1. Introduction

Plasmonic nanoantennas can concentrate light into deep nanoscale and generate strong local electric field enhancements due to surface plasmon resonances [1,2]. The strong field enhancements make them play a crucial role in many technologies and applications, including surface-enhanced Raman scattering (SERS) [3,4], surface-enhanced infrared absorption (SEIRA) [5,6], emitter fluorescence and emission [7,8], plasmon−exciton coupling [9–11] and nonlinear optics [12,13]. Thus, many efforts have been devoted to maximize the local electric field enhancement of plasmonic nanoantennas. For individual plasmonic nanoantennas, turning the geometries [14,15] especially the gap size [2,16,17] of an antenna is an efficient way to increase its electric field enhancement. However, quantum effects appear when the gap size reaches subnanometer regime, which impede the further increment of field enhancement [18,19]. Furthermore, some applications require the antennas to have certain gap sizes [12,20–22]. For example, to obtain strong enough signal in the fluorescence enhancement application, certain distance between the emitter and antenna is needed to avoid quenching effect [21]. Integrating nanoantennas with other metal or dielectric photonic structures has also been studied, where the local fields of the nanoantennas can be largely increased [23–27]. In these coupled structures, the main strategy is to amplify the effective excitation field felt by the nanoantennas. The amplified excitation field is usually obtained by using a periodical pattern (photonic crystal) or film which, however, make the coupled structure much larger than the working wavelength.

Recently, dielectric nanostructures with high refractive index have drawn much attention as they exhibit strong magnetic and electric resonant responses while their material losses are low [28–30]. These properties make them attractive for many nanophotonic applications such as metasurfaces [31,32], matematerials [33], structural colors [34], and optical nanoantennas [35–38]. It should be pointed out that the sizes of these dielectric structures with low-order magnetic and electric resonances [28–30] are much smaller than the periodical dielectric structures mentioned before [25,26]. Reports have shown that the combinations of dielectric and plasmonic nanostructures can modify the linear and nonlinear far field behaviors of the coupled structures [39–44] or the emissions of an emitter nearby [45,46]. The strong optical responses of dielectric nanostructures are usually accompanied by significant far field scatterings and considerable electric and/or magnetic near field enhancements. For common dielectric nanostructures, the electric or magnetic near fields are typically distributed around the entire structure volume. For example, a magnetic dipole mode generally shows a rotating electric field around the structure [30]. The spatially wide distributions of the electric fields in dielectric nanostructures are unfavorable to achieving strong enough field enhancements compared to their plasmonic counterparts. On the other hand, such a distribution indicates that the electric field enhancement of a small plasmonic nanoantenna can be boosted if we put the antenna in the region of the enhanced electric field of the dielectric structure. However, this kind of combination has not been paid enough attention, despite a few preliminary demonstrations [45].

In this work, we theoretically study a hybrid structure combining a plasmonic nanoantenna and a dielectric nanostructure, where ultrahigh local electric field enhancement can be obtained. The plasmonic nanoantenna is a common gold (Au) nanorod dimer which has been widely seen in lots of studies and applications [2,47]. We mainly focus on the dielectric nanocavity which is a concentric disk−ring structure. For a lossless dielectric material n = 3.3, the electric field enhancement at the gap center of the Au antenna in the hybrid system reaches 382 times with a gap size of 5 nm for the antenna. This value is about 15 times higher than that of the individual Au antenna. The different roles of dielectric nanostructure in the hybrid are analyzed for better understanding the huge field enhancement achieved. More calculations show that our configuration is applicable to plasmonic antennas and dielectric nanocavity with various geometries and different materials. The ultrahigh field enhancement is also spectrally tunable by adjusting the resonance of dielectric nanocavity. The cases with experimentally feasible structures will also be discussed.

