1. Introduction

The initial observation of enhanced optical transmission (EOT) through thin metallic films perforated with subwavelength apertures [1] has stimulated many fundamental studies as well as application-driven research over the past decade. The phenomenon has been observed in various structures, including perforated and continuous metal films [2–5]. While many attributed the excitation of surface plasmon polaritons (SPPs) on two surfaces of the metal film as the origin of this effect [6–8], others have also suggested that EOT is caused by the interference between diffracted evanescent waves generated by subwavelength features and questioned the role of SPPs in EOT [9–11]. The debate surrounding this issue emerged from observations of the discrepancy between the theoretical prediction of SPP spectral locations and the observed EOT peak positions [6].

More recently, the influential role of localized surface plasmons (LSPs) in EOT has been revealed by investigations of metallic films with various aperture shapes [4,12–16]. In contrast to the SPP resonances originating from periodicity present within the structure, LSPs are individual resonances occurring within the apertures whose characteristics are sensitive to the aperture geometry and the optical properties of the materials filling the apertures. Complex apertures generally offer higher coupling efficiencies to unpolarized light than simple square or rectangular apertures. For example, it has been demonstrated that cross-shaped holes can provide larger transmission than square or rectangular holes of same surface area [15], whereas the spectral locations of LSP resonances can be tuned by simply adjusting the widths or lengths of the arms of the crosses [14,15]. The interplay between SPP and LSP resonances, along with the scattering and diffraction of incident light by subwavelength features in thin metal films can give rise to rich spectral behaviour. For example, it has been shown that the excitation of Wood’s anomalies (WAs) and SPP resonances can alter the characteristics of the LSP resonances [14,16,17]; and the coupling between scattering and SPP excitation yields the asymmetric Fano resonance [18] line shape and the red-shift of the transmission peaks in the transmission spectrum of hole-array structures [19].

Here, we investigate computationally and experimentally the optical properties of thin metallic films perforated with periodic arrays of cross-shaped apertures, with an emphasis on the effects of periodicity on the transmission of the structure. By taking into account the response of an isolated aperture, we profile the role of LSPs, WAs and SPPs and show that EOT through the structure is attributable to LSP resonances of the apertures. For arrays of periodically arranged aperture arrays in metallic films, excited WAs and SPPs interfere with LSPs within individual apertures and give rise to an asymmetric spectral profile that can be interpreted as the excitation of Fano resonances occurring between the broad LSP resonances and the narrow-band periodicity-related resonances. This work complements the earlier investigation of resonant properties of cross-shaped apertures [14,15] and clarifies some of the controversy surrounding the physics of EOT, helping to develop a more complete understanding of the EOT phenomenon.

2. Spectral responses of periodic aperture arrays

Figure 1 shows a schematic of the structure used in this study, in which p is the lattice constant of the aperture arrays and l and w are the arm-length and the arm-width of the crosses, respectively. Here we assume the incident light propagates along the z-axis with electric field polarized along the y-axis. The aperture arrays were fabricated in a 140-nm-thick gold (Au) film on a glass substrate using focused ion beam milling. Details of the sample fabrication and characterization as well as the finite element method (FEM) based computational investigation, can be found in Ref. 14. Figure 2 shows the measured transmission spectra of four aperture arrays of various lattice constants; the detailed geometric parameters of the structure are given in the key. We see that as the period of the structure increases, the location of the transmission maximum of the LSP peak [14] (dashed arrow), and the location of the transmission minimum (solid arrow) situated just before this peak, shift to longer wavelengths.

 

Fig. 1 A schematic of the structure used in this study.

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Fig. 2 Measured transmission spectra of four fabricated samples. The geometric parameters of the structure are given in the key. The solid arrows and the triangles show the periodicity-dependent transmission minimum and maximum of interest, respectively.

