Plasmonic nanostructures with strong Fano resonance are of fundamental interest. Here, our systematic simulations show that rational positioning of a silver plasmonic heptamer above a highly reflective substrate mirror can significantly enhance its intrinsic Fano-resonance intensity. The silver nanodisk heptamer positioned at an appropriate distance above the reflective substrate enables 2.4 times field enhancement and 3.6 times deeper Fano-dip respectively compared to the heptamer directly placed on silicon oxide substrate. Besides, our results indicate that the Fano-dip position does not shift when the silver nanodisk heptamer gradually shifts away from the reflective substrate mirror (≥60 nm).
© 2017 Optical Society of America
Fano resonance, arising from the coherent interference of “bright” and “dark” plasmon modes and resulting in extinction features with narrow and asymmetric line shapes, has attracted much interest in recent years due to its various potential applications in biosensors, surface-enhanced Raman scattering (SERS) and plasmonic rulers [1–9]. The “bright” mode, possessing finite dipole moments, has a broad and superradiant spectrum due to the radiative damping. In contrast, the “dark” mode, possessing zero or nearly zero dipole moments, has a narrow and subradiant spectrum due to its inefficient coupling ability to incident light [10–12]. If the energy of “bright” and “dark” mode overlaps, the “dark” mode can be excited indirectly by near field coupling to optically excited “bright” mode . The energy exchange of two modes gives rise to a Fano resonance in the optical spectrum, which is significantly sensitive to the local dielectric environment .
Achieving the strongest possible Fano resonances and understanding the coupling behaviors of resonance modes are essential for the applications of Fano-type optical systems. In the past years, many efforts have been made to explore the optimal configuration and appropriate materials for generating pronounced Fano resonances. For example, Fano resonances have been demonstrated in numerous plasmonic systems such as ring-disk cavities, metamaterials, and coupled clusters of nanoparticles [3–6, 10–19]. As one of the most important planar plasmonic nanoclusters [14–18, 20–24], the nanoparticles heptamer can support Fano resonances due to the strong coupling between their superradiant and subradiant plasmon modes. Multiple nanoscale electromagnetic “hot spots” supported by the multi-gaps in the heptamer are highly sensitive to the change of their local dielectric environment, and has been utilized in developing ultrasensitive nanoscale sensors [13, 18, 25, 26]. Unfortunately, the Fano resonances of the heptamer still undergo many challenges such as low field enhancement factor and shallow Fano dip in applications. To further enhance the light-matter interactions, a possible approach is to introduce a reflective metallic mirror in plasmonic systems. For example, many studies demonstrated that suitable positioning of plasmonic antenna above a reflective substrate can enhance its optical properties through constructive interference of scattered waves [27–33].
In this work, we investigate the Fano resonance behavior of plasmonic heptamers that are located on a reflective mirror separated by a dielectric spacer. Systematic numerical studies indicate that the Fano resonance, produced by the interference between “bright” and “dark” modes in plasmonic heptamer, can be significantly enhanced by the reflective mirror through the interference of the scattered wave from the heptamer itself and the reflective metallic mirror. With optimized spacer thickness, the Fano-dip depth and field enhancement factor of this system is almost 3.6 and 2.4 times higher respectively compared to the bare planar plasmonic heptamer. Besides, in such a hybrid plasmonic system, the “dark mode” dominated Fano dip has a fixed position when the distance between the heptamer and reflective mirror increases gradually from 60 nm to 420 nm, which is different from the shifting trend of the “bright mode”-dominated resonance peak position. Therefore, our study provides a solution using metallic substrate to enhance field enhancement factor and dip depth of Fano resonances even further without modifying the geometry of the plasmonic structures and the Fano dip position, which may find potential applications in surface-enhanced spectroscopy and plasmonic rulers.
