Plasmonic fanoholes: on the gradual
transition from suppressed to enhanced
optical transmission through nanohole arrays
in metal films of increasing film thickness
E
VANS. H. K
ANG,
1H
UGOE
KINGE,
1,2ANDM
AGNUSP. J
ONSSON1,*1Laboratory of Organic Electronics, Linköping University, SE-601 74 Norrköping, Sweden 2Platen High School, 591 86 Motala, Sweden
*magnus.jonsson@liu.se
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.
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],
#354894 https://doi.org/10.1364/OME.9.001404
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 Fig. 1 glass spectr nm, r throug 2. Methods Normal incide Solutions (Lu and 1100 nm matched layer the periodic s be 1 nm for a coated with a of the silver w (0-2um), 6 co wave normal source. Trans nanohole arra absorption (A quare nanohol ays has also bee
investigate th reasing metal on resonances o the transmiss termediate thic onance althoug consistent with of the Fano as eak in transmis th optical pro Methods secti tems, as confi the plasmon r ms may not b hich forms imp
5–47].
. (a) A sketch of t substrate, with n ra obtained by the
ed line) film thick gh non-perforated ence zero-orde umerical, versio m along the pr rs (PML) boun structure in the ll three axes. T silver nanoho was provided b oefficients, wa to the surface o smission (T) a ay depending o = 1 − T − R). le arrays [26,4 en described by he evolution o film thickness in the system, sion dip for ul cknesses, both gh they both o h Fano interfe symmetry para ssion. We focu operties obtain ion). The mai firmed for sym
resonance and be well repres lications when the investigated na nanohole diameter FDTD method fo knesses (d = 110 films of the same
er transmission on 8.19.1416). ropagation dire ndary condition e xy-plane. The The simulation le structure an y the built-in m avelength of 3
of the film with and reflection on the illumina 42,43]. The de y Fano profiles f the plasmon s. Using absorp we show that e ltrathin films to h the dip and t originate from ference effects ameter leads to us the study on ned by the fin
in conclusions mmetric freesta corresponding sented by eith n employing na anohole system, ba r d, periodicity p or ultrathin (t = 10 nm, p = 200 nm thicknesses. n and absorptio The simulation ection z. Anti-ns were respec e mesh size ov consists of a g nd with air as s material databa 00-1170 nm f h a wavelength (R) monitors ation direction etailed line sh s [44]. nic properties
ption (and nea each resonance o close to the the peak are p that same res s and we sho o a monotonic square nanoho nite-difference s should be ap anding nanoho g strong light-in her dip or pea
anohole films f ased on a perforate and thickness t. 0 nm, black line) a m). Dashed lines s on spectra were n size was 150 -symmetric, sy ctively used fo ver the entire si
glass substrate surrounding me ase in the softw for the bandwi h range of 300-s were in300-stalle to calculate th hape of optica of nanohole a arfield) peaks a e gradually mo peak position positioned far sonance excitat ow how the c shift of the r ole arrays in sil time-domain pplicable also ole films. The
nteraction of p ak of the tran for various app
ed silver film on a (b) Transmission and thick (t = 200 show transmission e obtained usin 0-300 nm along ymmetric and or x, y and z to ilver volume w (refractive ind edium. The per ware (Ag (Silve idth settings). -1170 nm was ed over and u he transmission ally thick arrays for as probes oves from for thick from the tion. The thickness resonance lver films (FDTD) to other e findings plasmonic nsmission plications a n 0 n ng FDTD g x and y, perfectly establish was set to dex = 1.5) rmittivity er) - Palik A plane-used as a under the n (T) and
Fig. 2 illumi a func peak a 3. Results a Figure 2(a) sh silver films w nm unless oth blueshifts and to the emerge higher energie We use a illumination, identify absor them with the are presented one primary r to the transmi Fig. 2(a)-2(c (SRSPPs) ass between the surrounded by 2. (a) Transmissio ination of light sou ction of film thickn and dip versus film and discussio hows transmiss with thickness herwise stated d decrease in in ence of a peak es. Intermediat absorption spec
BI) and air si rptive plasmon e features seen versus thickne resonance at ar
ission dip, situ )). This reson sociated with metal-air and y asymmetric m on and absorption urce (d = 110 nm, ness. (e) Relative m thickness.
