric nanoparticles.63 Not long ago, Lassiter et al.65 and Hentschel et al.66 reported that the symmetry of a heptamer may be lowered to the C2v point group by adjusting the size of one of the surrounding particles or position of the central particle, which greatly influences the resonant energy and modulation depth of the Fano resonance. Cui et al.67,68 demonstrated that the symmetry of a heptamer is lowered to point group D2h by applying uniaxial mechanical stress, and a new Fano resonance appears in the spectrum for polarization that is parallel to mechanical stress but not perpendicular polarization; the new Fano resonance is caused by a B3u mode that evolves from the dark B1u mode of a symmetric heptamer. Recently, we also found that in plasmonic pentamers with D2h symmetry, multiple Fano resonances are excited because of the excitation of dark subradiant B3u and B2u modes.69 According to plasmon hybridization theory,70 the B3u and B2u modes may hybridize with the plasmons of added particles for a heptamer with D2h point group symmetry, and additional features may also appear in the spectra. In this paper, we show that multiple Fano resonances can be excited in hexamers with D2h symmetry because of the excitation of dark B3u and B2u modes. When a central particle is introduced to form a heptamer, we demonstrate that aside from influence on the resonant behaviors or development of spectral features for a certain polarization, several hybridized dark subradiant modes are excited for both polarizations. Up to eight kinds of Fano resonances are observed in the spectra, and a wide tunability of the spectral features is achieved by adjusting the geometric parameters. This work reveals that cluster symmetry engineering is an effective method for tuning spectral features and generating multiple Fano resonances. The proposed method can be used on plasmonic clusters with other symmetries. ACS Paragon Plus Environment

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2. Methods The spectra, near-field enhancement and current density vector distributions presented in this paper are calculated using the finite-difference time-domain (FDTD) method. In the simulations, a realistic dielectric function for gold is used (Johnson and Christy).71 The size of the unit cell is 2 × 2 × 2 nm3, and the structures are embedded in water with the refractive index of n = 1.33. During FDTD calculations, a normal incident pulse with linear polarization is used to excite the structures. Perfectly matched layers (PML) around the structures are used to simulate the open space, and all of the near-field properties are calculated at the middle cross-section of the structures. The colorscale for the field enhancements is linear, and the colorscale is the same for all panels.

3. Results and Discussion Multiple Fano Resonances in Hexamers. Figure 1a shows the geometries of two kinds of hexamers, which are composed of gold nanorings. The outer radius of the four rings on the left and the right sides is denoted as r′, and the outer radius of the two other rings is denoted as r. When r = r′, the hexamer on the left panel of Figure 1a belongs to the symmetry of point group D6h, and the structure symmetry can be lowered by adjusting the size of the nanorings. When r ≠ r′, the hexamer presented on the right panel of Figure 1a belongs to the symmetry of point group D2h, and optical responses considerably change. Assuming that the other geometric parameters are constants, the evolutions of the extinction spectra against r when the polarization is along the x and y axes are shown in Figures 1b and 1c, respectively. The spectra exhibit two sets of Fano resonances for both polarizations, and all of the Fano dips redshift with increasing r. The modulation depth decreases simultaneously for the two sets of Fano resonances with higher energies. The two other sets of Fano resonances with lower energies appear in the spectra when r > 75 nm for both polarizations. However, the modulation depths increase with increasing r. ACS Paragon Plus Environment

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In a recent work, we studied multiple Fano resonances in plasmonic pentamers that also had the D2h point group symmetry.69 Spectral variations with changes in central particle size are similar to those shown in Figures 1b and 1c. In the following discussion, we show that both structures share the same mechanism for the generation of multiple Fano resonances. The near-field enhancement and current density vector distributions at the spectral positions of the bright mode and the multiple Fano resonances are presented in Figure 2. Molecular point group theory can be used to analyze the plasmonic properties of the hextamers.72 A hexamer has two parts. One part consists of a quadrumer, which comprises four left and right rings. The other part consists of the dimer, which is composed of two top and bottom rings. The symmetry of the quadrumer belongs to the D2h point group. Brandl et al.73 studied the optical properties of nanoparticle quadrumers with symmetric configurations having the symmetry of point group D4h. They showed that under in-plane excitation, only four Eu modes have non-zero dipole moments, and plasmon modes can be expressed as a linear combination of the four Eu modes. For quadrumers with the symmetry of point group D2h, the four Eu modes of the symmetric quadrumers evolve into two B3u and B2u modes when the polarization is along the x and y axes, respectively (Figure S1). The B3u and B2u modes have non-zero dipole moments and can couple to light for quadrumers with D2h symmetry. The symmetry of the dimer belongs to the D∞h point group, and only the Πu mode and Σu+ mode are bright and can be excited for x and y polarization, respectively (Figure S2). Similar to a plasmonic heptamer, the irreducible representations of the hexamer are the sum of the representations of the quadrumer and dimer.74,75 Under in-plane x-polarization excitation, the plasmon modes of the hexamer are constructed as linear combinations of the two B3u and one Πu basis modes. Superradiant bright resonances are generated when the plasmons of each ring oscillate in-phase (Figure 2a), and the increase in overall dipole moments causes broadening of the bright ACS Paragon Plus Environment

