Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films

We investigate field enhancements by one-dimensional periodic arrays of tapered slits fabricated to a high quality (nm precision) using focused ion beam milling in a 180 nm-thick gold film. Tapering of periodic slits in metal was recently shown to boost the extraordinary optical transmission (EOT) exhibited by similar, but non-tapered, plasmonic structures. Here, both simulated and experimental reflection spectra, along with high-resolution two-photon luminescence (TPL) scanning optical images and simulated electric field plots of the metal slits, are compared, revealing good correspondence between spectral dependences and field intensity enhancements (FEs) estimated via the local TPL. Experimentally investigated structures had a fixed taper angle α=20.5° for two different widths, w=80 and 130 nm, having gaps g=25 and 65 nm, respectively, both fabricated at two different periods, Λ=500  and 700 nm. We attributed the obtained FE reaching ∼110 to nanofocusing and resonant interference of counter-propagating plasmons by the periodic tapered gaps. As both simulated and experimentally achieved FEs depend on taper angle, gold film thickness, period and gap of the slit arrays, the resonances can actually be tuned in the wavelength range from visible to infrared, making this configuration promising for a wide range of practical applications, e.g. within surface-enhanced spectroscopies.


Introduction
The phenomenon of extraordinary optical transmission (EOT) has triggered numerous investigations and findings [1] since its discovery [2], and several interesting configurations ranging from both random and periodic hole arrays [1,2] to slit arrays [3][4][5][6][7][8][9] have been characterized, while new high-quality structures continue to pose more fascinating and promising applications. However, to date the majority of the investigated slit arrays have consisted of only straight slits, i.e. arrays of slits each having parallel walls through the thickness of the metal film [1,[3][4][5][6][7][8][9]. It is interesting to also examine in detail plasmonic slits having walls tapered at an angle through the metal film thickness.
Recently, one-dimensional (1D) gratings of closed plasmonic V-grooves were treated theoretically [10], and we experimentally investigated the field intensity enhancements (FE) ascribed to the surface plasmon (SP) nanofocusing by the closed tapered shape at the V-groove bottom [11]. In addition, we very recently investigated 2D V-groove arrays, e.g. via scanning Raman microscopy, thereby directly applying the demonstrated SP nanofocusing at the V-groove bottom, and revealing that (V-shaped) tapering is indeed among the important geometrical parameters when aiming at the fabrication of plasmonic structures with relatively large FEs suitable for surface-enhanced sensing [12].
To follow this idea, we also very recently investigated (open) periodic tapered slits in a gold film via both reflection and transmission spectra for relatively large 65 nm gaps at the bottom and slit periods of 500 and 700 nm [13]. To summarize, these investigations demonstrated that the EOT phenomenon can be influenced and even further enhanced by using tapered slits (instead of slits with parallel walls) [13]. Nevertheless, to date no direct characterization of the FEs achievable within the nm gaps of the (open) tapered slit configuration has been performed, but this could reveal additional possibilities of slits being used as substrates for surface-enhanced Raman scattering.
One well-established experimental technique for the evaluation of FE in nanostructures is two-photon photoluminescence (TPL) from metals, which was earlier described [14,15] using spatially resolved TPL studies [16,17] and near-field imaging [18] used in the characterization of local FEs. We have previously used TPL signals in scanning optical microscopy to facilitate direct estimations of the local FE (at a diffraction-limited resolution) achieved with various types of sample, such as individual metal nanostrips [19], periodic metal nanoparticles [20] and fractal shaped metal nanostructures [21]. 3 In this paper, we investigate (500 and 700 nm) periodic arrays of high-quality tapered slits fabricated using focused ion beam (FIB) milling in a 180 nm-thick gold film, with the high sample quality being demonstrated via detailed scanning electron microscopy (SEM) images. Compared to our previous experimental reflection and transmission characterization of a tapered slit configuration [13], the present investigation involves much smaller gaps of only 25 nm, and the comparison with those of 65-nm-gaps. Here, we demonstrate very good agreement between experimental and simulated reflection spectra, obtained for both resonant and non-resonant excitation of the slits. In addition, we use for the first time TPL microscopy to map local FE in narrow nm-gaps at the bottom of the periodic tapered slits and obtain good correspondence between the estimated spectral FE dependence and both reflection and transmission as well as simulated spatial field distributions within the tapered slits. Finally, we show additional simulations elucidating the effect of tapered slit arrays on reflection, absorption and transmission during regular illumination (from the side with the widest slit opening) versus inverse illumination (from the side with the narrowest openings).
