Introduction

Plasmonic nanoparticles and their assemblies are well-known optical nanoantennas and have been intensively studied in nanophotonics due to the fascinating optical properties originated from localized surface plasmon resonance (LSPR)1,2. Among the various kinds of metallic nanostructures, plasmonic dimer antennas (PDAs) which are often constructed by a pair of strongly interacting metallic nanoparticles, e.g., a dimer consisting of two arms and a gap between them, have been frequently studied3,4,5. Despite the numerous similarities with traditional RF antenna in terms of collecting and emitting electromagnetic wave6,7, the LSPRs in PDA offer tremendous extraordinary and anomalous optical responses such as strong light confinement and scattering8,9,10,11. Moreover, the resonance features of a PDA are intimately related to the size, shape, the dielectric functions of the compositions and the ambient enviroment12,13. The virtues of LSPR grant PDA promising applications in single molecule detecting14, enhanced light-matter interaction15, optical nano-circuit16,17, enhancement of optical nonlinear effects18,19 and plasmon-assisted particle trapping and micromanipulations20,21 etc. In addition, since PDAs represent one of the simplest coupling systems, they are quite suitable for studying plasmon hybridizations and coherent plasmonic phenomena such as Fano resonance and electromagnetically induced transparency (EIT)22,23,24,25.

To this end, a great deal of attention has been focused on the antenna mode (AM) of a PDA which is basically an electric dipolar plasmon resonance sustained by the solid metallic parts. The nanogap of a PDA provides the feeding port to excite the AM or to tune the equivalent circuit property10,13,16,26. However, in such plasmonic nanostructures, not only the solid metallic parts but also their inverse counterparts (e.g., the dielectric gap layer embedded between the metals) play significant roles. The LSPRs associated with the solid metallic parts usually give rise to prominent electric resonances while the inverse parts favor magnetic resonances, according to the Babinet principle27,28,29. It is more fundamental to realize that PDAs are actually composite structures with the arms being the solid part and the dielectric gap being the inverse part, simultaneously30,31,32,33,34,35. Different to the AM, cavity modes (CMs) are strongly confined in the dielectric layer with small modal volume and high quality factor31,32. In view of the multipole expansions, the lower-order CMs give rise to the fundamental magnetic multipoles34,35. More interesting, one of the CMs has been shown to generate remarkable toroidal dipole response. The toroidal dipole response could yield interesting consequences such as the formation of anapole36, toroidal induced transparency37,38,39 and enhanced optical scattering force40. In this context, one would expect that a PDA may support both AM and CMs in the same band and it shall be of great interest to explore the couplings between them. We note that they were respectively analyzed in detail in a very recent work41. However, studies on the AM-CM coupling effects are still missing.

In this study, we examine the AM-CM coupling effects by carefully adjusting the geometry and the gap layer material in a PDA consisting of two identical silver nanorods. By deliberately making the AM and CMs spectrally overlapped, we are able to simultaneously or selectively obtain destructive and cumulative responses from them, depending on the angular symmetry of the CMs. Both far-field and near-field characteristics of the designed PDAs are examined by full-wave simulations based on the finite integral technique (FIT)42. The results show that the magnetic dipolar CM fully decouples from the electric bonding dipolar AM and they collectively generate accumulative scattering enhancement. On the contrary, the toroidal dipolar CM violently competes with the AM in the near field, yielding Fano resonance or EIT-like features in the spectrum.

