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Metal antennas-substrate coupled structures have unique features of strong nanoscale light confinement and field enhancement at the gap, which make them attractive and promising in a variety of applications such as sensing, lasing, and solar cell. Here, we built a coupled system consisting of a gold spherical semishell antenna and gold substrate. Through numerical simulation, it is found that due to the unique geometric shape of the antenna, the near-field enhancement area of the localized resonance is enlarged dramatically in the designed plasmonic structure, which is beneficial to increasing the active region, allowing more molecular adsorbed and also replaced easily. Moreover, the far-field extinction spectra of the localized dipole mode in the designed structure has higher quality factor and is more robust to the gap separation than its solid counterpart, which may relax the fabrication tolerances.
© 2015 Optical Society of America
1. Introduction
Metal plasmonic nanoantennas, the properties of which are essentially determined by their resonance modes, are of interest for both fundamental studies and various applications. Antennas with various compositions, shapes and geometries have been demonstrated, each possessing unique properties and potential applications. The near-field coupling of two or more nanoantennas with nanometer-sized separations provides an additional degree of freedom to manipulate the plasmonic activity of the nanoantennas [1–5]. It causes the formation of plasmonic gap modes with localized “hot spots”, which can significantly improve performance of molecular sensors and solar cells. Fine tuning of the separations between coupled metal nanoantennas is an important way to realize specific optical response. However, it is a technological challenge on nanometer scale.
An alternative system consisting of a metal antenna separated from a metal film/substrate can also lead to the mode coupling. It has the advantage of easily fabrication with well-defined spacing. Many literatures have reported the mode coupling characteristics in the metal nanoantenna-substrate coupled system [6–19]. It can be depicted as a coupling between the metal nanoantenna dipole/multi-pole and its image, giving rise to the formation of the symmetric or anti-symmetric mode [8, 9]. P. Nordlander et. al. have described concisely the interaction between particle plasmon resonance and the surface plasmon of a metallic film as a tunable impurity problem, in analogue of the spinless Anderson-Fano model which used to depict the interaction of a localized electronic state with a continuous band of electronic states [11,12].
When metal antennas are arranged periodically, propagating surface plasmon modes (PSP) on the metal substrate will also be evolved due to the overcoming of momentum mismatch by the grating vectors. Strong coupling between guided surface plasmon and the dipole/multi-pole mode of nanoantenna may lead to the anticrossing behavior with a large Rabi splitting energy, forming new hybridized states with different resonance energies and localized field distributions [13, 20,21]. Generally, all these modes coupling can lead to high field enhancements and the resonance quality factor improvement, which are critical for applications like lasing [22], solar cells, sensing [13,23,24], and SERS [25, 26]. However, in most of the metal nanoantenna-substrate coupling systems, hot spot with enormous near-field enhancement factor occurs at the gap, which is usually very narrow. In some specific applications such as sensing or SERS, it may be difficult to localize molecules selectively only at the gap and allow for adsorbing or replacing molecules easily. On the other hand, for application in solar cells, it is beneficial to accommodate more active material at the near-field. So the active region with high E field enhancement near nanoantennas is desired.
Here, we proposed a metal antenna-substrate coupling system consisting of a metal semispherical nanoshell (SNS) as the nanoantenna. By simulating the plasmonic near-field distribution and far-field spectral characteristics of the coupled system and comparing with its solid counterpart, i.e., metal semisphere-substrate system, it is found that large energy concentration with huge field enhanced area can be formed around the metal nanoantennas thanks to the peculiar geometric shape of the SNS. It is beneficial for huge amount of active material accommodation and easily replacement, which is highly applicable in sensing, SERS spectroscopy, solar cells or other fields.
