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Abstract
We study the evolution from suppressed to enhanced optical transmission through metal nanohole arrays with increasing film thickness. Due to Fano interferences, the plasmon resonances gradually shift from transmission dips for ultrathin films to peaks for thick films, accompanied by a Fano asymmetry parameter that increases with film thickness. For intermediate thicknesses, both peaks and dips in transmission are far from the plasmon resonances, and hence, also far from the spectral positions of maximum light absorption and nearfield enhancements. Calculations for various hole diameters and periodicities confirm the universality of our conclusions.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Since the discovery of extraordinary transmission through nanoscale holes in metallic films [1], nanohole surfaces have been intensely investigated [2–7] and enabled a vast number of applications, including various biosensing schemes [8–21], optical trapping [22,23], and light-to-heat conversion [24]. The main phenomenon is based on enhanced light interaction with the metal film via excitation of plasmonic charge oscillations by the nanoholes. For opaque metal films, excitation of plasmons aid light to go through the film, resulting in transmission peaks (extraordinary optical transmission, EOT) and enhanced transmission compared with the bare metal film [1]. For metal films sufficiently thin to be semitransparent also without holes (optically thin), the addition of nanoholes can instead suppress the transmission compared to the non-perforated film, resulting in transmission dips and suppressed transmission [25,26]. Figure 1 shows simulated examples of both these situations, for square arrays of nanoholes in 10 nm (black) and 200 nm (red) thick silver films.
Fig. 1 (a) A sketch of the investigated nanohole system, based on a perforated silver film on a glass substrate, with nanohole diameter d, periodicity p and thickness t. (b) Transmission spectra obtained by the FDTD method for ultrathin (t = 10 nm, black line) and thick (t = 200 nm, red line) film thicknesses (d = 110 nm, p = 200 nm). Dashed lines show transmission through non-perforated films of the same thicknesses.
Assuming that the plasmon resonance positions coincide with the transmission peaks for thick nanohole films and with the dips for very thin films, the question arises regarding what happens for intermediate thicknesses. Hence, how do the plasmon resonance position(s) evolve in relation to transmission peaks and dips for increasing nanohole film thicknesses? In the literature, the plasmon resonances of nanohole films in optically thin films have been associated with both transmission dips (typically referred to as extinction peaks) and transmission peaks [27–31]. It has also been suggested that both dips and peaks originate from different types of plasmonic resonances [32–36]. Other reports focus on explaining each transmission dip-peak pair as a result of only one resonance that is interfering with the continuum state [25,26,37–39]. Such so-called Fano interference effects are indeed well known to create dip-peak line shapes in various systems, with the resonance in the system positioned somewhere between the dip and the peak [40]. The Fano approach has been applied to describe the plasmonic behavior of ultrathin plasmonic systems, including one-dimensional ultrathin gratings [37], triangular nanohole arrays of varying hole diameter [41], as well as square nanohole arrays [26,42,43]. The detailed line shape of optically thick nanohole arrays has also been described by Fano profiles [44].
Here, we investigate the evolution of the plasmonic properties of nanohole arrays for gradually increasing metal film thickness. Using absorption (and nearfield) peaks as probes for the plasmon resonances in the system, we show that each resonance gradually moves from being close to the transmission dip for ultrathin films to close to the peak position for thick films. For intermediate thicknesses, both the dip and the peak are positioned far from the plasmon resonance although they both originate from that same resonance excitation. The results are consistent with Fano interference effects and we show how the thickness dependence of the Fano asymmetry parameter leads to a monotonic shift of the resonance from dip to peak in transmission. We focus the study on square nanohole arrays in silver films on glass, with optical properties obtained by the finite-difference time-domain (FDTD) method (see Methods section). The main conclusions should be applicable also to other nanohole systems, as confirmed for symmetric freestanding nanohole films. The findings highlight that the plasmon resonance and corresponding strong light-interaction of plasmonic nanohole films may not be well represented by either dip or peak of the transmission spectrum, which forms implications when employing nanohole films for various applications [8,24,30,31,45–47].