2. Structure and simulation methods
Figure 1 schematically illustrates the designed symmetric planar Ag plasmonic nanodisk heptamer consisting of a large nanodisk (with diameter of 90 nm, labeled as D1) and six small nanodisks (with diameter of 80 nm, labeled as D2) with an interparticle distance L (L = 100 nm) located on a reflective substrate. The thickness of all Ag plasmonic disks is set to be 30 nm. The reflective substrate is comprised of SiO2/Ag/SiO2 triple-layer film stacks, in which the SiO2 layer between Ag film and Ag heptamers is used as a spacer layer with a variable thickness H, the Ag film is used as a reflective mirror with a fixed thickness h (h = 60 nm, which is optically thick), and the SiO2 layer under the Ag film is a support film with infinite optical thickness. Experimentally measured refractive index data of Ag (Johnson and Christy) and SiO2 (Palik) was used for the numerical calculations [34, 35]. The polarization of electric field E is parallel to a specific interparticle axis shown in Fig. 1 (i.e. y-polarized incidence), and the wave vector k of incident light is perpendicular to the substrate. Both finite difference time domain method (FDTD, Lumerical Solutions, used for calculating all the spectra and electric field distribution of plasmon modes) and finite element method (FEM, Comsol Multiphysics, only used for calculating the surface charge distribution of plasmon modes) were used for simulations. In Lumerical Solutions, the simulation space is rectangular (X span = Y span = Z span = 1500 nm). Both the optical spectra and electric field profiles were obtained using a TFSF source with spectral range from 300 nm to 900 nm. An override 3 nm mesh around the structures was used and perfectly matched layer (PML) boundary condition was set for all three dimensions. The substrate was extended to the edge of the simulation space, and the total scattering cross sections were obtained by integrating the scattered power flux over an enclosed surface outside the TFSF source. In Comsol Multiphysics, we used a plane wave source to calculate the surface charge distribution by the boundary value expression of electromagnetic field, and other conditions were similar to those used in Lumerical Solutions.
3. Results and discussion
To investigate the reflective-substrate-enhanced Fano resonance in Ag plasmonic heptamer, we first systematically calculated the optical scattering spectrum of the Ag heptamer placed on a bare SiO2 substrate without the reflective layer [Fig. 2(a)] and the result is shown in Fig. 2(b). Two obvious scattering peaks (i and iii) and an obvious Fano dip (ii) in scattering spectrum indicate that two plasmon resonance modes with strong coupling exist in the Ag heptamer. To understand the origin of the above-mentioned plasmon-resonance modes, we analyzed the charge distribution (i-iii) and field distribution (iv-vi) at different characteristic wavelengths, and the results are shown in Fig. 2(c). In the heptamer nanostructure, the dipolar plasmon of large central nanodisk hybridizes with that from the hexamer of the other six small nanodisks, resulting in a “bright” superradiant plasmon mode and a “dark” subradiant plasmon mode. For the “bright” superradiant mode, dipolar plasmons of all nanodisks oscillate in phase and in the same direction, and it exhibits an extremely broad spectrum due to large radiative damping. It is noteworthy that the peak position of the “bright” superradiant mode cannot be exactly determined from the scattering spectrum due to the strong coupling between the “bright” and “dark” modes. But, the in-phase charge distribution of two scattering peaks [Fig. 2(c), i and iii] is an indication for the “bright” superradiant mode. For the “dark” subradiant mode, the dipolar moment of the center nanodisk opposes the dipole moment of the surrounding six satellite nanodisks [Fig. 2(c), ii], leading to a narrow mode due to zero or nearly zero dipole moments. Therefore, the formation of the distinct Fano dip in the scattering spectrum [Fig. 2(b), ii] is due to the destructive interference between the narrow “dark” subradiant mode and the broad “bright” supperradiant mode. We also examined how the coherent Fano dip of the Ag plasmon heptamer is affected by the size (D1) of central nanodisk, as shown in Fig. 2(d). For the smallest central nanodisk (D1 = 50 nm), the Ag heptamer exhibits a single plasmon resonance near 550 nm, which is the “bright” superradiant bonding mode dominated by six surrounding nanodisks. The “dark” subradiant antibonding mode is subdued due to the small scattering cross section of central nanodisk and the weak near-field coupling between center-disk and hexamer. For larger central nanodisk (D1 = 70 nm), the bright mode is slightly red shifted and broadened due to the slightly increased radiation damping. A very weak Fano resonance (at nominally 550 nm) appears in the scattering spectrum of the cluster because the “dark” mode is activated by the increased near-field coupling between center-disk and hexamer. Both broadened and red-shifted spectra of the “bright” and “dark” modes were observed when increasing D1 to 100 nm in Ag plasmon heptamer due to the significantly increased near-field coupling and radiative damping. Meanwhile, deepened and strengthened Fano dip of Ag heptamer was obtained when increasing D1 due to the significantly activated “dark” mode, in which the net dipolar moment gradually getting close to zero. This spectral behavior of Fano resonance is consistent with the previously reported literature .