Results

Coupling between the antenna dipolar mode and the cavity modes

Figure 1a schematically shows the PDA structure which is a typical homodimer with two identical silver nanorods loaded with a dielectric layer of thickness d inside the gap. The two cylindrical nanorods are both of radius R and length L. The dielectric constant of the gap material is set to be εload and that of the silver is taken from Johnson and Christy43. The whole structure is assumed to be freestanding in air and illuminated by a normally incident plane wave (k along direction) that is linearly polarized along the x axis. Firstly, we set R = 50 nm, L = 90 nm, d = 20 nm and check how the scattering spectrum evolves with various εload. The calculated optical scattering efficiency σscs for εload = 1, 3, 6, 12 and 18 are shown in Fig. 1b–f. It is seen that for εload = 1 the spectrum has a broad peak centered at f ≈ 530 THz (see Fig. 1b). This peak corresponds to the electric dipolar AM resonance which is also known as the bonding hybridization resonance from the individual dipolar modes on the two nanorods22. As the gap dielectric constant increases to εload = 3 (Fig. 1c), a narrow Lorentz-shape peak (marked by the red upward arrow) is superimposed on the AM peak which red shifts to f = 462 THz. With loaded dielectric material of εload = 6, it is seen in Fig. 1d that the narrow peak (f = 358 THz) resides at the left shoulder of the broad AM resonance. More interestingly, another resonance feature shows up near f = 540 THz, apparently with a quite different flavor. This resonance reduces rather than adds up to the AM resonance profile. It also leads to an asymmetric line shape with a Fano-like dip, as marked by the downward blue arrow in Fig. 1d. Following this trend, when εload is continuously increased to 12, which is the situation shown in Fig. 1e, both the upward-arrow-marked peak and downward-arrow-marked dip red shift. However, their relative magnitudes with respect to the AM background (envelope) exhibit different changing characteristics. The strength of the Lorentzian peak nearly does not change while that of the Fano dip visually increases as it approaches the resonance center frequency of the AM. It is seen that the original AM peak becomes a deep EIT-like dip and splits into two separate peaks at f = 398 THz and 444 THz, respectively. This indicates a strong interaction of the AM with another resonance mode (we will later show that it is a CM with toroidal response). Notice that in Fig. 1e, there is another tiny Fano dip at f ≈ 505 THz (marked by the downward green arrow) which must come from a higher-order mode. Finally, Fig. 1f shows that for εload = 18, this high-energy dip looks apparent as it now spectrally approaches the AM resonance center frequency.

Figure 1
figure 1

Schematic of the plasmonic dimer antenna and typical scattering spectra.

(a) Schematic figure of the antenna and the excitation configuration. The scattering efficiency spectrum σSCS of a PDA with L = 90 nm, R = 50 nm and d = 20 nm for (b) εload = 1, (c) εload = 3, (d) εload = 6, (e) εload = 12 and (f) εload = 18.

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It is reasonably to infer from the above observations that the sub-features in the spectra, e.g., the peaks and the Fano-like dips, may come from another family of resonances that are distinct from the prominent AM. To clarify that, we focus on the PDA structure studied in Fig. 1e. Figure 2a shows the absorption efficiency σACS together with the scattering efficiency σSCS of the whole structure. The FIT results were further corroborated by a solver (COMSOL Multiphysics) of finite element method (FEM)44. It is seen that the FEM results (symbol) agree very well with the FIT ones (red line). Different to σSCS whose envelop is a broad resonance spectrum with small quality factor, the σACS shows three narrow peaks at f = 265 THz, 408 THz and 505 THz with high quality factors. This is because that the σSCS of the PDA is dominated by the electric dipolar AM with large radiation loss while the σACS substantially reflects the CMs with Ohmic loss caused by the induced localized currents in the metallic arms close to the gap.

Figure 2
figure 2

Optical spectra and the near-field details for different frequency.

(a) The σSCS (red line) and σACS (blue dashed line) spectra of the PDA with L = 90 nm, R = 50 nm, d = 20 nm and εload = 12. The red dots are results calculated by the FEM. (b–f) The electric field amplitude |E| at xoz plane for CM11, AM1, CM10, AM2 and CM20 in order. (h–l) The out-of-plane electric fields Ex (colors) and the in-plane magnetic field (arrows) at the yoz plane across the dielectric layer. (m–q) The corresponding surface charge distribution.