2. Methods

The simulations were carried out by using commercial finite-difference time-domain (FDTD) software (Lumerical FDTD). The mesh size around the antenna structures is 0.5*0.5*0.5 nm³. The excitation source is the Total-field scattered-field (TFSF) plane wave. The polarization is along the antenna. Perfectly matched layer (PML) boundary conditions were used in the simulations. The surrounding index for simulations is n = 1. The dielectric constants of the Au and Si are taken from Palik’s book [48].

The absorption cross section for a structure is obtained by normalizing the power flowing into the plasmonic nanoantenna structure by the plane wave intensity. In calculations, we set a power monitor box surrounding the nanoantenna (6 two-dimensional monitors in total), and then get the transmission of each monitor. The transmission function in the software returns the amount of power transmitted through a power monitor or a profile monitor, normalized to the source power. By adding the 6 transmissions and multiplied by the source area one can get the absorption cross section. The scattering cross section can be obtained in a similar way, where the only difference is that the monitors are placed in only scattered light region (for absorption, the monitors are in the total field region). The corresponding scattering power monitor box now covers both the plasmonic antenna and the dielectric structure. The extinction cross section equals the sum of absorption and scattering cross sections.

3. Results and discussion

We first investigate a hybrid system with a simple nanodisk as the dielectric nanocavity. Figure 1(a) shows the schematic of a coupled structure of a plasmonic nanoantenna and a dielectric nanodisk. The polarization of the normally incident plane wave is along the antenna (x-axis). The diameter and height of the dielectric disk are both 160 nm. The plasmonic nanoantenna consists of two identical Au nanorods. The total length and the diameter of each Au nanorod are 26 nm and 10 nm, respectively. The diameter of the hemisphere at both ends of the nanorod is 10 nm. The surface distance between the two nanorods is 5 nm, as shown in Fig. 1(a). A spacer is added between the antenna and the dielectric nanodisk. The height of the spacer is 5 nm, and its refractive index is n = 1.46. The refractive index of the dielectric nanodisk is taken to be n = 3.3 (e.g., GaP at proper wavelengths).

 

Fig. 1 Far-field optical responses and near field enhancement of a coupled system of a plasmonic nanoantenna and a dielectric nanodisk. (a) Schematic of a coupled structure under normal incident illumination. The polarization of the incident wave is along the antenna (x-axis). (b) The absorption spectra of the individual (black) and coupled (red) plasmonic antenna, and the scattering spectrum of the individual dielectric disk (blue). The scattering of the disk is multiplied by 0.1 for clearer comparison. (c, d) The resonant electric near-field profiles on the y = 0 plane of (c) the individual dielectric disk at λ = 615 nm and (d) the coupled system at λ = 637 nm. The dashed lines show the outline of the disk. (e) Electric field enhancement at the center of the Au antenna in the coupled system (red). The case for the individual Au antenna (black) is also shown for comparison.

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The individual nanodisk shows a main peak at λ = 615 nm on its scattering spectrum (Fig. 1(b)), which is dominated by a magnetic dipole resonance. Similar results have been demonstrated in many other works [30,38]. This strong far field resonance usually corresponds to a considerable electric field enhancement around the entire structure as shown in Fig. 1(c). Such a spatial feature of the field distribution indicates that the dielectric disk could facilitate the optical responses of a small plasmonic structure placed nearby. The plasmonic nanoantenna has a hybridized mode of two electric dipole plasmon resonances of the rods [2,47], and the hybridized mode is near λ = 600 nm which is around the magnetic dipole mode of the nanodisk (Fig. 1(b)). Due to the small size of the Au antenna, its absorption cross section is much larger than its scattering cross section [49].