2. Methods
Normal incidence zero-order transmission and absorption spectra were obtained using FDTD Solutions (Lumerical, version 8.19.1416). The simulation size was 150-300 nm along x and y, and 1100 nm along the propagation direction z. Anti-symmetric, symmetric and perfectly matched layers (PML) boundary conditions were respectively used for x, y and z to establish the periodic structure in the xy-plane. The mesh size over the entire silver volume was set to be 1 nm for all three axes. The simulation consists of a glass substrate (refractive index = 1.5) coated with a silver nanohole structure and with air as surrounding medium. The permittivity of the silver was provided by the built-in material database in the software (Ag (Silver) - Palik (0-2um), 6 coefficients, wavelength of 300-1170 nm for the bandwidth settings). A plane-wave normal to the surface of the film with a wavelength range of 300-1170 nm was used as a source. Transmission (T) and reflection (R) monitors were installed over and under the nanohole array depending on the illumination direction to calculate the transmission (T) and absorption (A = 1 − T − R).
3. Results and discussion
Figure 2(a) shows transmission spectra for square arrays of 110 nm in diameter nanoholes in silver films with thickness varying from 10 nm to 200 nm. The periodicity was kept at 200 nm unless otherwise stated. We see a clear transmission dip for the thinnest films, which blueshifts and decrease in intensity for increasing thicknesses. Increasing thickness also leads to the emergence of a peak that is redshifted from the dip and an additional peak-dip pair at higher energies. Intermediate thicknesses around 50 nm show both clear dips and peaks.
Fig. 2 (a) Transmission and absorption spectra using (b) back illumination and (c) front illumination of light source (d = 110 nm, p = 200 nm). (d) Extracted peak and dip positions as a function of film thickness. (e) Relative position of absorption peak between the transmission peak and dip versus film thickness.
We use absorption spectra based on light illumination from both the glass side (back illumination, BI) and air side (front illumination, FI) of the nanohole samples in order to identify absorptive plasmon resonances in the system (Figs. 2(b) and 2(c)) and to compare them with the features seen in the transmission spectra. The identified peak and dip positions are presented versus thickness in Fig. 2(d). The thinnest sample with 10 nm thickness shows one primary resonance at around 2.0 eV for both illumination directions. The position is close to the transmission dip, situated at slightly larger energies (indicated by the red dashed line in Fig. 2(a)-2(c)). This resonance is attributed to short-range surface plasmon polaritons (SRSPPs) associated with the symmetric (in terms of charge distribution) coupled mode between the metal-air and metal-glass interfaces [25,26,37,48]. Note that for thin films surrounded by asymmetric media (e.g. air and glass substrate in our study) the contribution of the long-range modes becomes negligible and only SRSPPs are observable [25,26,49]. Increasing nanohole film thickness reduces the coupling between the two interfaces, which results in a blueshift of the resonance towards the position of the non-coupled single interface surface plasmon polaritons (SISPPs) of the metal-glass interface. Indeed, for optically thick nanohole films, this mode is primarily excited by back illumination from the glass side (compare Figs. 2(b) and 2(c)). The resonance position for thick films is close to the corresponding transmission peak observed in Fig. 2(a), indicated by the pink dashed line at around 2.7 eV.
Illumination from the front side reveals the emergence of an additional high-energy resonance for increasing film thicknesses. This resonance is associated with the metal-air interface and it redshifts towards the SISPP mode of the metal-air interface for increasing thicknesses. The transmission spectra for thick samples show a peak close to this resonance position (indicated by the pink dashed line at around 3.25 eV).
The behavior of both lower and higher energy resonances obtained from the absorption spectra is in accordance with the effects of coupling on the dispersion relations for SPPs for glass-metal-air systems (dispersion curves are presented in Fig. 4 in Appendix A) [50]. For the same grating coupling condition (i.e. same momentum), the dispersion relations predict blueshift with increasing film thickness for the lower energy metal-glass interface resonance and redshift for the higher energy metal-air interface resonance. Based on this principle, we can predict approximate resonance positions from the dispersion relations by treating the nanohole array as an empty lattice with momentum equal to 2π/(periodicity). Comparison with resonances directly extracted from the absorption peaks for various film thickness and hole diameters reveals their common origin from SPPs (see Appendix A). The comparison also show deviation to lower energies for the systems with finite-sized holes, attributed to limitations of the empty lattice approximation [25]. We also note that the absorption positions overall overlap with the resonance positions predicted from the optical nearfields, obtained by averaging the simulated nearfield 5 nm over the metal film (NF top) or 5 nm into the glass substrate (NF bottom, see Fig. 2(d)). A detailed comparison between absorption spectra and averaged nearfield is also presented in Fig. 5 in Appendix B.