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To identify these resonances, we show in Fig. 2b–f the electric field amplitude over the xoz plane for f = 265 THz, 398 THz, 409 THz, 444 THz and 505 THz, respectively. It is seen that at f = 265 THz, the electric field is basically confined in the gap region with a zero-field node in the center (see Fig. 2b). This strongly suggests that it originates from a plasmonic cavity mode. Figure 2h shows the snapshot of the out-of-plane electric field Ex (see the color contour) in the dielectric layer across the origin. We label this resonance as ‘CM11’ where the subscript represents the radial and azimuthal node numbers in the Ex pattern. Furthermore, the yoz in-plane magnetic field vectors are shown by arrows which exhibit a large magnetic moment along the y direction. This magnetic moment is formed by the anti-directional going conduction currents on the opposite gap surfaces, given by the so called magnetic resonance30.

Figure 2c shows that for the dominated scattering peak at f = 398 THz at the lower-frequency side of the Fano dip, there are hot spots both inside the gap region and near the antenna terminals. Strong electric field around the antenna terminals is exactly a signature of the AM. In fact, here it is identified as an electric dipolar resonance that strongly radiates, despite of the slight asymmetric characteristic along the z axis due to retardation. At the same time, Fig. 2c shows that the electric field is also much stronger inside the gap, with the zero-field node appearing near the lateral boundary. Figure 2i indicates that at this frequency the PDA also sustains the CM10 resonance in the gap region. These imply hybridization between the dipolar AM and the cavity mode CM10. For convenience, here we label the peak by ‘AM1’ to distinguish it from the other hybridized mode ‘AM2’ that contributes to the second overwhelming scattering peak at f = 444 THz. Figure 2d shows the electric field pattern for the scattering dip at f = 409 THz that falls in between AM1 and AM2. Obviously, the field around the antenna terminals supposedly produced by the AM nearly vanishes (see Fig. 2d) compared to that of AM1 (Fig. 2c) and AM2 (Fig. 2e). We note that this vanishing AM field highlights one of the important features of Fano resonance: the “bright” mode excitation is substantially suppressed at the Fano dip frequency24. In a similar manner, we label this resonance as ‘CM10’ according to the Ex field pattern shown in Fig. 2j wherein the in- plane magnetic field is in a circular form confined in the gap region. Such magnetic field confinement gives rise to a toroidal dipole response, as observed in circular patch metal-dielectric-metal (MDM) antennas34,35. For frequency f = 444 THz beyond the Fano dip, the scattering peak from ‘AM2’ emerges. Figure 2e shows that the hot spots around the antenna terminals recover to some extent (the frequency is away from the AM resonance center frequency) but those inside the gap diminish. The near field maps for the high-energy minor dip at f ≈ 505 THz are shown in Fig. 2f,l. Both of them help to confirm that the gap mode at this frequency is ‘CM20’.

To see more properties of these modes, we additionally examined the resonance-induced surface charges. Figure 2m–q plot the surface charge distribution for the labeled peak and dip frequencies in Fig. 2a. Overall, the induced charges at the two arms of the PDA are basically of opposite sign because that the whole frequency band is covered by the bonding dipolar AM resonance. However, the fine structures of the charge distributions on the opposing interfaces across the gap are determined by the respective CM resonance. For example, Fig. 2m shows that for CM11, the positive and negative charges on the two inner interfaces across the gap separate along the y axis, with a neutral node around the origin. Meanwhile, Fig. 2n–p show that for AM1, CM10 and AM2, the induced opposite charges around the gap distribute alternatively in the radial direction without azimuthal zero node. We note that this “positive-negative” ring-like charge distribution is very similar to the reported fine structure in nanosphere heterodimers at the Fano dip frequency23. Such distribution to some extent is ascribed to the gap cavity between the metallic arms. Indeed, the suppression of the AM at the Fano dip is more clearly seen in Fig. 2o where the metallic arms are mostly neutralized in the terminals and the surface charges accumulate near the gap interfaces. Figure 2q shows that for the CM20 resonance, the charges near the gap have connected ring-like pattern.