Let us turn to the coupled structure of the plasmonic nanoantenna and the dielectric nanodisk. The absorption spectrum of the plasmonic antenna in the coupled structure is shown in Fig. 1(b). Compared to the individual antenna, the resonant absorption cross section of the Au antenna in the coupled structure is obviously enhanced. This enhancement can be understood by the fact that the effective excitation field felt by the Au antenna is larger than that of the plane wave. As expected, the electric near field around the Au antenna in the coupled structure is also obviously enhanced. Figure 1(d) shows the resonant electric field distribution (λ = 637 nm) of the coupled structure on the y = 0 plane. The field around the Au antenna still shows a typical profile of an individual two-wire antenna. The resonant electric field enhancements at the gap center for the coupled and individual Au antenna are around 80 and 25, respectively (Fig. 1(e)). The field enhancement of the coupled structure is more than 3 times higher than that of the individual Au antenna. A redshift of the resonance of the Au antenna in the coupled structure is noticed (Fig. 1(e)). This is due to the fact that a plasmon resonance redshifts with the surrounding index. It can be easily verified that a dielectric disk with the electric dipole resonance cannot efficiently enhance the electric field of the Au antenna. This is due to the fact that there is almost no electric field enhancement on the top of the disk with the electric dipole resonance.

We have demonstrated that the electric field enhancement around the dielectric nanodisk can facilitate the electric near field of a small Au antenna (Fig. 1), and the relative field enhancement for the antenna is ~3. The electric near field should be further enhanced if a small plasmonic nanoantenna is placed near a dielectric nanostructure with larger field enhancement. It has been shown that a dielectric disk−ring structure has efficient magnetic and electric field enhancements around it [38]. Therefore, it could serve as a good candidate for the further enhancement of the electric near field of a plasmonic antenna. Figure 2(a) illustrates a schematic of such a coupled structure under normal incident illumination. The polarization of the incident wave is along the x-axis. The radius and height of the dielectric disk are 75 and 210 nm, respectively. The inner and outer radius of the dielectric ring are 𝑅_𝑖𝑛 = 270 and 𝑅_𝑜𝑢𝑡 = 450 nm, respectively. The height of the ring is also 210 nm. The refractive index of disk and ring are both n = 3.3. A spacer is added between the antenna and the dielectric nanodisk. The height of the spacer is 5 nm, and its refractive index is n = 1.46. The Au antenna is the same as that in Fig. 1. With the chosen geometric parameters, the dielectric disk−ring structure shows a sharp resonance peak around λ = 637 nm on its scattering spectrum (Fig. 2(b)). The resonant electric field distribution is indeed larger than that of an individual dielectric nanodisk (Figs. 1(c) and 2(d)). For the Au antenna in the coupled structure, an absorption peak appears around the resonance of the dielectric disk−ring (λ = 637 nm) and its magnitude is greatly enhanced (Fig. 2(c)). Although the Au antenna is greatly affected by the dielectric structure, the influence of the Au antenna on the dielectric structure is negligible (Fig. 2(b)). This is because the resonant response of the individual plasmonic antenna is much weaker than that of the dielectric disk−ring structure. Thus, the resonance position of the coupled Au antenna is determined by the dielectric nanostructure.

 

Fig. 2 Far-field optical responses and near-field enhancement of a coupled system of a Au nanoantenna and a dielectric disk−ring structure. (a) Schematic of the coupled structure under normal incidence. The polarization of the incident wave is along the x-axis. The Au antenna is the same as that in Fig. 1. (b) The extinction spectra of the individual disk−ring (black) and the coupled structure (red). (c) The absorption spectra of the individual (black) and coupled (red) Au antenna. The absorption of the individual antenna is multiplied by 10 for clearer comparison. (d) The electric near-field profiles on the y = 0 plane of the coupled system (top) and the individual dielectric disk−ring structure (bottom). The wavelength is λ = 637 nm. The dashed lines show the outline of the dielectric structures. (e) Electric field enhancement at the gap center of the individual (black) and coupled (red) Au antenna. The case for the Au antenna on a substrate (blue) is also shown for comparison.