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modes (Figure 1b). When the plasmons of the quadrumer (the two B3u modes) oscillate out-of-phase with those of the dimer (the one Πu mode), the dipole moments of these two parts cancel each other, resulting in weak radiative damping that forms two kinds of dark subradiant modes (Figures 2b-2d). Destructive interferences between the bright modes and dark subradiant modes lead to the generation of the two sets of Fano resonances observed in Figure 1b, and these shift to lower energies with increasing r because of the reduced resonance energy of the dimer. The two hybridized dark subradiant modes also belong to B3u irreducible representations. The field enhancement between the quadrumer and dimer is weak for the B3u dark mode with higher energies (Figure 2b), which corresponds to antibonding resonance. By contrast, the field enhancement in the gap regions is strong for the dark B3u mode with lower energies (Figures 2c and 2d), which corresponds to bonding resonance. When polarization occurs along the y axis, the optical responses of the hexamers are similar to those in the x-polarization. However, the plasmon resonances are constructed as linear combinations of the two B2u modes (the quadrumer) and one Σu+ mode (the dimer). The near-field distributions of the two kinds of hybridized dark subradiant modes are presented in Figures 2e, 2f and 2g, 2h, respectively. The two hybridized dark modes belong to B2u irreducible representations, which are antibonding and bonding resonances for dark modes with higher and lower energies, respectively. At the spectral position of the Fano resonance corresponding to the B2u antibonding dark mode, a stronger near-field enhancement is observed in the quadrumer gap regions for a cluster with a larger r (Figures 2e and 2f). Thus, although the dipole moment of the dimer increases with increasing r, the dipole moment of the quadrumer increases more effectively. The overall dipole moment is stronger for a hexamer with a large r than for one with a small r, and the modulation depth of this set of Fano resonances decreases with increasing r. The spectral evolution of the other set of Fano resonances corresponding to the B2u bonding dark mode is similar to that of heptamers reported in previous ACS Paragon Plus Environment

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studies.65,66 Cancellation of the dipole moments is more effective for a hexamer with a larger r, and the modulation depth of the Fano resonance increases with increasing r (Figures 2g and 2h). Plasmonic clusters can be treated as artificial molecules; the structure of symmetric plasmonic hexamer is analogous to that of a benzene molecule, and optical responses considerably change when a central particle is introduced.36 The hexamers discussed in this study or pentamers we reported in the previous work may be analogous to molecules with the symmetry of point group D2h, such as the C2H4 molecule. The B3u and B2u antibonding dark modes are analogous to the two CH bending modes of vibration in the C2H4 molecule (Figures 2b and 2e, 2f). The B3u and B2u bonding dark modes are in analogous to the two CH stretching modes of vibration (Figures 2c, 2d and 2g, 2h). One may expect that the hybridized dark subradiant modes exist in similar plasmonic structures. For example, when the sizes of specific particles are adjusted, Fano resonances corresponding to these dark subradiant modes will appear in spectra for the large clusters proposed by Dregely et al.50 We then study the influence on spectral features by adjusting the separation S. Traditionally, plasmon coupling strength decreases with increasing separation, resulting in a decrease in the modulation depth of Fano resonances generated in plasmonic clusters. However, hexamers with the symmetry of point group D2h have different optical responses. Figures 3a and 3b present the relationships between the extinction spectra and separation S when r = 60 and 100 nm and the polarization is along the y axis. The Fano dip is stronger for a hexamer with a large separation than that for a hexamer with a small separation, and the Fano dips slightly blueshift with increasing S. When r = 60 nm, the near-field distributions for the two hexamers with different S (Figures 4a and 4b) reveal that field enhancement in the gap regions at the spectral positions of the resonance dips is weaker for the hexamer with a larger separation. This result implies that plasmon coupling strength of the B2u antibonding dark mode do decrease with increasing S, but unlike previous studies on plasmonic clusters, the two parts of the hexamers (the quadrumer and the dimer) have different ACS Paragon Plus Environment