As a matter of fact, there are several other CMs in this frequency band with undistinguishable peak in the σSCS spectrum due to the weak excitation (see Supporting Information, Fig. S1). To make our discussions more concise and simple, hereafter, we ignore them and the CM20 mode and specifically focus on the CM11 and CM10 modes. Figure 2h,j demonstrate that the CM11 and the CM10 have quite different symmetry pattern. It is thus expected that their modal overlapping with the AM must be distinct, yielding weak and/or strong mutual interactions, respectively. Note that a pure dipolar AM has relatively homogenous electric field in the gap region, with approximately zero azimuthal quantum number (m = 0). As a consequence, the field overlap integral between CMnm and AM is determined by , here δ denotes the Dirac delta function. It is immediately clear that CMs with m = 0 have nonzero modal overlapping with the AM, otherwise they are orthogonal to the AM. This argument holds as long as both the AM and CMs have negligible in-plane electric field.

The AM and CM can be excited by the different component of the incoming wave (E or H), therefore different σSCS spectra can be obtained in other configurations of incident plane wave (see Supporting Information, Fig. S2a). The same features can be also seen in the radiation decay rate of an electric dipole source (see Supporting Information, Fig. S2b).

It is now unambiguous that the CM11 and the CM10 have quite different interaction with the AM. The CM11 mode shows no considerable effect on the AM, but simply presents a cumulative peak in the scattering spectrum (Fig. 1). On the other hand, the CM10 mode interacts strongly with the AM, leading to a Fano (or EIT-like) dip (see Fig. 2a). More importantly, the interaction strongly suppresses the AM in the near fields due to destructive competition on the surface charge distribution, as demonstrated in Fig. 2d,o. To gain deeper understanding of the underlying physics, we have performed multipole decompositions of the total scattering fields for the PDA structure in Fig. 2. Figure 3a shows the σSCS from the irreducible Cartesian multipoles that include the electric dipole (ED), the magnetic dipole (MD), the toroidal dipole (TD), the ED-TD cross term notated as ‘P · T*’(see the Supporting Information) and the electric quadrupole (EQ) and magnetic quadrupole (MQ)36,37,38,39,40. It is seen in Fig. 3a (note that the y-axis is in logarithmic scale) that the σSCS of the ED (red line) dominates and leads to the broad AM resonance envelope of the total σSCS shown in Fig. 2a. It is therefore reasonable to consider that the AM mode gives rise to the ED which is relatively bright, namely efficiently excitable and radiating. More importantly, at the CM10 resonance f = 409 THz, the scattering efficiency from ED shows a dip. This is a direct proof that the AM is suppressed by the Fano resonance induced by the coupling between the AM and CM10 mode that is absent in a typical and commonly encountered PDA. The σSCS of the MD (see the blue line in Fig. 3a) is much smaller than that of the ED with an exception near f = 265 THz that is exactly the resonance frequency of the CM11, indicating that the CM11 gives rise to a MD response, consistent with the preceding discussions. Different to the MD, the TD scattering efficiency (green line in Fig. 3a) in the whole frequency band is at least two orders of magnitude smaller than that from the ED, even near the resonance frequency of CM10 (f = 409 THz). We note that in most cases the scattering ability of a TD is indeed much weaker than an ED39,40. Figure 3a further shows that the scattering from EQ and MQ is relatively negligible. However, we can infer that there is in fact a CM resonance giving rise to MQ response at f ≈ 374 THz (see blue dashed line in Fig. 3a and Fig. S1 in the Supporting Information).

Figure 3
figure 3

Decomposed scattering from fundamental moments and their radiation pattern.

(a) The scattering efficiency σSCS of the irreducible multipoles in the Cartesian coordinates. (b) The scattering efficiency σSCS of the spherical dipole related to a1 and b1 and the total σSCS. (c) The radiation pattern of ED, MD, TD and their summation in the θ = 90° plane for the CM11 resonance at f = 265 THz. Note that the far field intensity from the TD is artificially amplified 1000 times to increase the visibility. (d) Same as (c) but for the CM10-mode induced Fano dip at f = 409 THz. The MD and TD term are multiplied by 10.