We expect that the new tapered slit configuration can lead to improvements in several promising applications already involving EOT, as well as in possible new applications in surface-enhanced sensing.

Sample geometries and reflection spectra
The experimentally investigated sample consists of 1D periodic line arrays of parallel tapered slits in a gold film, with each array covering ∼30 × 30 µm 2 and separated from other arrays by at least 500 µm. The geometric parameters of the slits were a fixed taper angle α = 20.5 • for two different widths, w = 80 and 130 nm, having gaps on the exit side g = 25 and 65 nm, respectively, both fabricated at two array periods, = 500 and 700 nm ( figure 1(a)). The arrays were fabricated by FIB milling, and obtained SEM images show the good quality and reproducibility of each slit ( figure 1(b)). Using the FIB to completely mill out the gold film across test areas, e.g., having only a few slits, and obtaining SEM images at tilted angles facilitates the characterization of the geometric tapered slit parameters (figure 1(c)).
We use reflection spectroscopy [22] to map the SP resonances of the tapered slit arrays before investigations with TPL microscopy. Our experimental setup for reflection spectroscopy has been described in detail previously for experiments with gold nanostrip antennas directly on glass substrates [19,23]. Here, we use a similar method, but with a ×60 objective (numerical aperture (NA) = 0.85) and take the reference spectra R gold from the smooth gold film (instead of from the glass substrate) in order to compare directly with reflection R slits from tapered slit arrays. Note that, in contrast to previous reflection spectroscopy experiments [19,23], we do not cover the sample with index matching oil.
We support the experimental characterizations with theoretical reflection spectra simulated using the Green function surface integral equation method, recently treated in detail for closed V-grooves [10]. Here, we simulate reflection spectra specifically for tapered open slit arrays having the same geometric parameters as those of the fabricated sample (figure 2). Throughout the paper we use the refractive index 1.5 of glass for all considered wavelengths, and for gold we apply linear interpolation of the Johnson and Christy data [24] to obtain the refractive index at the wavelength of interest. In the simulation of figure 2, light is collected within an angle of ±50 • and then averaged over a set of calculations performed for each angle of incidence (stepped by 1 • ) in the range 0 • -50 • , corresponding approximately to the NA = 0.85 objective used for illumination and collection in the experiment. We also treat the theoretical results in a similar way by normalizing with respect to the reflection from a planar gold surface, thereby making simulations and experimental reflection spectra directly comparable.
We show reflection spectra for resonant p-polarized excitation and detection (figures 2(a) and (c)), i.e. with electric field in the xz-plane and perpendicular to the tapered slit, as well as for the fundamentally different non-resonant s-polarized excitation and detection (figures 2(b) and (d)), i.e. with electric field parallel to the slits [13]. First of all, it is important to note the large difference in reflection levels obtained with p-versus s-polarized configurations. In addition, for resonant p-polarized excitation and detection, the reflection spectra reveal a clear dependence on the array period (figure 2), with the shortest period ( = 500 nm, gaps g = 25 and 65 nm) exhibiting strong experimental reflection dips around the wavelength 740 nm, whereas arrays with the longer period ( = 700 nm, gaps g = 25 and 65 nm) have considerably weaker resonances approaching 700 nm for this polarization configuration (figure 2(a)). On the other hand, for the non-resonant s-polarized excitation and detection, all arrays only have a minor reflection dip fixed around 500 nm wavelength (figure 2(b)).
For each polarization configuration, there is a good correlation between the resonances appearing in simulated and experimental reflection spectra. In fact, realizing that there is a ∼50 nm blue shift in the experiments compared with the simulated spectra, even subtle details such as 'shoulders' or weaker dips are clearly reproduced in the simulation. Note that for s-polarized configuration the spectral termination towards unity for short wavelengths approaching 400 nm is mainly due to the limitations of the experimental setup caused by low lamp intensity and weak signals (from both the reference and the sample) in this range.