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Figure 2(d) shows the electric near field enhancement of the coupled system (top) and the individual dielectric disk−ring structure (bottom) at the resonance wavelength of λ = 637 nm on the y = 0 plane. One observes a huge enhancement of local electric field in the gap of the Au antenna. This is due to the combination of field enhancement of the dielectric structure with that of the Au antenna. Figure 2(e) shows the electric field enhancement at the gap center of the Au antenna in the coupled system (red line), and it is denoted by |$E_C$|/|$E_0$|. It reaches a value around 382 at the peak. This peak value is about 15 times higher than that of the individual plasmonic antenna (black line). Note that the height of the spacer also affects the electric field enhancement at the center of the Au antenna. So, we change the height of the spacer to perform simulations and find that the maximal |$E_C$|/|$E_0$| is achieved when the spacer has a height of 5 nm. And this will be the default height for the spacer.

From Fig. 2(d), one finds that the relative enhancement value 15 is larger than the field enhancement provided by the dielectric disk−ring. In order to better understand the role of dielectric structure in the coupled system, we carried out more calculations. It is found that the dielectric structure plays two roles in the coupled system. The first one is that the dielectric structure can provide an enhanced local field which works as the amplified excitation field for the Au antenna. The other one is that the dielectric substrate can cause the redshift of the resonance of the Au antenna, where the field enhancement of the antenna can also be modified correspondingly. To quantitatively characterize the influence of dielectric substrate on the field enhancement of an antenna, we calculate the situation where a Au antenna is placed on an infinite cylinder. The corresponding electric field enhancement at the gap center of the antenna is denoted by |$E_{\text{C}}^{\text{sub}}$|/|$E_0$|. And we use |$E_{\text{C}}^0$|/|$E_0$| to denote the field enhancement at the gap center of an individual Au antenna. Figure 2(e) shows the |$E_{\text{C}}^{\text{sub}}$|/|$E_{\text{C}}^0$| spectrum of the Au antenna on substrate. The field enhancement is increased with substrate (|$E_{\text{C}}^{\text{sub}}$|/|$E_0$|> |$E_{\text{C}}^0$|/|$E_0$|). Thus, the relative enhancement |$E_C$|/|$E_{\text{C}}^{\text{sub}}$| is smaller than |$E_C$|/|$E_{\text{C}}^0$|, and the value of the resonant |$E_C$|/|$E_{\text{C}}^{\text{sub}}$| (~8.5) is rational in comparison with the field enhancement provided by the individual dielectric disk−ring (Fig. 2(d)).

The resonant coupling between the plasmonic antenna and the dielectric disk−ring is important to obtain a high field enhancement. To illustrate this, we calculate the coupled structures with different lengths of the Au nanorod while the size of dielectric structure is fixed. Both the individual antenna and antenna on substrate show spectral redshift with the rod length (Figs. 3(a) and 3(b)). For each length, the spectrum of the coupled antenna−dielectric structure shows the same resonance position at λ = 637 nm (Fig. 3(c)). This is due to the fact that the dielectric disk−ring structure determines the resonance position of the coupled system as discussed before. For the length of 26 nm, where the Au antenna on substrate shows a resonance around λ = 637 nm which matches that of the disk−ring structure, the resonant field enhancement |$E_C$|/|$E_0$| reaches a maximal value (Fig. 3(c)). For the other lengths, the |$E_C$|/|$E_0$| decreases with the mismatch between the resonant positions of the dielectric disk−ring and the Au antenna on substrate.

 

Fig. 3 Electric field enhancements with different lengths L of each Au nanorod. The dielectric disk−ring is the same as that in Fig. 2. The diameter of each gold nanorod and the gap size are 10 and 5 nm, respectively. (a-c) Spectra of electric near field enhancement of (a) individual Au antennas, (b) Au antennas on substrate and (c) Au antennas in the coupled systems.