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Figure 3b shows the decomposed scattering spectra from multipole moments in the spherical coordinate (see Supporting Information) and the total σSCS (solid black line). The scattering efficiency from spherical scattering coefficients a1 and b1 are the main contributions: their sum basically recovers the total σSCS. We would like to emphasize that the σSCS related to a1 contains both the ED and TD parts in Fig. 3a 36,40,45. We further note that the scattering dip in the σSCS spectrum is essentially different to the recently reported toroidal induced transparency which is basically ascribed to the scattering cancellation between the ED and TD36,37,38. The scattering cancellation demands comparable strength of the individual scattered powers from both the ED and TD, which is not the case in our system. Figure 3a confirms that the TD scatters much more weakly (two orders of magnitude lower) as compared to the ED. In view of that, we would ascribe the observed scattering dip here to Fano suppression induced by the strong near field competition (mainly inside the gap region) between the AM and the CM10 mode.

In addition to the scattering properties shown in Fig. 3a,b, the radiation pattern can present more angular and directional information. Figure 3c,d show the far field intensity on the plane of θ = 90°, at f = 265 THz (the magnetic resonance) and f = 409 THz (the Fano dip), respectively. The polar plots compare contributions from the ED (red line), MD (blue line), TD (green line) and their vectorial summation (black line). Notice that in Fig. 3c the far field strength of TD is artificially amplified by 1000 times. Both radiation patterns have typical dipolar form but with different strength and orientation feature. Primarily, the scattering patterns of the ED and TD have the same angular momentum since they are both parallel to the electric component (along the x axis) of the incident wave and belong to the spherical dipole related to a1 36,40,45. Regarding the scattering pattern of the MD, it is rotated by 90° with respect to that of ED and TD. The MD is parallel with the magnetic component (along the y axis) and belongs to the spherical dipole related to b1 45. The orthogonal ED and MD are crucial for unidirectional scattering46,47,48 and spin-dependent photon emissions49. Here the designed PDA loaded with εload = 3 also exhibits the backward scattering suppression at the CM11 resonance (Supporting Information Fig. S3).

Coupled oscillator model

According to the scattering characteristics of the different modes of the PDA shown in Figs 2 and 3, we can employ a classical coupled oscillator model (COM) to understand the mode interactions in the proposed PDA50,51. Specifically, Fig. 3 shows that both the ED and MD contribute to the scattered field with different strength and channel. Therefore, it is reasonable to consider the AM as a bright mode and the CM11 mode as a sub-bright mode. On the other hand, the CM10 mode excitation is affected by the AM due to the strong near field coupling. In this regard, the CM10 can be considered as a dark mode despite of its weak direct excitation by the incoming wave. Figure 4a sketches the scheme of the COM where Gp (Gm) represents the coupling of AM (CM11) to the external drive, κ being the coupling strength between the AM and CM10. The energy spectrum of each oscillator is schematically shown in the right side of Fig. 4a. The dynamic equations of this system follows50,51

Figure 4
figure 4

Coupled oscillator model and the fitting to numerical data.

(a) Schematic of the coupled oscillator model for the AM-CM interactions. The coupling coefficient between the AM and CM10 is κ. Their individual resonance spectra are schematically shown at the right side. (b) The σECS spectrum of the PDA numerically calculated by the FIT (circles) and the fitted result from the coupled oscillator model (line).

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where χp, χm and χt denote the responses of the bright, the sub-bright and the dark modes, respectively. The three modes have eigenfrequency ωp, ωm and ωt and intrinsic dissipation γp, γm and γt, respectively. In Equation (1) we have set zero coupling coefficients between χm and χp (χt) since they are spectrally far away and considered to be orthogonal. The extinction spectrum of the whole coupled system is measured by −ωIm(χp + χm) which accounts the total dissipated powers. Figure 4b shows that the model results agree qualitatively with the numerically calculated extinction spectrum σECS. The fitted parameters are ωp = 440.38 THz, ωm = 265.2 THz, ωt = 410.1 THz, γp = 170.79 THz, γm = 3.828 THz, γt = 4.1 THz, κ = 120.78 THz, Gp = 1910.45 and Gm = 18.36. Despite of the small discrepancy between the model (line) and the FIT numerical results (circles), it is seen that the model essentially captures the features of the coexistence of scattering enhancement and suppression.