Increasing depths in the reflection spectra should be related to both increasing absorption/transmission and scattering by tapered slit arrays. Hence, the significant dip in reflectivity obtained even with a relatively high NA of 0.85, where most scattered light would actually be recollected within the large spatial angle of the objective, indicates that a major part of this dip can be ascribed to possible changed polarization of the scattered light, as well as to increased absorption or transmission by tapered slit arrays. For resonant p-polarized excitation and detection, the strong dips are clearly related to the array period and are relatively much less affected by slit width (figures 2(a) and (c)). Conversely, for the non-resonant s-polarized case increasing depth obtained in the reflection spectra is mainly governed by the larger slit width (130 nm vs 80 nm) and subsequently the shorter period (500 nm vs 700 nm), in good agreement with the expected behavior, and originates from the relatively larger area (filling ratio) covered by open slits where less light is reflected (figure 2(b) and (d)). That is, according to both experiment and simulations, for the non-resonant case, the lowest reflection is obtained with the shortest period = 500 nm and the largest width w = 130 nm.

Two-photon photoluminescence microscopy mapping local field enhancements
Our experimental setup for TPL microscopy is essentially the same as that described in detail for previous experiments [25]. It consists of a scanning optical microscope in reflection geometry built on the base of a commercial microscope and a computer-controlled 2D piezoelectric translation stage (steps down to 50 nm, accuracy ∼4 nm). The linearly polarized light beam from a mode-locked pulsed (pulse duration ∼200 fs, repetition rate ∼80 MHz) Ti-sapphire laser (λ = 730-850 nm, δλ ∼ 10 nm, average power ∼300 mW) is used as a source of sample illumination at the fundamental harmonic (FH) frequency. After passing through an optical isolator (to avoid back-reflection), a half-wave plate, a polarizer and a wavelength selective beam splitter, the laser beam is focused on the sample surface at normal incidence with a Mitutoyo infinity-corrected ×100, NA = 0.7, objective. The illumination power is selected in the range 0.2-0.7 mW, depending on the wavelength and the obtained TPL signals. The TPL radiation generated in reflection and the reflected FH beam are collected with the same objective, separated by the wavelength-selective beam splitter, directed through appropriate filters and detected with two photomultiplier tubes, the tube for TPL photons being connected with a photon counter. The TPL detection has been improved compared with earlier investigations [25,26], leading to very low TPL dark counts, usually ∼20 counts per second (cps).
Typical FH and TPL images (3 × 3 µm 2 ) obtained at 750 nm excitation wavelength, 100 ms integration time at each point and 50 nm steps between points for the array with 700 nm periodicity and very narrow (w = 80 nm) slit entrance width reveal bright lines along the slits resonantly excited at p-polarized illumination, indicated by a white arrow (figures 3(a) and (b)). Here, we do not show TPL images for the non-resonant s-polarized configuration, where we obtained relatively much weaker TPL signals, as expected from the weaker dips in the reflection spectra (figures 2(b)-(d)), and indeed a significantly stronger TPL from slits excited with p-polarized light should also be expected directly from the polarization properties of channel plasmon polaritons [29]. In order to have significant TPL signals at relatively low incident powers, we did not use polarized TPL detection. For an incident power of less than 0.7 mW, the obtained maximum TPL signal for resonant p-polarized excitation was ∼ 220 cps, which is comparable to that obtained from plasmon nanofocusing by periodic closed V-grooves [12].
The simultaneous recording of TPL and FH signals as a function of scan coordinates results in the matching FH and TPL images (e.g. figures 3(a) and (b)) and facilitates direct comparison of FH and TPL cross-sections (figure 3(c)). Here, the cross-sections of FH images obtained in the parallel-polarized configuration of excitation and detection replicate well (with diffractionlimited resolution) the longest 700 nm period of the slit array ( figure 3(c)). The transmission as well as stronger (depolarized) scattering at the open slits causes the slits to appear dark in the FH image ( figure 3(b)), compared to practically mirror-like reflection at flat areas in-between the slits. On the other hand, the TPL images exhibit the strongest signals directly from the slits and hence the resulting FH and TPL cross-sections clearly oscillate between maxima of TPL and FH, respectively ( figure 3(c)). Based on the cross-sections, we estimate FH and TPL resolutions at a full-width at half-maximum of ∼0.7 µm and ∼0.5 µm, respectively.