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resonance energies, and the hexamers can be treated as detuned electrical dipoles. Bozhevolnyi et al.76,77 demonstrated that for two scatterers, the scattering asymmetry is maximized when the retardation phase and phase difference are equal to π/2. Although the resonance energies of the quadrumer and dimer change with the variation of the separation S, there is an optimal separation to obtain the maximum asymmetry. The top line in Figure 3a is the extinction spectrum of the hexamer with S = 400 nm. Almost no near-field interactions occur between these nanorings, and the Fano resonance vanishes in this case. Figures 4c and 4d present the near-field distributions of the B2u bonding dark mode for the two hexamers with r = 100 nm (Figure 3b), which features a mechanism identical to that for the B2u antibonding dark mode. When the polarization is along the x axis, a similar result is obtained (Figure S3). Multiple Fano Resonances in Heptamers. A central nanoring is introduced to form a heptamer, as shown in the inset of Figure 5, and the main panels show the variations of the extinction spectra against r. Compared with those in hexamers (Figure 1), another set of Fano resonances with lower energies are observed in the spectra for both polarizations. The variations in the resonance positions and modulation depths of the other Fano resonances are similar to those in the hexamers. However, some of the Fano resonances are caused by different factors. When the polarization is along the x axis, the newly generated Fano resonance is significantly redshifted with increasing r, and the modulation depth decreases at the same time (Figure 5a). For y-polarization excitation, the spectral position and modulation depth are almost unchanged for the newly generated Fano resonance (Figure 5b). To understand the factors causing these spectral features, near-field properties at the spectral positions of the multiple Fano resonances are investigated (Figure 6). Figure 6a presents the near-field enhancement and current density vector distributions for the Fano resonance around 819 nm of the heptamer with r = 60 nm under x-polarization excitation. The charge distributions in the ACS Paragon Plus Environment

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surrounding rings are identical to the corresponding Fano resonance of the hexamer, namely, the B3u antibonding dark subradiant mode (Figure 2b). The plasmons of the central ring oscillate in-phase with that of the two top and bottom rings (the dimer), and the net dipole moment is also reduced because of the cancellation with that of the four left and right rings (the quadrumer). The destructive interference with bright modes leads to the generation of the Fano resonance. The near-field properties of the Fano resonance around 944 nm for the heptamer with r = 90 nm are shown in Figure 6b. One may have expected that the Fano resonance should be related to the B3u bonding dark subradiant mode of the hexamer (Figure 2c). However, charge distributions reveal that the Fano resonance is related to the B3u antibonding dark mode (Figure 2b). The two Fano resonances shown in Figures 6a and 6b are caused by the same kind of dark subradiant mode. The dark mode cannot be excited when the heptamer has D6h symmetry. Thus, the modulation depth of the Fano resonance is weaker when r approaches 75 nm. According to the plasmon hybridization theory, there are hybridized resonances related to the B3u bonding dark subradiant mode of the hexamers, which are investigated in the following section. For the heptamer with r = 60 nm, the near-field distributions of the newly generated Fano resonance shown in Figure 6c imply that the plasmons of the central ring oscillate out-of-phase with the surrounding rings and have the same mechanism as that of a symmetric heptamer. When r is increased to 90 nm (Figure 6d), plasmon coupling strength is considerably enhanced, field enhancements in the gap regions are increased, and the Fano resonance shifts to lower energies. The dipole moments of the surrounding rings increase with increasing r, and radiative damping of the dark mode simultaneously increases, which leads to the decrease in modulation depth. Figure 6e shows the near-field properties of the Fano resonance around 827 nm for the heptamer with r = 60 nm when the polarization is along the y axis. The corresponding dark subradiant mode is a hybridized resonance related to the B2u antibonding mode of the hexamer (Figure 2e). The ACS Paragon Plus Environment