Scattering efficiency tuning

It should be stressed that both modal field overlap (nonzero inner product of eigenmodes) and spectral overlap are necessary prerequisites to guarantee strong coupling between the AM and CM modes. In this regard, it is interesting to see how the scattering spectra are affected by these factors in realistic design. Figure 5a–d show the σSCS contour maps in the frequency band from f = 200 THz to 600 THz with varying εload, d, L and R, respectively. The default parameters are kept the same as those in Fig. 2. Firstly we see that all the σSCS maps exhibit a dominating broad band coming from the AM resonance. There are also three visible narrow bands from the CM11, CM10 and CM20 resonances. It is clear that the CM11 band is a scattering enhanced one and the CM10 and CM20 bands correspond to two Fano bands with suppressed scattering. More interestingly, the strong Fano dip induced by the CM10 cuts through the dominating AM band in the entire frequency range. It thus introduces an anti-crossing feature, reflecting the strong interaction between the AM and the CM10 modes. The resonance frequencies of the CMs are theoretically predictable based on a Fabry-Perot model41, or approximately by applying the Neumann boundary condition for cylindrical gap SPPs at the lateral interface between the gap layer and the exterior medium for a circular MDM cavity30,33. The principle of this method is based on the fact that the resonance frequency of CMnm versus shall approximately fall on the dispersion of the gap SPPs, where is the n-th zero point of the derivative of m-th Bessel function30,33,52. Therefore the resonance frequencies of the CMs are mainly determined by two factors: (1) the effective radius Reff and (2) the wave vector of the gap SPP kgsp, both of which are closely related to the geometry and loaded material εload. The design parameter dependent resonance frequencies of the CM11, CM10 and CM20 cavity modes are theoretically obtained and shown in Fig. 5 (black dashed lines). The theoretical prediction clearly follows the local maximum and minimum of the color contour. The small discrepancy between the theory and numerical results comes from two facts: (i) we use the transfer matrix method of a 2D multilayer, assuming ideal TM wave to get kgsp. But for a finite-sized structure the gap SPPs are TM-like waves; (ii) The effective radius Reff ≈ R is an approximation and may be further modified according to the actual field distributions.

Figure 5
figure 5

The scattering efficiency (σSCS) contour in the frequency—parameter space.

(a) εload from 1 to 21. (b) L from 40 nm to 160 nm. (c) R from 30 nm to 70 nm. (d) d from 5 nm to 100 nm. The default parameter values are the same in Fig. 2. The dashed black lines show the resonance frequency dependence on the respective design parameters, obtained by the theoretical prediction for the CM11, CM10 and CM20 modes.

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In more details, Fig. 5a shows that as the loaded material dielectric function increases from εload = 1 to 21, both the AM band and the CM bands redshift. However, the AM band is less sensitive than the CM bands with respect to the εload variation. In particular, for roughly εload ≥ 9, the AM band becomes flat at fixed frequency range from f = 400 THz to 500 THz. Thus it is possible to adjust the CM bands independently by altering the loaded material. Figure 5a further shows that for air load, e.g., with εload = 1, the resonance frequency of CMs is beyond f = 600 THz which is far from the AM band. This is one of the reasons for the absence of the AM-CM coupling effect in the literature. The red-shift of the CM bands is caused by the increased propagating constant kgsp in the high dielectric constant layer. With regard to the AM, Alú et al. have demonstrated that the load can be applied to tune the scattering properties of the total antenna. The optical capacitance of the dielectric load is approximately Cload = εloadπR2/d10,26,53. In this view, the red-shift of the AM band is a straightforward result from the resonance condition . However, this argument is valid only when we are dealing with a pure electric dipolar mode. As long as the AM is hybridized with the CMs, the situation becomes more complicated.