We now turn our attention to how the Fano resonances of Ag plamonic heptamers are affected by an Ag reflective film in Fig. 1. By fixing the nanodisk sizes (D1 = 90 nm, D2 = 80 nm), interparticle distance (L = 100 nm, corresponding to a nanogap of 15 nm) and reflective film thickness (h = 60 nm), we change the spacer layer SiO2 thickness (H) between Ag film and Ag heptamers to optimize the antenna-substrate distance. By tuning the spacer layer SiO2 thickness H, both the optical properties of the SiO2/Ag/SiO2 film and the scattering cross sections of Ag heptamer can be modulated. In the case that no Ag heptamer is present, a weak asymmetric Fabry–Perot (F-P) resonator comprised of Air/SiO2/Ag triple-layer film stacks leads to different optical absorption rate (A) at different incident wavelength. The calculated optical absorption rate of SiO2/Ag/SiO2 film at different spacer layer thickness H is presented in Fig. 3(a). The destructive interference between the light beams reflected respectively from the Air/SiO2 interface and the SiO2/Ag interface confines the optical energy in the weak asymmetric F-P cavity, which leads to a constructive absorption on the surface of Ag film. The ideal spacer layer thickness HMAX for absorption peak associated with the maximum constructive interference of the electric field at a specific wavelength λ is calculated by :Fig. 3(a)], λ is the incident wavelength, nλ is the refractive index of the SiO2 at incident wavelength, and δλ is the penetration depth of incident wavelength in the Ag reflective film.
When the antennas are placed on the SiO2/Ag/SiO2 film, the SiO2 thickness HMAX for maximum constructive interference of the electric field associated with the maximum scattering cross section of Ag heptamer changes due to interference effects. The calculated scattering spectra of the Ag heptamers placed on the SiO2/Ag/SiO2 film as a function of wavelength and spacer layer thickness H are presented in Fig. 3(b). Compared to the case in which no heptamer is presented (the black dotted arrow), HMAX decreases substantially due to the phase shift in the incident beam and/or interference effects resulted from the unique scattering cross sections of the antennas  or the mismatch between the radiation quality factor and absorption quality of optical antennas factor . All of the above factors have an effect on the substantial decreases of HMAX, and each factor dominates the spectrum behavior in a different wavelength with a given spacer layer thickness. The peak position of the “bright” superradiant mode [see Fig. 3(b)] redshift as increasing the thickness of spacer layer SiO2 in the same mode order due to the interference of the scattered wave from the heptamer and underlying structure. However, the Fano dip in the scattering spectra has an almost fixed position [the white dotted arrow in Fig. 3(b)] when the Ag heptamer is away from the Ag reflective mirror with a large thickness of spacer layer SiO2 (H≥60 nm) due to the zero or nearly zero dipole moments of the “dark” mode. In this case, the “dark” mode couples inefficiently to incident light as well as reflective light from underlying Ag mirror. When H gradually decreases to be less than 60 nm, the Fano dip weakly red-shifts [see Fig. 3(c)] due to the coupling between the “dark” plasmon mode of Ag heptamer with the image plasmon modes or surface plasmon polaritons (SPPs) supported by the Ag reflective film [29,33,36]. In order to explore the effect of SiO2 space layer, we simulated the optical properties of Ag heptamer/Air/Ag film/SiO2 [see Fig. 3(d)], which is obtained by replacing the SiO2 spacer layer in Ag heptamer/SiO2/Ag film/SiO2 system by air. After systematic investigation, two major viewpoints are proposed: (1) the asymmetric F-P cavity supported by the SiO2/Ag/SiO2 reflective film has a weak effect upon the scattering intensity of Ag plasmon heptamer, and (2) The SiO2 spacer layer caused the red shift of the resonances peak positions due to the large damping. In general, the Fano resonance properties are intrinsically determined by the given plasmonic assembly and the Fano dip position usually experiences shift when it is enhanced via plasmon coupling. However, our results indicate that it is feasible to enhance Fano resonance properties of the nanoantennas without modifying its features and peak positions by using a metallic mirror.