2. Structure and simulation
The proposed metal nanoantenna-substrate structure is illustrated schematically in the inset of Fig. 1(a). The inner (r2) and outer radius (r1) are used to describe the size of the SNS antenna, and they are 50 nm and 70 nm, respectively. The thickness of the semi-shell (r1-r2) is 20 nm. The thickness of the metal film is set at 100 nm, which can be regarded as a metal substrate with an infinite thickness. The gap between the nanoantenna and the metal film is controlled by the thickness of the inserted dielectric layer. It is selected as SiO2 with the refractive index of 1.47. To compare the mode coupling in different systems, the plasmonic properties of the solid counterpart of SNS, a semi-sphere with the radius of r1 = 70nm (schematically shown in the inset of Fig. 1(b)), were also computed. The structures were both excited by a linearly polarized plane wave at normal incidence. Finite difference time domain (FDTD) method [27] was used in the numerical computation of the extinction, absorption, reflection spectra and electric field distribution, including both x-polarized and z-polarized incidence. The refractive indexes of the metal (Au) and the substrate (SiO2) used in the computation were the fitting results to the experimental values from reference [28] using Lorentz-Drude model done by Lumerical software. Perfectly matched layer (PML) were used at the boundaries. The total field/scattered field (TFSF) source implemented in the software was used as excitation source for the extinction (sum of scattering and absorption) efficiency calculation.
Fig. 1 Extinction spectra of isolated SNS and SNS-substrate coupled system (a) and solid semisphere-substrate coupled system (b) with different gap distances, inset: schematic illustration of the SNS-substrate coupled structure and semisphere-substrate coupled structure. (c) Resonance energy shift of SNS and solid semisphere coupled system with different gap.
3. Results and discussions
Figure 1(a) show the extinction spectra evolutions of a SNS coupled with the Au substrate. The gap between SNS and substrate was varied from 0 nm to 50 nm. As illustrated, a pronounced extinction band situated at 670 nm is observed for a separated SNS. After the SNS is coupled with the gold substrate, the extinction band redshifts, with the width narrowed obviously. Figure 1(b) demonstrates the extinction spectra of a solid semisphere-substrate coupled system. A resonance band is observed at 560 nm for a single semisphere. It also exhibits red shift after coupling with gold film. The plasmonic resonance peaks as a function of the nanoantenna-substrate gap distance are summarized and compared in Fig. 1(c). As shown, with the decrease of the gap, an obvious red-shift of the extinction band is observed for the solid semisphere-substrate coupled system. This shift corresponds to what is predicted in refs [8–10] for resonance of a nanoparticle as it is moving towards a metal film. The mode energy shift results from image-like interactions between the nanopaticle and the metal film, following a z−3 behavior, where z is gap distance. In comparison, the shift of the resonance energy is slight for a SNS-gold film coupled structure.
Figure 2(a)-(d) illustrate the E field distributions of the two different coupling structures with a gap distance of 10 nm. The excitation wavelength is at their respective plasmon resonance peak. The scales are the same for all the figures. From the E field distributions of the SNS-substrate coupled structure showed in Figs. 2(a) and 2(b) (x, z-polarized incidence respectively), it can be confirmed that the resonance absorptions observed in Fig. 1 are related to a dipole plasmon oscillation. For z-polarization, enormous enhanced field was observed inside the SNS. For x-polarization, besides the dipole characteristic field confined near the outer surface, intensive E field was also observed at inner space of the SNS. In comparison, from the E field distributions of the semisphere-substrate coupled structure showed in Figs. 2(c) and 2(d), large field enhancement was observed only near the gap and the outer space of the solid semisphere.
Fig. 2 E-field distribution of SNS-substrate coupled system under (a) z-polarized (b) x-polarized incidence; E-field distribution of semisphere-substrate coupled system under c) z-polarized (b) x-polarized incidence; Two dimensional area with different enhancement factors (e) z-polarized (f) x-polarized incidence.
To compare the E intensity distribution in detail, we classified the E field enhancement factors into three levels: E/E0 = 10, 15 and 20, where E is the field intensity near the structure, and E0 is field of the incident light. The areas with different levels of enhancement factors were calculated from the 2-dimensional maps shown in Figs. 2(a)-(d). The results were compared in Figs. 2(e) and 2(f) for z- and x-polarized incidence respectively. Obviously, the E field enhancement factors under x-polarized incidence are larger than those under x-polarized incidence by about 2 orders of magnitude. Under z-polarized incidence, the area of SNS does not show superiority over that of semisphere coupled structure. However, for x-polarized incidence, the enhanced areas for SNS are always larger than those of semisphere for the three different enhance factors levels. There are about 2-fold increase in the enhanced area for the SNS-substrate coupled system.