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Next, we investigate the resonant electric field enhancements with different geometries of the hybrid system. The configuration for each coupled system is the same as that in Fig. 2. For each case, one can calculate the resonant electric field enhancements at the center of the Au antenna for the coupled system (|$E_C$|/|$E_0$|), the individual Au antenna (|${\text{E}}_{\text{C}}^0$|/|$E_0$|) and the Au antenna on the substrate (|${\text{E}}_{\text{C}}^{\text{sub}}$|/|$E_0$|), respectively. Then the relative field enhancements |$E_C$|/|${\text{E}}_{\text{C}}^0$| and |$E_C$|/|${\text{E}}_{\text{C}}^{\text{sub}}$| can be both obtained. Figure 4(a) shows the results with varying the gap distance between the two Au nanorods from 3 nm to 12 nm. For the sake of comparison, we restrict the resonant wavelength to be λ = 637 nm for each gap, and the length L of the Au nanorod is optimized to obtain the maximal resonant |$E_C$|/|$E_0$| similar to that in Fig. 3. In other words, this can be done by turning the length of Au nanorod to make the resonance of the antenna on substrate match a given resonant wavelength (λ = 637 nm). The other geometries are the same as that in Fig. 2. The resonant |$E_C$|/|$E_0$| (black) increases dramatically with decreasing the gap distance between the two Au nanorods. The main reason is that the field enhancement of individual Au antenna |${\text{E}}_{\text{C}}^0$|/|$E_0$| (or antenna on substrate|${\text{E}}_{\text{C}}^{\text{sub}}$|/|$E_0$|) increases significantly with decreasing the gap [47]. The corresponding relative electric field enhancements |$E_C$|/|${\text{E}}_{\text{C}}^{\text{sub}}$| and |$E_C$|/|${\text{E}}_{\text{C}}^0$| keep almost the same value around ~8.5 and ~15, respectively, with different gap sizes.

 

Fig. 4 Electric field enhancement with varying the geometries of the coupled system. (a, b) Resonant electric field enhancement |$E_C$|/|$E_0$| of the Au antenna in the coupled system (black) and the corresponding relative enhancements (|$E_C$|/|${\text{E}}_{\text{C}}^0$|, blue; |$E_C$|/|${\text{E}}_{\text{C}}^{\text{sub}}$|, red) as a function of (a) the gap distance between the two Au nanorods and (b) the diameter of each Au nanorod. The dielectric disk−ring structure is the same as that in Fig. 2. For each case, the length L of the Au nanorod is optimized to obtain the maximal resonant |$E_C$|/|$E_0$|. (c) Resonant |$E_C$|/|$E_0$| (black), |$E_C$|/|${\text{E}}_{\text{C}}^0$| (blue) and |$E_C$|/|${\text{E}}_{\text{C}}^{\text{sub}}$| (red) as a function of the resonant wavelength of the dielectric disk−ring structure. The length of the Au nanorod is also optimized to obtain the maximal resonant |$E_C$|/|$E_0$| for each case.

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Figure 4(b) shows the results with varying the diameter of Au nanorod from 5 nm to 22 nm. We also restrict the resonant wavelength to be λ = 637 nm for each case, and the length L of the Au nanorod is also optimized to obtain the maximal resonant |$E_C$|/|$E_0$|. Thus, the corresponding length of the Au nanorod increases with its diameter. The other geometries are the same as that in Fig. 2. The resonant |$E_C$|/|$E_0$| of the coupled system reaches maximal (~400) at 12 nm, and it changes slowly in the range from 10 to 22 nm. On the other hand, the relative field enhancements (|$E_C$|/|${\text{E}}_{\text{C}}^{\text{sub}}$| and |$E_C$|/|${\text{E}}_{\text{C}}^0$|) decrease with the diameter of Au antenna. This is understandable based on the electric field distribution around the dielectric disk−ring in Fig. 2(d). As the diameter (size) of the Au antenna increases, the average amplified excitation field felt by the antenna, which is provided by the dielectric disk−ring, decreases. For the behavior of the resonant |$E_C$|/|$E_0$|, the leading factor is the Au antenna itself as its resonant |${\text{E}}_{\text{C}}^0$|/|$E_0$| (or |${\text{E}}_{\text{C}}^{\text{sub}}$|/|$E_0$|) also shows a maximal value with a certain size [47]. The combination of the two factors, namely the |${\text{E}}_{\text{C}}^0$|/|$E_0$| behavior and the amplified field around the dielectric disk−ring, leads to the maximal |$E_C$|/|${\text{E}}_{\text{C}}^0$| at the diameter of 12 nm.