Turning to the relation between plasmon resonance positions and extrema in the transmission spectra, we find that the resonances are close to the dips for ultrathin films while they are closer to the peaks for the thickest films. For intermediate thicknesses, the resonances gradually move from the dips to the peaks. This behavior is illustrated for the lower energy mode in Fig. 2(e), which presents resonance (absorption, BI) position relative to the transmission peak (value of 1) and dip (value of 0). The plasmon resonance is half way between the dip and peak for thicknesses around 40-50 nm, which corresponds to typical thicknesses used in practical devices [24,29,46]. Similar results are found for different nanohole diameters and periodicities as well as for symmetric freestanding nanohole arrays surrounded by air (see Figs. 6-10 in Appendices C, D and E).
We employ a Fano approach to investigate if the transition of the resonance from transmission dip to transmission peak for increasing film thicknesses is consistent with Fano interference between the plasmon resonance of the nanohole array and the non-resonant transmission via continuum states. The final transmission TFano upon Fano interference is given by [40,43,44,51,52]:
where q is the Fano asymmetry parameter (known to be negative for nanohole systems [44]), Td is associated with the direct transmission without coupling with the discrete resonant state (approximated as linear), and Tc is associated with transmission due to coupling between the discrete and continuum states. ε is the reduced energy given by the resonance position ER and the linewidth ΓR. Figure 3(a) presents examples of normalized Fano profiles for different |q| values and illustrates how the asymmetry parameter drastically affects the transmission spectrum, resulting in a transmission dip for low values (e.g. |q| = 0.3), a dip-peak behavior for intermediate values (e.g. |q| = 1), and primarily a transmission peak for higher values of q (e.g. |q| = 2). Note also that the resonance energy shifts from being close to the transmission dip to close to peak with increasing |q|. Transmission spectra for ultrathin (Fig. 3(b)), intermediate (Fig. 3(c)), and thick (Fig. 3(d)) nanohole films could all be accurately reproduced by the Fano approach according to Eq. (1) (see Fig. 11 in Appendix F for the same plots in logarithmic scale). Importantly, ER and ΓR were not treated as fit parameters, but directly determined from the absorption resonance spectra (BI), which are also presented in Appendices C and D.Fig. 3 (a) Normalized Fano profiles for different |q| values. Exemplary Fano fits to Eq. (1) for (b) t = 10 nm, (c) t = 50 nm, and (d) t = 200 nm (d = 110 nm and p = 200 nm). Extracted |q| value is designated in each plot. The fit parameters with their standard deviations are as follows: (b) |q| = (0.293 ± 0.003), Tc = (0.722 ± 0.006), Td = (0.298 ± 0.010 eV−1) × E – (0.482 ± 0.022), (c) |q| = (1.033 ± 0.007), Tc = (0.291 ± 0.004), Td = (0.433 ± 0.010 eV−1) × E – (1.191 ± 0.029), (d) |q| = (2.103 ± 0.021), Tc = (0.0028 ± 0.0001), Td = (0.022 ± 0.0005 eV−1) × E – (0.061 ± 0.001). (e) |q| as a function of film thickness for various hole diameters and (f) |q| as a function of hole diameter for various film thicknesses (p = 200 nm). (g) |q| as a function of film thickness for various periodicities and (h) |q| as a function of periodicity for various film thicknesses (d = 110 nm).
In order to reveal effects of nanohole array dimensions on the Fano interference, we plot the extracted |q| values from the Fano fits versus thickness, diameter and periodicity (Figs. 3(e)-3(h), see Appendices C and D for corresponding spectra and extracted peak and dip positions for the metal-glass interface). First, we note that |q| increases monotonically with increasing thickness of the nanohole films (Figs. 3(e) and 3(g)). This is in agreement with low |q| for nanohole films exhibiting transmission dips and higher |q| for nanohole films showing more clear transmission peaks. This trend holds for different diameters and periodicities of nanoholes (investigated from 40 nm to 180 nm in diameter, and from 150 nm to 300 nm in periodicity) and agrees with q being related to the ratio between the resonant transition amplitude and the non-resonant direct transition amplitude [26,40,44]. Increasing thickness rapidly lowers the direct transmission through the film and thereby increases |q|, as also in accordance with coupled-mode theory [38,39]. The results are consistent with previous reports for 100 nm and 200 nm thick gold nanohole films [44]. Varying hole diameter shows a non-monotonic effect on q (Fig. 3(f)). This is related to two factors, both being strongly dependent on nanohole diameter; one is the direct transmission through the nanoholes and the other is the resonance amplitude. Larger hole diameters are expected to provide enhanced direct transmission through the nanoholes, thereby explaining the correspondingly smaller |q|. Meanwhile, excessively small nanohole diameters, such as 40 nm, can reduce the resonance amplitude (Appendix C), which also leads to reduced values of |q|. Furthermore, increasing periodicity of the nanohole array reduces the number of holes per area, resulting in less transmission through the nanoholes and subsequently larger |q| (Fig. 3(h)). Hence, we conclude that all our observations for metal nanohole surfaces of increasing film thickness can be described by Fano interference effects, including the gradual shift of the plasmon resonance from dip to peak in the transmission spectra.