Considering instead typical FH and TPL images from the most densely packed slit array having the widest w = 130 nm slit and the shortest 500 nm period (figures 4(a) and (b)), we are not able to resolve individual slits in the FH image, while it is still possible to resolve each slit in the TPL image. At the same time, cross-sections of the FH and TPL images also demonstrate these different resolution capabilities (figure 4(c)). As compared to FH images, improved TPL resolution should be expected due to the shorter wavelengths, as well as the square TPL dependence on intensity, leading generally to √ 2 better TPL resolution and explaining why slits are resolved in the TPL image, whereas FH images are blurred. Furthermore, the nonlinear TPL signal originates from the narrow gap at the bottom of the slits, where FE by nanofocusing is strongest, whereas the linear FH signal merely maps decreased reflection at the entire slit entrance width.
The mutual correlation between FH and TPL cross-sections obtained across slits (figure 3(c)) indicates that FH light (with polarization perpendicular to the slits) is transmitted, strongly damped or effectively scattered into other polarizations by the slits. Absorption and transmission of SPs focused towards the slit bottom dominate, as will also be demonstrated by our simulations (figure 8). For this reason, one should not expect very efficient collection of the TPL emitted at the bottom of the slits, since part of this would be reabsorbed or transmitted by the slits. It should be noted here that SPs (re)-excited at the relatively short TPL wavelengths will also be damped more strongly and have considerably shorter propagation lengths of only a few micrometers.
Applications of TPL scanning optical microscopy to the characterization of local FE (of the incident FH radiation) in gold nanostructures can be considered well established [27,28,30]. For each slit array, we obtained TPL images of a fixed ∼3 × 3 µm 2 area for six different FH excitation wavelengths in the range λ = 730-850 nm. All measurements were obtained for p-polarization, with the first five taken at wavelength steps of 15 nm and the last one shifted by 60 nm to λ = 850 nm. Taking cross-sections averaged over ten adjacent lines in these TPL images, similar to the one shown in figure 3(c), we can evaluate the dependence of typical TPL levels, e.g. those from the narrow gap of the slits, on the excitation wavelength, slit width and period.
A quantitative evaluation of FEs can be carried out by comparing TPL signals from each slit to that from a smooth gold film [27,28,30]. Following this approach, the FE factor α can be written where TPL is the obtained TPL signal, P is the used average incident power and A is the area producing the enhancement. Here, A ref is taken as the area of the focused FH beam crosssection, i.e. ∼π(0.35 µm) 2 , whereas A slit is estimated to be part of the edges closest to the slit bottom, where the expected FE is largest [13], and being illuminated along the crosssection of the focused FH beam. Based on simulations of the field magnitude distributions in slit arrays [13], we estimate the effective width actually producing TPL to be twice the projection of the lowest 1/3 of slit side walls corresponding to ∼20 nm, resulting in an area A slit = 0.02 µm × 0.7 µm = 0.014 µm 2 , i.e. an area reduction of ∼27 compared to that of the reference TPL. At the same time, an important issue concerns the actual TPL light propagation from the slit bottom towards the detector, since this will be limited by the slit taper angle (e.g. 20.5 • corresponding to NA = 0.17), which is smaller than the high NA of 0.7 used to obtain reference signals with the TPL setup. We approximate this limitation on the TPL to reach the objective by taking into account only the slit taper angle, since most of the TPL enhancement originates from the bottom of the slits where the FE is strongest. Hence, in our FE estimate we take this smaller detectable angle into account by multiplying TPL slits levels with 0.7/0.17 for a slit array having a taper angle of 20.5 • .
Using calibrated TPL signals obtained from smooth gold film regions (e.g. ∼2.9 kcps at λ = 730 nm and an incident FH power of 25 mW), we evaluate the FE dependence on FH excitation wavelengths from 730 to 850 nm based on TPL levels obtained in the slit arrays exposed to p-polarized light (figure 5). We estimate the largest FE factors of up to ∼110 from the 500 nm periodic array having the narrow (w = 80 nm) slits. Indeed, the slit arrays with the shortest 500 nm period, having a significant dip in reflection spectra around 740 nm, should be expected to exhibit the largest FE for excitation wavelengths in this range. Likewise, the significantly lower FE for arrays with a larger (700 nm) period is also in good agreement with the lower and decreasing dips in reflection spectra at wavelengths above 730 nm (figures 2(a) and (c)). All in all, within the wavelength interval 730-850 nm accessible with our excitation laser and detection range of the experimental setup, we obtain qualitatively good agreement of the estimated FEs (figure 5) with the shape expected from both experimental and simulated reflection spectra (figures 2(a) and (c)). Since the main TPL originates from the resonant p-polarized excitation of the slits (cf also spectra, figures 2(b) and (d)), we only estimated the FE levels achieved in that configuration.