To better understand the ideal spacer layer thickness for maximum constructive interference of scattered waves for a certain plasmonic assembly, we investigated the influence of the spacer thickness H on the near-field enhancement at a fixed wavelength (Fano-dip position, λ = 591.7 nm). Figure 4(a) shows the calculated field enhancement in the gap region of an Ag heptamer on an Ag reflective substrate when varying the spacer thicknesses H at the Fano-dip position. When the Ag nanodisk heptamer positioned at an appropriate distance above SiO2/Ag/ SiO2 reflective substrate, 2.1 [m = 0, H = 60 nm, green dotted line in Fig. 4(a)] and 2.4 times [m = 1, H = 260 nm, blue dotted line in Fig. 4(a)] field enhancement can be achieved respectively compared to that generated from the heptamer placed on SiO2 substrate [field enhancement = 13.081, red dotted line in Fig. 4(a)]. Note that the same mesh size of 3 nm was used for all types of structures in the numerical simulations to ensure the comparison of the field enhancement reasonable. It is also important to note that the minimum field enhancement at the thicknesses of 160 nm and 360 nm was resulted from the destructive interference of the scattered wave from the heptamer itself and the reflective metallic mirror. Compared to the case in which the Ag heptamer is directly placed on SiO2 dielectric substrate (red line: No mirror), two radically enhanced calculated scattering spectra with a deepened Fano dip can be obtained in the Ag heptamer placed on a SiO2/Ag/SiO2 reflective substrate (the ideal spacer layer thickness H = 60 and 260 nm), as shown in Fig. 4(b). The corresponding electric field distribution at the Fano-dip position in X-Z plane is shown in Fig. 4(c). For H = 60 nm, the calculated scattering spectrum is broader than the case of H = 260 nm due to the near-field coupling between Ag heptamer and Ag reflective substrate at a small distance. If the depth of Fano dip is defined as the intensity difference of scattering cross section between the dip and the lower peak, the depth of Fano dip are measured to be 0.23 µm2 for H = 60 nm and 0.24 µm2 for H = 260 nm, which is 3.4 and 3.6 times relative to the values from the heptamer directly placed on SiO2 substrate, respectively. We have also investigated the effect of SiO2 thickness H for the cases of D1 = 80 nm and 100 nm (not shown here) to elaborate how the influence of substrate mirror is performed. For the case of D1 = 80 nm and 100 nm, the trend of the scattering spectra and Fano-dip position is consistent with the case of D1 = 90 nm as we change the spacer layer SiO2 thickness (H) between Ag film and Ag heptamers. The dominated constructive interference between the scattered wave from the heptamer and underlying structure is modulated by the thickness of SiO2 layer. Both the ratios of the depth of Fano dip and field enhancement are determined by comparing the values from the heptamer directly placed on SiO2 substrate, which only exhibit slight change due to the low shape sensitivity in nanoantenna/dielectric layer/metal reflector configuration. Therefore, our results provide an effective approach and optimal structure configuration to enhance the depth of Fano dip, electric field intensity and scattering cross section via a reflective mirror without modifying the geometry of the plasmonic structures and shifting the Fano dip position, which may find various applications in plasmon-enhanced light-matter interactions.