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plasmons of the central ring oscillate in-phase with the quadrumer but out-of-phase with the dimer. The overall dipole moment of the structure is increased, and radiative damping is enhanced. Moreover, the modulation depth is weaker than that of the hexamer. The near-field distributions of the Fano resonance around 1112 nm for the heptamer with r = 90 nm shown in Figure 6f reveal that the corresponding dark subradiant mode is related to the B2u bonding mode of the hexamer (Figure 2g), which corresponds to the additional Fano resonance that Cui et al.67 observed for polarization parallel to mechanical stress. The higher order resonance of the central ring is involved in the formation of the hybridized dark mode. There are stronger surface plasmon coupling, and the Fano resonances shift to lower energies compared with that in the hexamers. The mechanism causing the newly generated Fano resonances shown in Figures 6g and 6h is also the same as that in symmetric heptamers. The plasmons of the two top and bottom rings are not effectively excited. Adjusting the dimer size results only in a slight change in the modulation depth of the Fano resonance, and the Fano resonance only slightly redshifts with increasing r. Plasmon Hybridization Schemes. To obtain further insights, the optical properties of the heptamers with different central rings are investigated. First, we study the plasmon hybridization schemes, considering only dipole resonances. According to the plasmon hybridization theory, the plasmon response of a heptamer is an interaction between the plasmon response of a hexamer and that of a monomer. This response is also an interaction between the plasmon response of a pentamer and that of a dimer. The same hybridization behavior can be observed for both points of view. The optical properties of pentamers with the symmetry of point group D2h are similar to that of hexamers (Figure S4).69 The pentamers also possess two B3u and B2u dark subradiant modes, which interact with the plasmons of the dimer to generate hybridized resonances in heptamers. The full plasmon hybridization schemes when the polarization is along the x axis are presented in Figure 7a. The left panel shows the interaction between the B3u bonding mode of the hexamer and ACS Paragon Plus Environment

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dipole mode of the central ring, which leads to the generation of two hybridized plasmon resonances. Dipole moment cancellations occur for both hybridized modes, which are dark and subradiant. The right panel shows the interaction between the B3u bonding mode of the pentamer and the Πu mode of the dimer, which results in the two kinds of hybridized dark subradiant modes observed in Figure 5a. The inset of Figure 7a presents the two other hybridization schemes, which involves the corresponding B3u bright antibonding modes of the hexamer and pentamer. The interactions lead to the generation of two bright superradiant resonances and two dark subradiant resonances. The two dark modes have high resonance energies, which are not observed in the following studies and are not discussed. The variations in the extinction spectra of the heptamers with r = 60 nm against the central ring radius R are shown in Figure 7b. Two Fano resonances are observed in each spectrum. The modulation depth of the Fano resonance with higher energy is weak, and the spectral feature has not changed much. The other Fano resonance with lower energy redshifts with increasing R, and the modulation depth is significantly increased. Figure 8a presents the near-field properties of the Fano resonance around 789 nm for the heptamer with R = 60 nm. The Fano resonance is caused by the destructive interference between the bright modes and antibonding dark mode shown in the left panel of Figure 7a, in which the plasmons of the top and bottom rings are not effectively excited. When R = 70 nm (Figure 8b), the near-field distributions of the Fano resonance reveal that the change distributions in the quadrumer have changed, and the dark mode evolves into the antibonding mode shown in the right panel of Figure 7a. It is also found that higher order resonance of the central ring is involved to form the dark mode when R = 100 nm (Figure 8c).68 The corresponding bonding dark mode leads to the generation of other Fano resonances with lower energy (Figure 8d), and the spectral variations are the same as that of symmetric heptamers. Figure 7c presents the relationship between the extinction spectra and central ring R for ACS Paragon Plus Environment