Simulations for air-suspended one-dimensional slit arrays
The theoretical simulations presented throughout this paper have all been obtained with the Green's function surface integral equation method for periodic structures [31,32], where the version of the method that we have used is identical to that described in more detail in our previous work [10], with the exception that in the case where we consider a perforated gold film placed on a glass substrate (figures 2(c) and (d)) we use a different Green's function. Very briefly, the method is based on an identity that allows us to calculate the magnetic field at any position outside scatterers as the sum of an incident field and an integral over the surfaces of scatterers, where the integrand involves a reference-medium Green's function, the magnetic field at the surfaces and the surface normal-derivative of the magnetic field. For positions inside scatterers, a similar relation exists, but with no incident field and with the Green's function modified for the material of the scatterers. Self-consistent equations for the magnetic field and its normal derivative at the surface of scatterers are obtained by letting the observation point approach the surfaces from both sides and by applying the electromagnetic boundary conditions. The resulting equations are discretized and solved on a computer, whereby we obtain the surface magnetic field and its normal derivative, and the starting equations can then be used to directly calculate the field at any other position of interest. For numerical reasons all corners in the considered geometries have been rounded with a 2 nm radius of curvature.

Tunability of resonances
For the above characterization the designed structure had intended resonances and spectral details in the detection range of our TPL microscopy setup. Here, we demonstrate the wide possibilities of tuning the resonances by proper adjustments of the slit taper angle, period, gold film thickness (slit depth) and gap width. Note that the spectra to be presented in figures 6-9 are all obtained with plane wave illumination and therefore cannot be directly compared to the simulated (and measured) reflection spectra in figure 2, where we average over illumination angles within ±50 • (NA of the objective).
We begin by visualizing the calculated electric field magnitude around periodic tapered slits in a gold film of fixed thickness h = 200 nm, suspended in air with tapered slits having fixed gap g = 10 nm, period = 500 nm and taper angle α = 20 • , and excited with p-polarized light at the resonance wavelength λ = 825 nm ( figure 6(a)). The electric field is indeed increased significantly by the periodic openings on the front side and focused towards the gap on the exit side via SPs in the tapered slits, where the maximum relative field magnitude exceeds ∼35 ( figure 6(a)). To investigate the influence of varying the slit taper angle α as well as the period , we also present a series of simulated transmission spectra for p-polarized light incident on 12 different arrays with period = 500, 600, 700 or 800 nm and taper angle α = 0 • , 20 • or 40 • in a gold film of fixed thickness h = 200 nm, with fixed slit gaps g = 10 nm at the exit side (figures 6(b)-(d)). It is observed that an isolated increase of the period leads to a red-shifted resonance position (cf any fixed taper angle of figures 6(b)-(d)), whereas the increasing of the taper angle α leads to a blue-shifted resonance position (figures 6(b)-(d)). At the same time these transmission spectra demonstrate a much improved tunability accessible by just varying the period of the slit arrays when the taper angle is relatively large, e.g. α = 40 • as in figure 6(d).
That is, the redshift in resonance position when selecting array periods from 500 to 800 nm is only ∼30 nm for straight slits (having taper angle α = 0), compared with the much larger redshift of ∼150 nm available for slit arrays with taper angle α = 40 • .
Note that, in the above discussion, we still did not apply the additional tunability available by adjusting also the film thickness and gap size. Here, an alternative way of demonstrating the large tunability can be to show the possibility of actually keeping a certain resonance position fixed by simultaneous proper adjustment of several parameters, whose separate adjustment would each lead to significant shifts in resonance. In figure 7, we use this approach to keep a resonance fixed around 830 nm, while still modifying the sample geometry by simultaneous adjustments of taper angle α = 0 • -40 • and film thickness (height h = 138-221 nm). In this connection, it should be noted that the resonance position can only be kept fixed for one array period at a time, since each period responds proportionally to adjustments in film thickness and slit taper angle. Again, the transmission spectra also demonstrate the widest tunability by array period for the largest slit taper angle of α = 40 • ( figure 7(d)). The influence of gap size will be demonstrated in figure 8.