4. Conclusions
The main message of this paper is that increasing the thickness of metal nanohole arrays from optically thin to optically thick films gradually shifts the plasmon resonances from the transmission dips towards the transmission peaks. This behavior is fully consistent with Fano interference effects, with an asymmetry parameter q that increases in magnitude with film thickness. We did not find evidence of simultaneous resonances at both transmission peaks and dips for any of the investigated systems. On the contrary, the results highlight that the plasmon resonances of metal nanohole arrays, in terms of both absorption and nearfield maxima, may be far from both dips and peaks in transmission spectra. These results are consistent for both asymmetric nanohole films on a substrate and for symmetric freestanding nanohole films. In turn, this deviation between transmission extrema and resonances is important to consider when designing plasmonic nanohole systems for use in different applications, such as for biosensors [8,30,31], light-to-heat conversion [24], or for strongly coupled systems [47,53]. We suggest that measuring absorption peaks, for example, using an integrating sphere, form a suitable approach to identify plasmon resonances in plasmonic nanohole systems and similar systems where Fano interference effects may otherwise disguise the true resonances.
Appendix
A. Empty lattice approximation (ELA)
Fig. 4 (a) Calculated dispersion relations for silver films without nanoholes. (b) SPP resonances calculated from (a) using the empty lattice approximation (ELA), and absorption peak positions (BI) obtained from FDTD simulations versus film thickness for various diameters. (c) SPP resonances and absorption peak positions versus nanohole diameter for various thicknesses. The horizontal dashed lines designate the SPP resonance energy for comparison.
B. Comparison between absorption and near-field spectra
Fig. 5 (a) Absorption spectra and nearfield data averaged over the surfaces parallel to the metal film (b) 5 nm over the metal-air interface and (c) 5 nm under the metal-glass interface, using back illumination (d = 110 nm, p = 200 nm). (d-f) Results obtained using front illumination corresponding to (a-c).
C. Simulated results for various diameters
Fig. 6 Transmission and absorption (both BI and FI) spectra for various film thicknesses and hole diameters (periodicity is fixed at 200 nm).
Fig. 7 Extracted peak and dip positions (top panels) and linewidths of the absorption peaks (bottom panels) as a function of film thickness for various hole diameters (periodicity is fixed at 200 nm).
D. Simulated results for various periodicities
Fig. 8 Transmission and absorption (both BI and FI) spectra for various film thicknesses and hole periodicities (hole diameter is fixed at 110 nm).
Fig. 9 Extracted peak and dip positions (top panels) and linewidths of the absorption peaks (bottom panels) as a function of film thickness for various hole periodicities (hole diameter is fixed at 110 nm).
E. Simulated spectra for freestanding nanohole arrays
Fig. 10 (a) Transmission and (b) absorption spectra for freestanding nanohole arrays surrounded by air (d = 110 nm, p = 200 nm).
F. Fano fits in logarithmic scale for comparison
Funding
Wenner-Gren Foundations; ÅForsk foundation; Swedish Foundation for Strategic Research; Royal Swedish Academy of Sciences; Swedish Research Foundation; Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO-Mat-LiU No 2009 00971).