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heptamers with r = 90 nm. The near-field distributions shown in Figures 8g and 8h imply that when R > 75 nm, the two sets of Fano resonances are also caused by the antibonding and bonding dark subradiant modes shown in the right panel of Figure 7a. Given the stronger plasmon coupling and reduced resonance energy of the top and bottom rings, the two Fano resonances redshift compared with that in the heptamers with r = 60 nm. The overall dipole moment of the surrounding rings is increased for r = 90 nm (Figure 8h), and the modulation depth of the Fano resonance related to the bonding dark mode is weaker compared with that of r = 60 nm (Figure 8d). Two other kinds of Fano resonances appear in the spectrum for the heptamer with R = 60 nm, and their near-field distributions are presented in Figures 8e and 8f. The charge distributions in the pentamer for the Fano resonance shown in Figure 8e are the same as that in Figure 8a. However, the dipole resonance of the nanorings with r = 90 nm is far from the Fano resonance, and the quadrupole resonance of the nanorings is involved in the formation of the dark subradiant mode. The formation of the bonding dark subradiant mode shown in the left panel of Figure 7a causes the other Fano resonance (Figure 8f). The dipole moment of the pentamer increases with increasing R, resulting in the decrease in modulation depth. The full plasmon hybridization schemes when the polarization is along the y axis are presented in Figure 9a. The left panel shows the interaction between the B2u antibonding mode of the hexamer and dipole mode of the central ring, and the right panel shows the interaction between the B2u antibonding mode of the pentamer and Σu+ mode of the dimer. The interactions lead to the formation of four kinds of hybridized dark subradiant modes. The inset presents the two other hybridization schemes, which form two bright surperradiant modes and two dark subradiant modes similar to those formed during x-polarization. Three sets of Fano resonances are observed in the extinction spectra of the heptamers with r = 60 nm (Figure 9b). The near-field distributions of the pronounced Fano resonance for the heptamer ACS Paragon Plus Environment

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with R = 60 nm (Figure 10a) reveal that the Fano resonanc is caused by the bonding dark subradiant mode shown in the right panel of Figure 9a. The plasmons of the central ring and dimer oscillate in-phase. The dipole moment of the three rings increases with increasing R (Figure 10b), which is stronger than that of the four left and right rings. Stronger radiative damping is observed for a heptamer with a larger central ring, and the modulation depth of the Fano resonance decreases with increasing R. Figures 10c and 10d show the near-field properties of the two other kinds of Fano resonances, which are caused by the antibonding and bonding dark subradiant modes shown in the left panel of Figure 9a. With increasing R, the two Fano resonances are redshifted due to the stronger surface plasmon coupling and reduced resonance energy of the central ring. Figure 9c shows the evolution of the extinction spectra versus central ring radius for the heptamers with r = 90 nm. Figure 10e presents the near-field distributions of the Fano resonance around 819 nm for the heptamer with R = 60 nm. The Fano resonance is related to the antibonding dark subradiant mode shown in the right panel of Figure 9a, which is not observed in Figure 5. The dark mode shifts to lower energies for a heptamer with a larger central ring, and the plasmons of the surrounding rings are excited more effectively. Hence, the overall dipole moment increases, and the modulation depth decreases. As shown in Figure 10f, the other Fano resonance around 1099 nm for the heptamer with R = 60 nm is caused by the corresponding bonding dark subradiant mode. The coupling strength between the central and surrounding rings increases with increasing R. The bonding mode splits into two dark subradiant resonances when R > 70 nm, and two sets of Fano resonances are generated. As shown in Figure 10h, the Fano resonance with lower energy is related to the bonding dark mode shown in the left panel of Figure 9a. For the other Fano resonance with higher energy (Figure 6f), although the change distributions on the surrounding rings are the same as those in Figure 10f, the higher order resonance of the central ring is excited and forms the dark subradiant mode.68 The two Fano resonances are almost at the same spectral position when R = 70 ACS Paragon Plus Environment