It is probably more feasible to tune the scattering of the antenna by adjusting its geometry parameters. Figure 5b plots the σSCS map for arm length L = 40 nm to 160 nm. It is seen that the AM band red-shifts rapidly while the CM bands stay nearly intact. This means that modulating the length of the metallic nanorod is an effective way to tune the AM band without affecting the CM bands much. We note that the CM bands also shift when L is very small because in that scenario the SPPs at the external interfaces of the metallic arms couple with the gap SPPs30. The CM bands are more sensitive than the AM band with respect to the radius variation, as shown in Fig. 5c. Gap cavity with bigger size favors gap SPP resonances at longer wavelength. It is also worth mentioning that the magnitude of σSCS falls quickly as R increases due to the reduced aspect ratio L/R. Figure 5d depicts the σSCS map as a function of the gap distance d. It is known that kgsp − ω curve descends and finally converges to that of the SPP at a metal-dielectric interface when d is large enough. As a result, the CM bands are blue-shifted and nearly saturate when d ≥ 60 nm for CM10 and CM20 bands. Figure 5d further shows that the AM bands slightly red shift as d increases. This is inconsistent to both the nano-circuit theory10,26 and the dipole plasmon ruler equation54 that have blue shifting prediction for increasing d. We argue that these long-wavelength limit theories are valid for solid metallic particles solely supporting electric modes, which is not the case in our system. In the proposed PDAs, the AM is no longer a pure electric mode since it strongly couples to the CM10 mode and also couples to the CM20 mode. As a matter of fact, this cavity-mediation-effect was recently reported in a nancube dimer with extremely short separation55. The failure of the dipole approximation at shot separation is ascribed to the inhomogeneous field induced by the cavity mode, similar to those studied here. We note that when we separate the CM10 and AM spectrally, the AM resonance frequency blue shifts as d increases (Supporting Information, Figs S4 and S5).

Discussion

In summary, we have systematically explored the anomalous scattering properties of nanoantennas made by silver nanorod homodimer that are deliberately designed to support spectrally overlapping longitudinal electric dipolar AM and transverse gap SPP CMs. It is found that the broad scattering peak of the AM is modulated by a cumulative narrow scattering peak and one or several Fano dips. By analyzing the near field characteristics, we confirm that the narrow peak is related to the CM11 resonance while the Fano dip corresponds to the CM10 resonance. By doing the multipole expansion, we have also demonstrated that CM11 has a prominent magnetic dipole response while the CM10 has a toroidal response. We believe that the physics shall be maintained and similar coupling effects should be observed even if the antenna is immersed in a different homogeneous dielectric materials or lies on a dielectric substrate. The porous anodized alumina template is probably an effective platform to fabricate the proposed structures4,5. Our findings provide more degree of freedom to manipulate the resonances in PDA, by utilizing both the AM and the CMs. The results presented here may find applications in plasmonic super-scattering and cloaking, optical sensing based on Fano resonance, spin-dependent and directional light emission and efficient light harvest employing optical antennas.

Methods

The full-wave electrodynamic simulations were done with a FIT solver (CST Microwave Studio 2011) and corroborated with a FEM solver (COMSOL Multiphysics 4.3a). The σSCS spectra were obtained by integrating the normal scattered Poynting over a spherical surface enclosing the PDA. In the same time, the σACS spectra were obtained by integrating the resistive losses over the PDA volume. The extinction is defined by their sum σECS = σSCS + σACS (see Supporting Information). For all the numerical simulations, the permittivity of silver ε(ω) is taken from the experimental results of Johson and Chrisity43 fitted by the following Drude-Lorentz model:

where ω is in unit of eV and ε∞ = 2.296, ωp = 9.161 eV, Γ0 = 0.020 eV, a1 = 12.06, a2 = 27.67, a3 = 5.524, ω01 = 5.043 eV, ω02 = 6.171 eV, ω03 = 4.404 eV, Γ1 = 0.935 eV, Γ2 = 1.641 eV and Γ3 = 0.499 eV.

Additional Information

How to cite this article: Zhang, Q. et al. Coexistence of Scattering Enhancement and Suppression by Plasmonic Cavity Modes in Loaded Dimer Gap-Antennas. Sci. Rep. 5, 17234; doi: 10.1038/srep17234 (2015).