In conclusion, we have proposed and demonstrated an approach to enhance the Fano resonance of plasmonic Ag nanodisk heptamer by introducing a reflective substrate mirror. In such a configuration, the incident light is reflected by the reflective film, while the Ag nanoheptamer serves as a scatterer for the reflected light. With enhanced light-matter interactions via interference effect, 2.4 times higher electric field intensity and 3.6 times deeper Fano dip can be obtained respectively compared to those from the heptamer directly placed on SiO2 substrate. Interestingly, the Fano-dip position in the proposed configuration does not shift when changing the thickness of the dielectric spacer (≥60 nm) due to the insufficient coupling of the plasmonic “dark” mode with the reflected light from underlying Ag mirror. Our investigations have not only revealed the ability to enhance the depth of Fano dip in Ag heptamer by a reflected metal film, but also demonstrated how to achieve maximal field enhancement and scattering section in the Ag plasmonic heptamer through optimizing the thickness of spacer layer. These results provide insights for the further enhancement of the depth of Fano dip for ultrasensitive nanoscale sensors and the electric field around the nanostructure surface for surface-enhanced spectroscopy.
National Natural Science Foundation of China (NSFC) (Grant nos.11274107 and 11574078); Foundation for the Authors of National Excellent Doctoral Dissertation of the People's Republic of China (201318); The Natural Science Foundation of Hunan Province (2015JJ1008, 2015RS4024).
References and links
1. C. Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003). [CrossRef]
2. B. Gallinet, T. Siegfried, H. Sigg, P. Nordlander, and O. J. F. Martin, “Plasmonic radiance: probing structure at the Ångström scale with visible light,” Nano Lett. 13(2), 497–503 (2013). [CrossRef] [PubMed]
3. N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar metamaterial analogue of electromagnetically induced transparency for plasmonic sensing,” Nano Lett. 10(4), 1103–1107 (2010). [CrossRef] [PubMed]
4. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]
5. C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayers,” Nat. Mater. 11(1), 69–75 (2012). [CrossRef] [PubMed]
7. K. E. Chong, B. Hopkins, I. Staude, A. E. Miroshnichenko, J. Dominguez, M. Decker, D. N. Neshev, I. Brener, and Y. S. Kivshar, “Observation of Fano resonances in all-dielectric nanoparticle oligomers,” Small 10(10), 1985–1990 (2014). [CrossRef] [PubMed]
8. S. Li, Y. Wang, R. Jiao, L. Wang, G. Duan, and L. Yu, “Fano resonances based on multimode and degenerate mode interference in plasmonic resonator system,” Opt. Express 25(4), 3525–3533 (2017). [CrossRef] [PubMed]
9. S. Zhang, G. C. Li, Y. Chen, X. Zhu, S. D. Liu, D. Y. Lei, and H. Duan, “Pronounced Fano resonance in single gold split nanodisks with 15 nm split gaps for intensive second harmonic generation,” ACS Nano 10(12), 11105–11114 (2016). [CrossRef] [PubMed]
12. X. Zhu, Z. Yang, Y. Chen, and H. Duan, “Plasmon modes and substrate-induced Fano dip in gold nano-octahedra,” Plasmonics 10(5), 1013–1021 (2015). [CrossRef]
13. S. Zhang, K. Bao, N. J. Halas, H. Xu, and P. Nordlander, “Substrate-induced Fano resonances of a plasmonic nanocube: a route to increased-sensitivity localized surface plasmon resonance sensors revealed,” Nano Lett. 11(4), 1657–1663 (2011). [CrossRef] [PubMed]
14. J. A. Fan, K. Bao, C. Wu, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, G. Shvets, P. Nordlander, and F. Capasso, “Fano-like interference in self-assembled plasmonic quadrumer clusters,” Nano Lett. 10(11), 4680–4685 (2010). [CrossRef] [PubMed]