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nm (Figure 10g). Near-field enhancement of plasmonic nanostructure is very important for sensing applications. At the spectral positions of the Fano resonances generated in the hexamers, there are stronger surface plasmon coupling for the bonding dark modes, resulting in stronger near-field enhancement (Figure 2). For example, the maximum field enhancement value is about 10 for the B2u antibonding resonance (Figure 2f), and it is about 12 for the B2u bonding resonance (Figure 2g). Another possibility to enhance surface plasmon coupling strength is by decreasing the separation. For the hexamers with S = 90 nm, the maximum field enhancement value is enlarged to about 16 and 41 for the B2u antibonding and bonding resonances, respectively (Figure 4a and 4c). Near-field enhancement can be further improved when a central ring is introduced, and several hot spots are generated at the spectral positions of the Fano resonances (Figure 6). Surface plasmon coupling is also very weak for the antibonding dark modes of the heptamers, and the maximum field enhancement value is only about 8 (Figure 6e). On the contrary, there are very strong near-field enhancements for the bonding dark modes. The maximum field enhancement is about 54 for the B3u bonding resonance when the polarization is along the x axis (Figure 6d), and it increases to about 74 for the heptamer with a larger center ring (Figure 8h). When the polarization is along the y axis, the maximum enhancement value is about 24 and 33 for the two kinds of B2u bonding modes, respectively (Figure 6f and 6h). Surface plasmon coupling strength decreases with decreasing R for the B2u bonding mode shown on the left panel of Figure 9a, and the maximum field enhancement decreases to about 18 when R = 60 nm (Figure 10f). The maximum field enhancement for the other B2u bonding mode increases to about 35 when the central ring radius is enlarged to 100 nm (Figure 10h). In a former study, we showed that multiple Fano resonances can be excited in plasmonic clusters composed of split nanorings, in which the quadrupole mode of split rings are involved in the ACS Paragon Plus Environment

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generation of dark resonances.53 Aside from a pronounced Fano resonance, a kink at high-energy spectral positions is observed for a hexamer composed of equal-sized split nanorings (Figure S5). In the supporting information, we show that this spectral feature is related to the B3u bonding dark subradiant mode of the hexamers (Figure S6). Although the symmetry is broken for a hexamer composed of split nanorings, Fano resonances related to the B3u and B2u dark modes can be excited by adjusting the size of two top and bottom split rings. Considering the excitation of the quadrupole modes of split rings with different sizes, two other kinds of Fano resonances can be excited in a hexamer, and a very strong near-field enhancement occurs. Symmetry engineering is a favorable method for tuning spectral features, and it can be applied to plasmonic clusters with other symmetries. For example, Figure S7 in the supporting information demonstrates that Fano resonance can also be excited for hexamers with the symmetry of point group D3h, and another Fano resonance appears in spectra when a central particle is introduced (Figure S8). However, the optical responses do not depend on the polarization direction because of their high symmetry.

4. Conclusions In conclusion, plasmonic hexamers and heptamers with D2h point group symmetry are investigated in this paper, which provides a general understanding of multiple Fano resonances in plasmonic clusters with D2h symmetry. When the polarization is along the x and y axes, plasmon interactions between the two parts of a hexamer, that is, the quadrumer and dimer, lead to the formation of two B3u and B2u dark subradiant resonances. Four kinds of Fano resonances related to these dark subradiant modes appear in the spectra. When a central ring is introduced to form a heptamer, the B3u and B2u modes of the hexamers (or pentamers) interact with the plasmons of the central rings (or dimers), and the optical responses significantly change. Aside from the influence on ACS Paragon Plus Environment

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resonance behavior65,66 or appearance of an additional Fano resonance for a specific polarization,67,68 several hybridized dark subradiant modes are observed for both polarizations and up to eight kinds of Fano resonances appear in the spectra. By adjusting their particle size, a wide tunability of modulation depths and resonance energies for the multiple Fano resonances is achieved. Plasmonic clusters with D2h symmetry are very suitable for plasmon line shaping, and these structures can serve as platforms for multi-wavelength sensing applications. This study also reveals that cluster symmetry engineering is an effective method for generating multiple Fano resonances and tuning spectral features. A similar result is also obtained for plasmonic clusters with other symmetries.

Acknowledgment: This work was supported by the Natural Science Foundation of Shanxi Province (2012021010-3), the China Postdoctoral Science Foundation (2011M500048), and the National Natural Science Foundation of China (61108027 and 51205273).

Supporting Information Available: Optical properties of plasmonic quadrumer and pentamers with D2h symmetry, dimer with D∞h symmetry, hexamers and heptamers with D3h symmetry, hexamers composed of split rings, and spectra variations versus separation for hexamers under x-polarization excitation. This material is available free of charge via the Internet at http://pubs.acs.org.

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Figure Captions Figure 1. (a) Geometry of plasmonic hexamers with D6h and D2h point group symmetries. Extinction spectra evolution versus the outer radius r of the two top and bottom rings (the dimer). The polarization is along the (b) x axis and (c) y axis. The outer radius of the four left and right rings (the quadrumer) r′ = 75 nm, the width W = 30 nm, the thickness T = 40 nm, the separation S = 110 nm, and the refractive index of the surrounding medium is n = 1.33.