on
sion spectra fo varying from d. We see a cl
ntensity for inc that is redshif te thicknesses a ctra based on ide (front illum n resonances in in the transmi ess in Fig. 2(d round 2.0 eV fo ated at slightly nance is attrib the symmetric d metal-glass i media (e.g. air
n spectra using (b p = 200 nm). (d) position of absorp or square arrays 10 nm to 200 lear transmissi creasing thickn fted from the d around 50 nm s both light illu mination, FI) n the system ( ission spectra. ). The thinnest or both illumin y larger energie buted to shor c (in terms of interfaces [25
and glass subs
b) back illuminat Extracted peak an ption peak between
s of 110 nm in nm. The perio ion dip for the nesses. Increasi dip and an add show both clea umination from of the nanoho (Figs. 2(b) and The identified t sample with nation direction es (indicated b rt-range surfac f charge distri ,26,37,48]. No strate in our stu
tion and (c) front nd dip positions as n the transmission n diameter nan odicity was ke e thinnest film ing thickness a ditional peak-d
ar dips and pea m the glass si ole samples in d 2(c)) and to d peak and dip
10 nm thickne ns. The positio by the red dash ce plasmon p ibution) coupl ote that for th udy) the contri
t s n noholes in ept at 200 ms, which also leads dip pair at aks. ide (back n order to compare positions ess shows n is close ed line in polaritons led mode hin films ibution 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]: 2 R Fano d c 2 R ( ) , / 2 1 E E q T T T ε ε ε − + = + = Γ + (1)
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
the linewidth values and il spectrum, res for intermedia (e.g. |q| = 2). dip to close intermediate reproduced by same plots in but directly d in Appendices Fig. 3 (b) t = value follow ± 0.02 ± 0.02 (0.061 functi thickn thickn ΓR. Figure 3(a llustrates how ulting in a tran ate values (e.g
Note also that to peak with (Fig. 3(c)), a y the Fano ap n logarithmic s determined from s C and D. . (a) Normalized F = 10 nm, (c) t = 5 is designated in ws: (b) |q| = (0.293 22), (c) |q| = (1.033 29), (d) |q| = (2.10 1 ± 0.001). (e) |q| a ion of hole diamete ness for various p nesses (d = 110 nm a) presents exa w the asymmet nsmission dip . |q| = 1), and p t the resonance h increasing |q and thick (Fig pproach accord scale). Importa m the absorptio
Fano profiles for d 0 nm, and (d) t = each plot. The f 3 ± 0.003), Tc = (0 3 ± 0.007), Tc = (0 03 ± 0.021), Tc = as a function of fil er for various film periodicities and ( m).
amples of norm try parameter
for low values primarily a tran e energy shifts q|. Transmissio g. 3(d)) nano ding to Eq. (1) antly, ER and Γ on resonance s different |q| values 200 nm (d = 110 fit parameters wit .722 ± 0.006), Td = 0.291 ± 0.004), Td (0.0028 ± 0.0001) lm thickness for va m thicknesses (p = 2 (h) |q| as a functi malized Fano p drastically af s (e.g. |q| = 0.3 nsmission peak s from being cl on spectra for ohole films co ) (see Fig. 11 ΓR were not tre
spectra (BI), w s. Exemplary Fano 0 nm and p = 200 th their standard = (0.298 ± 0.010 e = (0.433 ± 0.010 e ), Td = (0.022 ± 0 arious hole diamet 200 nm). (g) |q| as ion of periodicity
profiles for dif ffects the tran 3), a dip-peak k for higher va lose to the tran r ultrathin (Fi ould all be a in Appendix eated as fit pa which are also p
o fits to Eq. (1) for nm). Extracted |q deviations are as eV−1) × E – (0.482 eV−1) × E – (1.191 .0005 eV−1) × E – ters and (f) |q| as a s a function of film y for various film
fferent |q| nsmission behavior alues of q nsmission ig. 3(b)), accurately F for the arameters, presented r | s 2 1 – a m m
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 lat Fig. 4 resona peak diame variou compa B. Comparis Fig. 5 metal using illumi ttice approxim 4. (a) Calculated ances calculated f positions (BI) ob eters. (c) SPP reso us thicknesses. Th arison. son between a 5. (a) Absorption film (b) 5 nm ov back illuminatio ination correspond mation (ELA) d dispersion relat from (a) using the btained from FD onances and abso he horizontal das absorption an
spectra and nearf er the metal-air in on (d = 110 nm, ding to (a-c).
tions for silver f e empty lattice app DTD simulations
orption peak posit shed lines designa nd near-field s
field data average nterface and (c) 5 p = 200 nm). (
films without nan proximation (ELA versus film thick tions versus nano
ate the SPP reso spectra
ed over the surfac nm under the met (d-f) Results obt
noholes. (b) SPP A), and absorption kness for various ohole diameter for onance energy for
ces parallel to the tal-glass interface, tained using front P n s r r e , t
C. Simulated Fig. 6 hole d Fig. 7 (botto at 200 d results for v 6. Transmission an diameters (periodic 7. Extracted peak om panels) as a fun 0 nm). various diame nd absorption (both city is fixed at 200
and dip positions nction of film thic
ters
h BI and FI) spec 0 nm).
(top panels) and ckness for various
ctra for various film
linewidths of the hole diameters (p m thicknesses and e absorption peaks periodicity is fixed d s d
D. Simulated Fig. 8 hole p Fig. 9 (botto fixed d results for v 8. Transmission an periodicities (hole 9. Extracted peak om panels) as a fun at 110 nm). various period nd absorption (both diameter is fixed a
and dip positions nction of film thic
dicities
h BI and FI) spec at 110 nm).
(top panels) and ckness for various
ctra for various film
linewidths of the s hole periodicities m thicknesses and e absorption peaks s (hole diameter is d s s
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