We also investigate the coupled systems with different working (resonant) wavelengths (Fig. 4(c)). For simplicity, we take the refractive index of the dielectric structure to be n = 3.3 for the investigated wavelength range. It is known that the resonant position of the dielectric disk−ring can be turned by changing the size of the structure [38]. The plasmon resonance of the Au antenna can be turned by varying the length of the nanorod for a given diameter which is fixed at 10 nm here. The resonant wavelengths are from 607 to 730 nm in Fig. 4(c). The length of the Au nanorod is also optimized to obtain the maximal resonant |$E_C$|/|$E_0$| (black) for each working wavelength. The relative enhancements |$E_C$|/|${\text{E}}_{\text{C}}^{\text{sub}}$| are almost the same with different working wavelengths. When the length of Au nanorod increases with the resonant wavelength, the size of the disk−ring and the corresponding size of the amplified field also increases. So the |$E_C$|/|${\text{E}}_{\text{C}}^{\text{sub}}$| does not show a decrement with the length of Au nanorod. On the other hand, the resonant |$E_C$|/|$E_0$| increases with working wavelength. This is mainly due to the fact that the Au antenna shows an increasing |${\text{E}}_{\text{C}}^0$|/|$E_0$| and |${\text{E}}_{\text{C}}^{\text{sub}}$|/|$E_0$| with working wavelength [47]. It can be easily verified that our hybrid configuration works well for antenna of a single nanorod too, where the near field around the nanorod can be increased a lot.

We also consider some experimentally feasible situations, where the antenna−dielectric hybrid structure is placed on a substrate. Figure 5(a) shows the schematic of such a system. The substrate is taken to be SiO₂ with the refractive index of n = 1.46. The antenna−dielectric coupled structure is the same as that in Fig. 2. A SiO₂ spacer is placed between the coupled structure and the substrate. The thickness of the spacer is 150 nm. Figure 5(b) shows the electric field enhancement at the center of the Au antenna in the coupled structure (|$E_C$|/|$E_0$|, red) and that of the individual Au antenna (|${\text{E}}_{\text{C}}^0$|/|$E_0$|, black). The resonant |$E_C$|/|$E_0$| in the coupled structure reaches 310, and this enhancement is 12 times higher than that of the individual antenna. Compared to the situation without substrate (Fig. 2), the electric field enhancement with substrate decreases from 382 to 310, but it can still maintain a relatively high value (more than 80%). The electric near-field profiles are also calculated (Fig. 5(c)), and they are similar to the situation without substrate (Fig. 2(d)). More calculations show that the |$E_C$|/|$E_0$| decreases even more when there is no spacer between the antenna−dielectric coupled structure and substrate. Next, we consider the widely investigated silicon (Si) as the material for the dielectric disk−ring structure and its refractive index is taken from Palik’s book [48]. Figure 5(d) shows the schematic of the system. The configuration of the coupled system is the same as that in Fig. 5(a). We also use SiO₂ as the spacer. The resonance of the Si structure can be turned by varying the geometries [38]. Here we also choose the working wavelength around λ = 637 nm for the sake of comparison. The radius and height of the Si disk are 63 and 180 nm, respectively. The inner radius, outer radius and height of the ring are $R_{in}$ = 300, $R_{out}$ = 456, and H = 180 nm, respectively. The spacer between the Si structure and the substrate is 150 nm in height. As expected, a high electric field enhancement ~220 times appears at the peak in such a coupled structure (red line in Fig. 5(e)). The Si is less efficient for local electric field enhancement compared to the former dielectric material (n = 3.3). This is mainly due to the absorption loss of Si in the visible range.