References
1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, P. A. Wolff, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6), 1114–1117 (1998). [CrossRef]
2. F. J. G. De Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007). [CrossRef]
3. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]
4. J. Parsons, E. Hendry, C. P. Burrows, B. Auguié, J. R. Sambles, and W. L. Barnes, “Localized surface-plasmon resonances in periodic nondiffracting metallic nanoparticle and nanohole arrays,” Phys. Rev. B Condens. Matter Mater. Phys. 79(7), 073412 (2009). [CrossRef]
5. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
6. S. G. Rodrigo, F. de León-Pérez, and L. Martín-Moreno, “Extraordinary Optical Transmission: Fundamentals and Applications,” Proc. IEEE 104(12), 2288–2306 (2016). [CrossRef]
7. Q. G. Du, H. Ren, C. E. Png, and H. Wang, “Extremely sharp transmission peak in optically thin aluminum film with hexagonal nanohole arrays,” J. Opt. 20(10), 105002 (2018). [CrossRef]
8. A. B. Dahlin, M. P. Jonsson, and F. Höök, “Specific self-assembly of single lipid vesicles in nanoplasmonic apertures in gold,” Adv. Mater. 20(8), 1436–1442 (2008). [CrossRef]
9. M. P. Jonsson, A. B. Dahlin, L. Feuz, S. Petronis, and F. Höök, “Locally functionalized short-range ordered nanoplasmonic pores for bioanalytical sensing,” Anal. Chem. 82(5), 2087–2094 (2010). [CrossRef] [PubMed]
10. A. G. Brolo, R. Gordon, B. Leathem, and K. L. Kavanagh, “Surface Plasmon Sensor Based on the Enhanced Light Transmission through Arrays of Nanoholes in Gold Films,” Langmuir 20(12), 4813–4815 (2004). [CrossRef] [PubMed]
11. A. Lesuffleur, H. Im, N. C. Lindquist, and S. H. Oh, “Periodic nanohole arrays with shape-enhanced plasmon resonance as real-time biosensors,” Appl. Phys. Lett. 90(24), 243110 (2007). [CrossRef]
12. O. Tokel, F. Inci, and U. Demirci, “Advances in Plasmonic Technologies for Point of Care Applications,” Chem. Rev. 114(11), 5728–5752 (2014). [CrossRef] [PubMed]
13. M. P. Murray-Methot, N. Menegazzo, and J. F. Masson, “Analytical and physical optimization of nanohole-array sensors prepared by modified nanosphere lithography,” Analyst (Lond.) 133(12), 1714–1721 (2008). [CrossRef] [PubMed]
14. A. A. Yanik, M. Huang, A. Artar, T. Y. Chang, and H. Altug, “Integrated nanoplasmonic-nanofluidic biosensors with targeted delivery of analytes,” Appl. Phys. Lett. 96(2), 021101 (2010). [CrossRef]
15. F. Eftekhari, C. Escobedo, J. Ferreira, X. Duan, E. M. Girotto, A. G. Brolo, R. Gordon, and D. Sinton, “Nanoholes as nanochannels: Flow-through plasmonic sensing,” Anal. Chem. 81(11), 4308–4311 (2009). [CrossRef] [PubMed]
16. L. Feuz, P. Jönsson, M. P. Jonsson, and F. Höök, “Improving the limit of detection of nanoscale sensors by directed binding to high-sensitivity areas,” ACS Nano 4(4), 2167–2177 (2010). [CrossRef] [PubMed]
17. J. A. Jackman, A. Rahim Ferhan, and N.-J. Cho, “Nanoplasmonic sensors for biointerfacial science,” Chem. Soc. Rev. 46(12), 3615–3660 (2017). [CrossRef] [PubMed]
18. M. C. Estevez, M. A. Otte, B. Sepulveda, and L. M. Lechuga, “Trends and challenges of refractometric nanoplasmonic biosensors: A review,” Anal. Chim. Acta 806, 55–73 (2014). [CrossRef] [PubMed]
19. A. Barik, L. M. Otto, D. Yoo, J. Jose, T. W. Johnson, and S. H. Oh, “Dielectrophoresis-enhanced plasmonic sensing with gold nanohole arrays,” Nano Lett. 14(4), 2006–2012 (2014). [CrossRef] [PubMed]
