Plasmonic fanoholes: on the gradual transition from suppressed to enhanced optical transmission through nanohole arrays in metal films of increasing film thickness

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


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][9][10][11][12][13][14][15][16][17][18][19][20][21], optical trapping [22,23], and lightto-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.
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][28][29][30][31].It has also been suggested that both dips and peaks originate from different types of plasmonic resonances [32][33][34][35][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][38][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 onedimensional ultrathin gratings [37], triangular nanohole arrays of varying hole diameter [41], as well as sq nanohole arra Here, we gradually incr for the plasmo being close to films.For int plasmon reso results are c dependence o from dip to pe on glass, wit method (see nanohole syst highlight that nanohole film spectrum, wh [8,24,30,31,45     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 T Fano 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]), T d is associated with the direct transmission without coupling with the discrete resonant state (approximated as linear), and T c is associated with transmission due to coupling between the discrete and continuum states.ε is the reduced energy given by the resonance position   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.

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.

A. Empty lat
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