15. J. B. Lassiter, H. Sobhani, J. A. Fan, J. Kundu, F. Capasso, P. Nordlander, and N. J. Halas, “Fano resonances in plasmonic nanoclusters: geometrical and chemical tunability,” Nano Lett. 10(8), 3184–3189 (2010). [CrossRef] [PubMed]
17. M. Rahmani, B. Luk’yanchuk, and M. Hong, “Fano resonance in novel plasmonic nanostructures,” Laser Photonics Rev. 7(3), 329–349 (2013). [CrossRef]
18. J. Ye, F. Wen, H. Sobhani, J. B. Lassiter, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmonic nanoclusters: near field properties of the Fano resonance interrogated with SERS,” Nano Lett. 12(3), 1660–1667 (2012). [CrossRef] [PubMed]
20. M. Frimmer, T. Coenen, and A. F. Koenderink, “Signature of a Fano resonance in a plasmonic metamolecule’s local density of optical states,” Phys. Rev. Lett. 108(7), 077404 (2012). [CrossRef] [PubMed]
21. M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett. 10(7), 2721–2726 (2010). [CrossRef] [PubMed]
22. M. Rahmani, B. Lukiyanchuk, B. Ng, A. Tavakkoli K G, Y. F. Liew, and M. H. Hong, “Generation of pronounced Fano resonances and tuning of subwavelength spatial light distribution in plasmonic pentamers,” Opt. Express 19(6), 4949–4956 (2011). [CrossRef] [PubMed]
23. S. N. Sheikholeslami, A. García-Etxarri, and J. A. Dionne, “Controlling the interplay of electric and magnetic modes via Fano-like plasmon resonances,” Nano Lett. 11(9), 3927–3934 (2011). [CrossRef] [PubMed]
24. F. Wen, J. Ye, N. Liu, P. Van Dorpe, P. Nordlander, and N. J. Halas, “Plasmon transmutation: inducing new modes in nanoclusters by adding dielectric nanoparticles,” Nano Lett. 12(9), 5020–5026 (2012). [CrossRef] [PubMed]
25. R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014). [CrossRef]
26. B. Zeng, Y. Gao, and F. J. Bartoli, “Rapid and highly sensitive detection using Fano resonances in ultrathin plasmonic nanogratings,” Appl. Phys. Lett. 105(16), 161106 (2014). [CrossRef]
28. L. V. Brown, X. Yang, K. Zhao, B. Y. Zheng, P. Nordlander, and N. J. Halas, “Fan-shaped gold nanoantennas above reflective substrates for surface-enhanced infrared absorption (SEIRA),” Nano Lett. 15(2), 1272–1280 (2015). [CrossRef] [PubMed]
29. Y. Chu, M. G. Banaee, and K. B. Crozier, “Double-resonance plasmon substrates for surface-enhanced Raman scattering with enhancement at excitation and stokes frequencies,” ACS Nano 4(5), 2804–2810 (2010). [CrossRef] [PubMed]
31. H. Y. Jeong, U. J. Kim, H. Kim, G. H. Han, H. Lee, M. S. Kim, Y. Jin, T. H. Ly, S. Y. Lee, Y. G. Roh, W. J. Joo, S. W. Hwang, Y. Park, and Y. H. Lee, “Optical gain in MoS2 via coupling with nanostructured substrate: fabry–perot interference and plasmonic excitation,” ACS Nano 10(9), 8192–8198 (2016). [CrossRef] [PubMed]
32. K. Ray, M. D. Mason, C. Yang, Z. Li, and R. D. Grober, “Single-molecule signal enhancement using a high-impedance ground plane substrate,” Appl. Phys. Lett. 85(23), 5520–5522 (2004). [CrossRef]
33. T. J. Seok, A. Jamshidi, M. Kim, S. Dhuey, A. Lakhani, H. Choo, P. J. Schuck, S. Cabrini, A. M. Schwartzberg, J. Bokor, E. Yablonovitch, and M. C. Wu, “Radiation engineering of optical antennas for maximum field enhancement,” Nano Lett. 11(7), 2606–2610 (2011). [CrossRef] [PubMed]
34. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
35. E. D. Palik, Handbook of optical constants of solids (Academic Press, 1998).
36. D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, “Directional Raman scattering from single molecules in the feed gaps of optical antennas,” Nano Lett. 13(5), 2194–2198 (2013). [CrossRef] [PubMed]