20. M. P. Jonsson, A. B. Dahlin, P. Jönsson, and F. Höök, “Nanoplasmonic biosensing with focus on short-range ordered nanoholes in thin metal films,” Biointerphases 3(3), FD30–FD40 (2008). [CrossRef] [PubMed]
21. J. M. McMahon, J. Henzie, T. W. Odom, G. C. Schatz, and S. K. Gray, “Tailoring the sensing capabilities of nanohole arrays in gold films with Rayleigh anomaly-surface plasmon polaritons,” Opt. Express 15(26), 18119–18129 (2007). [CrossRef] [PubMed]
22. M. L. Juan, R. Gordon, Y. Pang, F. Eftekhari, and R. Quidant, “Self-induced back-action optical trapping of dielectric nanoparticles,” Nat. Phys. 5(12), 915–919 (2009). [CrossRef]
23. Y. Pang and R. Gordon, “Optical trapping of 12 nm dielectric spheres using double-nanoholes in a gold film,” Nano Lett. 11(9), 3763–3767 (2011). [CrossRef] [PubMed]
24. D. Tordera, D. Zhao, A. V. Volkov, X. Crispin, and M. P. Jonsson, “Thermoplasmonic Semitransparent Nanohole Electrodes,” Nano Lett. 17(5), 3145–3151 (2017). [CrossRef] [PubMed]
25. S. G. Rodrigo, L. Martín-Moreno, A. Y. Nikitin, A. V. Kats, I. S. Spevak, and F. J. García-Vidal, “Extraordinary optical transmission through hole arrays in optically thin metal films,” Opt. Lett. 34(1), 4–6 (2009). [CrossRef] [PubMed]
26. J. Braun, B. Gompf, G. Kobiela, and M. Dressel, “How holes can obscure the view: suppressed transmission through an ultrathin metal film by a subwavelength hole array,” Phys. Rev. Lett. 103(20), 203901 (2009). [CrossRef] [PubMed]
27. J. Prikulis, P. Hanarp, L. Olofsson, D. Sutherland, and M. Käll, “Optical spectroscopy of nanometric holes in thin gold films,” Nano Lett. 4(6), 1003–1007 (2004). [CrossRef]
28. D. Gao, W. Chen, A. Mulchandani, and J. S. Schultz, “Detection of tumor markers based on extinction spectra of visible light passing through gold nanoholes,” Appl. Phys. Lett. 90(7), 073901 (2007). [CrossRef]
29. J. C. Sharpe, J. S. Mitchell, L. Lin, N. Sedoglavich, and R. J. Blaikie, “Gold nanohole array substrates as immunobiosensors,” Anal. Chem. 80(6), 2244–2249 (2008). [CrossRef] [PubMed]
30. M. P. Jonsson, P. Jönsson, A. B. Dahlin, and F. Höök, “Supported lipid bilayer formation and lipid-membrane-mediated biorecognition reactions studied with a new nanoplasmonic sensor template,” Nano Lett. 7(11), 3462–3468 (2007). [CrossRef] [PubMed]
31. A. B. Dahlin, “Sensing applications based on plasmonic nanopores: The hole story,” Analyst (Lond.) 140(14), 4748–4759 (2015). [CrossRef] [PubMed]
32. T. Sannomiya, O. Scholder, K. Jefimovs, C. Hafner, and A. B. Dahlin, “Investigation of plasmon resonances in metal films with nanohole arrays for biosensing applications,” Small 7(12), 1653–1663 (2011). [CrossRef] [PubMed]
33. M. Schwind, B. Kasemo, and I. Zorić, “Localized and propagating plasmons in metal films with nanoholes,” Nano Lett. 13(4), 1743–1750 (2013). [CrossRef] [PubMed]
34. T. M. Schmidt, M. Frederiksen, V. Bochenkov, and D. S. Sutherland, “Exploring plasmonic coupling in hole-cap arrays,” Beilstein J. Nanotechnol. 6(1), 1–10 (2015). [CrossRef] [PubMed]
35. V. E. Bochenkov, M. Frederiksen, and D. S. Sutherland, “Enhanced refractive index sensitivity of elevated short-range ordered nanohole arrays in optically thin plasmonic Au films,” Opt. Express 21(12), 14763–14770 (2013). [CrossRef] [PubMed]
36. J. Junesch, G. Emilsson, K. Xiong, S. Kumar, T. Sannomiya, H. Pace, J. Vörös, S.-H. Oh, M. Bally, and A. B. Dahlin, “Location-specific nanoplasmonic sensing of biomolecular binding to lipid membranes with negative curvature,” Nanoscale 7(37), 15080–15085 (2015). [CrossRef] [PubMed]