As we know, metal nanoantenna-substrate coupling system represents a highly tunable plasmonic structure with large local electric field enhancement, always accompanied by resonance plasmon resonance band shift or splitting. However, we have calculated SNS-substrate coupled system with different size SNS (not shown here), and similar results as those shown in Figs. 1 and 2 were obtained: enhanced field intensity with increased area and ignorable extinction band shift. It seems that the resonance energy is robust to the gap change due to the unique SNS shape. As we know, the extinction efficiency of the nanoantenna is given by the sum of the absorption efficiency and the scattering efficiency:
Where k is the wave vector in the ambient; is the polarizability, which is defined such that the complex amplitude of the polarization vector of the nanoantenna: .From image dipole model, assuming the nanoantenna as a polarizable dipole, an image dipole is induced in the film in response to the presence of a nanoantenna. The in-plane (parallel to the film) dipole moments of the image are opposite to those of the nanoantenna. For a solid semisphere, the image dipole weakens the restoring force of the antenna dipole. The effect became stronger with the decrease of the gap, inducing a continuous red-shift of the extinction band. In the case of the SNS, as the charge distribution shown in Fig. 3, the dipole mode can be assumed as a symmetric hybridization of two dipole plasmons; one for the outer surface P1 (particle plasmon) and another for the inner surface P2 (cavity plasmon) [29]. With the change of the gap, the force exerted by image dipole will alter P1 oscillation, but its effect on P2 is ignorable because the cavity plasmon does not depend on the influence from outside the shell [12]. Then the total polarization P change induced by the image dipole is small, and the plasmon extinction band shift is slight as the gap decreases. Moreover, it is worth noting that the presence of the inner surface polarization P1 gives rise to the large near field enhancement inside the SNS.
Fig. 3 (a) Charge distribution of SNS-substrate coupled system at dipole resonance. (b) Schematic illustration of the dipole mode and image mode of the SNS-substrate coupled system.
Next, the SNSs were placed onto gold film in a square array to investigate the interaction between the PSP and the dipole plasmon mode. The gap between the SNS array and gold films is 10 nm. The optical reflection spectra as a function of period and wavelength were calculated and shown in Fig. 4(a). The dashed line indicates the dipole resonance wavelengths of an isolated antenna. Two dark reflection branches corresponding to the lowest PSP modes (1, 0) and (1, 1) were also indicated. An anticrossing behavior can be observed clearly when the resonance wavelengths of the isolated SNS and the PSP are approximately equal, at a period of about 700 nm for the (1, 0) PSP mode. The anticrossing implies strong coupling between the PSPs and dipole mode. Similarly, the reflection spectra profile of the semisphere array-substrate coupled system is shown in Fig. 4(b). Anticrossing behavior was also observed. It occurs at a period of 600nm for the (1, 0) PSP mode.
Fig. 4 Reflection spectra profile versus different array period and wavelength of SNS coupled system (a) and semisphere coupled system (b).
Then, we compared the far field absorption spectra, defined as (1-reflection)), and near field distribution of the two coupled system at the period where the anticrossing behavior occurs. Figure 5(a) shows the selected absorption spectra for the SNS coupled system at an array period of 700 nm. Due to strong coupling at this period, two sharp absorption bands were observed. One at higher energy is indicated by peak i and another one by peak ii. Figure 5(b) and 5(c) are the E distributions at peak i wavelength with the incidence of z-and x-polarizations, respectively. Figure 5(d) and 5(e) are those at peak ii wavelength with the corresponding polarizations. At peak i, one can found that the enhanced field was localized around the SNS. Whereas, at peak ii, energy delocalized along the substrate can be seen at x-polarization. So the resonance at peak i arises mainly from the localized dipole resonance of the gold SNS, and the resonance at peak ii can be attributed mostly to the (1, 0) PSP mode on the gold film. The near-field intensity for the SNS array-substrate coupled system in Fig. 5(b) is increased obviously compared to that of the isolated SNS-substrate coupled system in Fig. 2(b), indicating that the interaction of the PSP and dipole mode can further enhance the near-field intensity.