 

Fig. 5 Experimentally feasible Au antenna−dielectric disk−ring coupled systems. (a) Schematic of a coupled system with substrate. The refractive index of substrate is n = 1.46. The coupled structure of the antenna and dielectric disk−ring is the same as that in Fig. 2. (b) Electric field enhancement at the center of the Au antenna in the coupled structure on the substrate. The case for the individual antenna (black) is also shown for comparison. (c) The electric near-field profiles on the y = 0 plane of the coupled structure on the substrate (top) and the dielectric structure with substrate (bottom). The wavelength is λ = 637 nm. The dashed lines show the outline of the structures. (d), (e) and (f) show the same contents as that in (a), (b) and (c), respectively. But the material of the dielectric disk−ring structure is now replaced by Si.

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We have focused on the local field enhancements of the coupled systems with Au as the material for the nanoantennas. Now let us turn to the coupled system with silver (Ag) nanoantennas. For simplicity, we also choose a working wavelength at λ = 637 nm. The configuration is the same as that in Fig. 2, and the only difference is that we here replace the Au antenna with a Ag one. The radius of each Ag nanorod is 5 nm, and their distance is still 5 nm. The length of each Ag nanorod is 32 nm to match the resonance at λ = 637 nm. Figure 6(a) shows the electric near-field profiles on the y = 0 plane of the coupled system (top) and the individual dielectric disk−ring structure (bottom). There is obvious electric field enhancement in gap of the Ag nanoantenna, which is similar to that of Au antenna (Fig. 2). Figure 6(b) provides the electric field enhancements |$E_C$|/|$E_0$|, |${\text{E}}_{\text{C}}^0$|/|$E_0$| and |${\text{E}}_{\text{C}}^{\text{sub}}$|/|$E_0$| calculated at the center of the Ag nanoantenna in three different situations similar to that in Fig. 2(e). The resonant field enhancement |$E_C$|/|$E_0$| of the coupled system reaches a value around 560 times. This value is even higher than the Au case (382). This is because the field enhancement |${\text{E}}_{\text{C}}^0$|/|$E_0$| of the individual Ag antenna is higher than the Au one. The corresponding resonant relative field enhancements are |$E_C$|/|${\text{E}}_{\text{C}}^0$| ≈8.5 and |$E_C$|/|${\text{E}}_{\text{C}}^{\text{sub}}$| ≈6.5, respectively.

 

Fig. 6 The near field enhancement of a coupled system of a Ag nanoantenna and a dielectric disk−ring structure. The configuration of the coupled system is the same as that in Fig. 2. The material and length of the plasmonic nanoantenna is now changed to Ag and L = 32 nm, respectively. (a) The electric near-field profiles on the y = 0 plane of the coupled system (top) and the individual dielectric disk−ring structure (bottom). The wavelength is λ = 637 nm. The dashed lines show the outline of the dielectric structures. (b) Electric field enhancements at the center of the individual (black) and coupled (red) Ag antenna. The case for the Ag antenna with substrate (blue) is also shown for comparison.

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4. Conclusion

In conclusion, we have demonstrated that ultrahigh electric field enhancement can be obtained in plasmonic nanoantenna−dielectric nanocavity hybrids. In a hybrid system, the nanocavity is a concentric disk−ring structure which has a size of one wavelength scale and a refractive index of n = 3.3, and the nanoantenna is a Au nanorod dimer with a gap size 5 nm. The resonant electric field enhancement at the gap center of the antenna in the hybrid system reaches 382-fold, which is about 15 times higher than that of the individual antenna. It is found that the dielectric structure plays two roles in the hybrid system. They are the amplified excitation field and an environment that causes the redshift of the antenna resonance. The corresponding field enhancement |$E_C$|/|$E_0$| depends on two factors, namely the relative enhancement and the field enhancement of the single antenna. For a given dielectric structure, the relative enhancement is related to spatial overlap between the antenna and the amplified excitation field provided by the dielectric structure. The hybrid strategy is applicable to the cases with various geometries and different materials of the hybrid system including experimentally feasible cases. It is reasonable to expect that even higher electric field enhancement can be obtained in plasmonic nanoantenna−dielectric nanocavity hybrids with higher field enhancement around a carefully designed dielectric nanocavity.