37. I. S. Spevak, A. Y. Nikitin, E. V. Bezuglyi, A. Levchenko, and A. V. Kats, “Resonantly suppressed transmission and anomalously enhanced light absorption in periodically modulated ultrathin metal films,” Phys. Rev. B Condens. Matter Mater. Phys. 79(16), 161406 (2009). [CrossRef]
38. J. W. Yoon, M. J. Jung, S. H. Song, and R. Magnusson, “Analytic theory of the resonance properties of metallic nanoslit arrays,” IEEE J. Quantum Electron. 48(7), 852–861 (2012). [CrossRef]
39. J. W. Yoon and R. Magnusson, “Fano resonance formula for lossy two-port systems,” Opt. Express 21(15), 17751–17759 (2013). [CrossRef] [PubMed]
40. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961). [CrossRef]
41. M. Liu, Y. Song, Y. Zhang, X. Wang, and C. Jin, “Mode Evolution and Transmission Suppression in a Perforated Ultrathin Metallic Film with a Triangular Array of Holes,” Plasmonics 7(3), 397–410 (2012). [CrossRef]
42. J. Braun, B. Gompf, T. Weiss, H. Giessen, M. Dressel, and U. Hübner, “Optical transmission through subwavelength hole arrays in ultrathin metal films,” Phys. Rev. B Condens. Matter Mater. Phys. 84(15), 155419 (2011). [CrossRef]
43. S.-H. Chang, S. Gray, and G. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13(8), 3150–3165 (2005). [CrossRef] [PubMed]
44. C. Genet, M. P. Van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4–6), 331–336 (2003). [CrossRef]
45. M. P. Jonsson, P. Jönsson, and F. Höök, “Simultaneous Nanoplasmonic and Quartz Crystal Microbalance Sensing: Analysis of Biomolecular Conformational Changes and Quantification of the Bound Molecular Mass,” Anal. Chem. 80(21), 7988–7995 (2008). [CrossRef] [PubMed]
46. M. Virk, K. Xiong, M. Svedendahl, M. Käll, and A. B. Dahlin, “A thermal plasmonic sensor platform: resistive heating of nanohole arrays,” Nano Lett. 14(6), 3544–3549 (2014). [CrossRef] [PubMed]
47. H. Wang, A. Toma, H.-Y. Wang, A. Bozzola, E. Miele, A. Haddadpour, G. Veronis, F. De Angelis, L. Wang, Q.-D. Chen, H.-L. Xu, H.-B. Sun, and R. P. Zaccaria, “The role of Rabi splitting tuning in the dynamics of strongly coupled J-aggregates and surface plasmon polaritons in nanohole arrays,” Nanoscale 8(27), 13445–13453 (2016). [CrossRef] [PubMed]
48. T. H. Park, N. Mirin, J. B. Lassiter, C. L. Nehl, N. J. Halas, and P. Nordlander, “Optical properties of a nanosized hole in a thin metallic film,” ACS Nano 2(1), 25–32 (2008). [CrossRef] [PubMed]
49. F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B Condens. Matter 44(11), 5855–5872 (1991). [CrossRef] [PubMed]
50. A. B. Dahlin, M. Mapar, K. Xiong, F. Mazzotta, F. Höök, and T. Sannomiya, “Plasmonic Nanopores in Metal-Insulator-Metal Films,” Adv. Opt. Mater. 2(6), 556–564 (2014). [CrossRef]
51. W. Zhang, A. K. Azad, J. Han, J. Xu, J. Chen, and X. C. Zhang, “Direct observation of a transition of a surface plasmon resonance from a photonic crystal effect,” Phys. Rev. Lett. 98(18), 183901 (2007). [CrossRef] [PubMed]
52. J. Han, A. K. Azad, M. Gong, X. Lu, and W. Zhang, “Coupling between surface plasmons and nonresonant transmission in subwavelength holes at terahertz frequencies,” Appl. Phys. Lett. 91(7), 071122 (2007). [CrossRef]
53. E. S. H. Kang, S. Chen, S. Sardar, D. Tordera, N. Armakavicius, V. Darakchieva, T. Shegai, and M. P. Jonsson, “Strong Plasmon-Exciton Coupling with Directional Absorption Features in Optically Thin Hybrid Nanohole Metasurfaces,” ACS Photonics 5(10), 4046–4055 (2018). [CrossRef]