Fig. 5 (a) Selected absorption spectra of SNS coupled system; E-field distribution at absorption peak i for (b) z- and (c) x-polarized incidence; E-field distribution at absorption peak ii for (d) and z- and (e) x-polarized incidence. The array period is 700 nm.
Figure 6(a) shows the selected absorption spectra of the semisphere array coupled systems. The period is 600 nm where anticrossing occurs for this system. Figures 6(b)-(e) demonstrate the corresponding E distribution for peak i and ii with different polarizations. In analogy to SNS in Fig. 5, peak i is related to localized dipole resonance, and peak ii is related to PSP mode. Since the near-field intensity distribution at the localized resonance is what we concerned about, so the E distributions at peak i are compared. As before, the two-dimensional E field distributions in Figs. 5(b), 5(c) and that in Figs. 6(b), 6(c) were classified in three different levels. Figures 7(a) and 7(b) are the area comparisons for z- and x-polarization respectively. To study the influence from PSP-LSP coupling, the results for three different periods of 600 nm, 700nm, and 800 nm were included for the SNS array coupled system. Three observations are remarkable: first, compared to Fig. 2, the enhanced area is increased obviously after the metal antennas are arrayed periodically, especially for z-polaried incidence. It is enlarged by about 103 times. Second, the near-field intensity distribution is dependent on the period. The maximum area is obtained at 700 nm period for SNS where anticrossing occurs. Third, for semisphere array on gold film with a period of 600 nm, the enhanced areas of the three levels of enhancement factors are all much smaller than those of SNS coupled system. For example, in the case of enhancement factor of E/E0 = 15 at z-polarization, the area for SNS at period 700nm is about 102 times as large as that of semiphere array coupled system.
Fig. 6 (a) Selected absorption spectra of semisphere coupled system; E-field distribution at absorption peak i for (b) z- and (c) x-polarized incidence; E-field distribution at absorption peak ii for (d) z- and (e) x-polarized incidence. The array period is 600 nm.
Fig. 7 Comparison of the two-dimensional area with different enhancement factors of SNS and semisphere coupled structures for (a) z- and (b) x-polarized incidence.
Comparing the absorption spectra in Figs. 5 and 6, it was found that the absorption peaks at the localized dipole resonance (peak i) both reach around 1 for the two cases of coupled system, but the full width at half maximum (FWHW) of the peaks are different. It is about 17 nm for the SNS coupled system, which is narrower than that of the semisphere coupled system. It is in correspondence with the fact that that more energy is concentrated near SNS than near the solid sphere in the near-field distribution map. The higher scattering, which can be evidenced from the field distribution for the semisphere coupled system, induces energy dissipation and damping broadening in the far field spectra. Thus, the quality factor of the localized dipole resonance is higher for SNS array-substrate coupled system. Due to the unique shape of the SNS, localized plasmon mode with high quality factor and large near-field enhancement area was obtained, which means more molecular or active material can be accommodated for stronger signal, and also easier to change the molecular due to the open inner space. Moreover, the localized resonance has the merit of energy robust to the gap distance.
4. Conclusion
In summary, we have built a gold SNS-substrate coupled system, and the near and far-field properties were numerically simulated. Compared to the solid semisphere-substrate coupled system in which hot spot occurs at the gap, the designed structure possesses high near field enhancement with enlarged area. Additionally, due to the unique geometric shape of the SNS, the localized dipole mode is insensitive to gap distance which may relax the fabrication tolerance.
Acknowledgment
The authors express their appreciations to Zhejiang Provincial Natural Science Foundation of China (Q14A040006), Natural Science Foundation of Ningbo City (2015A61008) and Opening Fund of Key Laboratory of Infrared Imaging Materials and Detectors of Chinese Academy of Science (IIMDKFJJ-13-02). The author gratefully acknowledges the support of K. C. Wong Education, Hong Kong.
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