Regular versus inverse orientation of illumination
In all of the above results, we selected the illumination direction from the wide side of the slit towards the narrow gap at the slit bottom (cf e.g. figure 6(a)). However, according to the reciprocity theorem, transmission through the slit array should actually be independent of the direction of illumination, i.e. of whether the illumination is regular, from the front, or inverse, from the rear of the slit array. This means that in a sense both nanofocusing of light and the reverse situation of nanodefocusing of light, corresponding to the tapered slit opening becoming smaller or larger in the direction of transmission through the structure, have exactly the same effect on the transmission [13]. Meanwhile, the reflection and absorption will in general be different in the two situations, and consequently it can be interesting to follow their behavior during illumination with both regular and inverse sample orientation.
As an example, we first visualize the simulated electric field magnitude around a 200nm-thick air-suspended gold film with slit taper angle α = 20 • , gap g = 50 nm and period = 500 nm during plane wave illumination with p-polarized light at the resonance wavelength of λ = 750 nm in regular orientation, as indicated by red arrows (figure 8(a)). This configuration is similar to that investigated via TPL microscopy in figure 4, except for having slightly smaller gaps g = 25 nm and the gold film being deposited on a glass substrate. From the visualized electric field magnitude one can imagine how illumination at the regular orientation of this array leads to nanofocusing and fields enhanced by a factor of ∼13 towards the narrow gap side in the tapered slit ( figure 8(a)). By squaring this enhancement factor for the field magnitude we obtain an FE (field intensity enhancement) of ∼169, compared with the FE of ∼110 estimated via TPL microscopy (figure 5). Furthermore, simulated reflection, transmission and absorption spectra for the above array geometry (h = 200 nm, α = 20 • and = 500 nm) with various gaps g = 0, 1, 3, 5, 10, 20 and 50 nm, all being illuminated with p-polarized light in the regular orientation, reveal strong dips in the reflection (up to 90% decrease in reflection at the resonance wavelength for the largest gap), as well as relatively high absorption levels through the narrowing slits (figures 8(b)-(d)). In contrast, for inverse orientation of the slit array the field magnitude does not show the same concentration of light and the absorption is much less ( figure 9).
For the regular orientation, the much larger absorption experienced when 'squeezing' light through the narrowing bottom of the slit is compensated for by lower reflection at the wide slit entrance. Likewise, for the inverse orientation the absorption in expanding slit openings is relatively lower, whereas the reflection is instead rather high due to the encountered larger area covered by flat metal and only very narrow slit openings in the metal (gaps g = 0-50 nm). Anyway, as expected from the reciprocity theorem, transmission is actually the same for regular and inverse illumination (figures 8(c) and 9(c)). These additional simulations elucidate the effect on reflection, absorption and transmission during regular versus inverse illumination and one could in fact also literally state: 'EOT is enhanced by nano-de-focusing'. On the other hand, the local FE is related in particular to the absorption and therefore the FE differs for the two excitation directions. Hence, if one could perform TPL on gaps from the rear, one would obtain different TPL signals. However, one should remember that the simulated results (figures [6][7][8][9] were all obtained for symmetric air-gold-air configurations and for the current experimental sample, fabricated on a relatively thick glass substrate, we did not have the possibility of performing accurate TPL investigations in the inverse illumination orientation.

Conclusion
In conclusion, we have investigated FEs by 1D periodic arrays of tapered slits fabricated with high quality (nm precision) using FIB milling in a 180 nm-thick gold film. Tapering of the periodic slits in metal was recently shown to boost the EOT exhibited by similar, but nontapered, plasmonic structures.
We compared both simulated and experimental reflection spectra, along with highresolution TPL scanning optical images and simulated electric field plots of the metal slits, revealing good correspondence between the spectral dependences and local TPL. The experimentally investigated structures had a fixed taper angle α = 20.5 • for two different widths, w = 80 and 130 nm, having gaps g = 25 and 65 nm, respectively, fabricated at two different periods, = 500 and 700 nm. We attributed the obtained FEs reaching ∼110 to nanofocusing and resonant interference of counter-propagating plasmons by the periodic tapered gaps.
Since both simulated and experimentally achieved FEs depend on taper angle, gold film thickness and period and gap of the slit arrays, the resonances can actually be tuned in the wavelength range from visible to infrared, making this new tapered slit configuration promising for improving a wide range of practical applications already involving EOT, as well as for possible new advances, e.g. within surface-enhanced spectroscopies and sensing [33][34][35].