Figure 2. Field enhancement (|E|/|Einc|) and current density vector distributions for plasmonic hexamers with D2h symmetry. The plasmon interactions between the quadrumer (four left and right rings) and dimer (the two top and bottom rings) lead to the formation of bright superradiant and dark subradiant modes of the hexamers. (a) Bright superradiant mode with r = 60 nm. The four Fano resonances observed in Figure 1 are caused by (b) B3u antibonding, (c, d) B3u bonding, (e, f) B2u antibonding, and (g, h) B2u bonding dark subradiant modes, respectively. Figure 3. Extinction spectra of plasmonic hexamers with D2h symmetry as a function of separation S. The outer radius of the dimer (a) r = 60 nm and (b) r = 100 nm. The polarization is along the y axis, and the other parameters are identical to those in Figure 1.

Figure 4. Near-field properties of hexamers with different separation S at the spectral positions labeled in Figure 3. B2u antibonding dark mode with (a) r = 60 nm, S = 90 nm, and (b) S = 160 nm. B2u bonding dark mode with (c) r = 100 nm, S = 90 nm, and (d) S = 160 nm. Figure 5. Relationship between the extinction spectra of heptamers with D2h symmetry and outer radius of the dimer r for (a) x-polarization, and (b) y-polarization. The central ring radius R = 90 nm, and the other parameters are identical to those in Figure 1.


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Figure 6. Near-field properties of the heptamers for x-polarization (upper row), and y-polarization (lower row) at the spectral positions labeled in Figure 5. The dark modes shown in (a, b) are related to the B3u antibonding mode of the hexamers. The Fano resonances of (c, d) and (g, h) have the same mechanism as that in symmetric heptamers. The dark modes shown in (e) and (f) are related to the B2u antibonding and bonding modes of the hexamers, respectively. Figure 7. (a) Plasmon hybridization schemes of plasmonic heptamers with D2h symmetry for x-polarization, where only dipole resonances are considered. The interactions between the B3u bonding mode of the hexamer (the pentamer) and dipole mode of the central ring (the dimer) lead to the generation of four kinds of hybridized dark subradiant resonances. The inset presents the two other hybridization schemes, which form two bright surperradiant modes and two dark subradiant modes. Extinction spectra versus central ring radius for heptamers with (b) r = 60 nm, and (c) r = 90 nm. The other parameters are identical to those in Figure 1.

Figure 8. Near-field properties of the heptamers for x-polarization at the spectral positions labeled in Figure 7. When r = 60 nm, the Fano resonances are caused by the (a) antibonding dark mode shown in the left panel of Figure 7a, (b, c) antibonding and (d) bonding dark modes shown in the right panel of Figure 7a. When r = 90 nm, the Fano resonances are caused by (e) a hybridized dark mode related to the quadrupole resonance of nanorings, (f) the bonding dark mode shown in the left panel of Figure 7a, (g) antibonding and (h) bonding dark modes shown in the right panel of Figure 7a.

Figure 9. (a) Plasmon hybridization schemes of plasmonic heptamers with D2h symmetry for y-polarization, where only dipole resonances are considered. The interactions between the B2u antibonding mode of the hexamer (the pentamer) and dipole mode of the central ring (the dimer) lead to the generation of four kinds of hybridized dark subradiant resonances. The inset presents the two other hybridization schemes, which form two bright surperradiant modes and two dark ACS Paragon Plus Environment

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subradiant modes. Extinction spectra versus central ring radius for heptamers with (b) r = 60 nm, and (c) r = 90 nm. The other parameters are identical to those in Figure 1.

Figure 10. Near-field properties of the heptamers for y-polarization at the spectral positions labeled in Figure 9. When r = 60 nm, the Fano resonances are caused by (a, b) the bonding dark mode shown in the right panel of Figure 9a, (c) antibonding, and (d) bonding dark modes shown in the left panel of Figure 9a. When r = 90 nm, the Fano resonances are caused by the (e) antibonding and (f) bonding dark modes shown in the right panel of Figure 9a, and (h) bonding dark modes shown in the left panel of Figure 9a. (g) The two bonding dark modes are almost at the same spectral positon when R = 70 nm.


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Excitation of Multiple Fano Resonances in Plasmonic Clusters with

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