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For a systematic comparison, we calculated the optical responses of different structures with p increasing from 400 nm to 700 nm in a step size of 100 nm with l and w fixed to 250 nm and 40 nm, respectively. Setting p as the only variable in the geometric parameters allows the elimination of effects on transmission introduced by variations in l and w in the structures. The FEM-based simulations of the transmission spectra of four aperture arrays are shown in Fig. 3 , along with the spectrum of an isolated aperture having the same values of l (250 nm) and w (40 nm). The transmittance of the single aperture has been rescaled to match the maximum transmission efficiency of the aperture arrays for the purposes of illustration. The trends observed in the simulated results agree well with the measurements, including the red-shifting of the transmission minimum (solid arrow), the modification of LSP peak profile as the periodicity increases and the robustness of the profile of the long-wavelength edge of the LSP peak. Furthermore, a transmission peak (indicated by the triangle markers in Fig. 2 and Fig. 3 for two spectra) located on the short-wavelength side of the periodicity-dependent transmission minimum becomes more noticeable in the computed spectrum. This short-wavelength peak and the adjacent transmission minimum form an asymmetric spectral feature that is not observed in the spectrum of the isolated aperture.

 

Fig. 3 Simulated transmission spectra of four structures with p ranges from 400 nm to 700 nm, and l and w are fixed to 250 nm and 40 nm, respectively. The periodicity-dependent transmission minimum and maximum are indicated as the arrows and the triangles, respectively.

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Comparing the transmission spectra of the aperture arrays with that of the single aperture, it is clear that, despite the arrays introducing a distinct periodicity-dependent asymmetric feature, the spectral features generated by aperture-array structure fall within the broad spectral region of the LSP resonance of the single aperture. Results from our previous investigation (Fig. 2 of Ref. 14) revealed that for structures of the same periodicity but different aperture geometries, the location of the asymmetric feature that lies on the short-wavelength side of the LSP peak remains fixed.

Figure 4 shows the positions of the transmission maxima (i.e. those indicated by triangles in Figs. 2 and 3) and minima (i.e. those indicated by arrows in Figs. 2 and 3) of the asymmetric profile as a function of structure periodicity, in which the rectangular and the circular markers represent the positions of the maximum and the minimum, respectively; the solid markers represent the results from FEM simulations and the open markers represent the results from sample measurements. The locations of (0, ± 1) SPP resonances (dashed line) and (0, ± 1) WA excitation (solid line) on Ag/glass interface, calculated from analytic expressions [6], are also displayed in Fig. 4. It can be seen that the wavelengths of the maxima closely follow the (0, ± 1) WA excitation conditions and the wavelengths of the minima coincide with those of the (0, ± 1) SPP resonances on Au/glass interface. These trends are similar to those reported by Xie et al. studying Bloch modes in 1D slit-aperture arrays [20]. It is worth noting that, although the transformation of the spectrum by the periodicity of the device shown in Fig. 2 and Fig. 3 are similar to what has been reported by Jiang et al. who investigated the rectangular-shaped aperture arrays and suggested that the transmission minimum was caused by the excitation of WAs [16], Fig. 4 reveals that these periodicity-induced transmission minima are related to SPP resonances, rather than WA excitation.

 

Fig. 4 The positions of the maxima and minima of Fano profile within the spectra as a function of structure periodicity. The theoretical locations of (0, ± 1) SPP resonances (dashed line) and (0, ± 1) WA excitation (solid line) on Ag/glass interface are also displayed.

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3. Field distributions

The asymmetric line-shape has been observed in the transmission/reflection spectra of various plasmonic nanostructures and many have applied the concept of Fano resonances to the interpretation of this feature [21]. Fano resonances were discovered by Ugo Fano in a quantum mechanical study of autoionization of atoms; it describes the asymmetric line-shape observed in the excitation spectra in terms of interference between a continuum and a discrete state [18]. As indicated in Fig. 3, the spectral overlapping of the broad LSP resonances of individual aperture and the narrow-band surface wave excitations (WA or SPP) arising from the periodicity of the structure satisfies the requirement for a Fano resonance. By investigating the electric field transformation around the maximum and minimum of the asymmetric spectral feature, the underlying nature of the trends observed in Fig. 4 can be revealed. Figure 5 shows FEM simulations of E_z, the electric field component normal to the metal surface that highlights the excitation status of the surface waves and LSPs, on the y-z plane through the centre of a cross-shaped aperture. The periodicity of the aperture arrays is 600 nm with a transmission spectrum shown as the brown dashed line in Fig. 3. To provide a clear view of the responses of the structure, fields at four wavelengths are displayed: (a) λ = 900 nm, (b) λ = 912 nm (corresponding to a WA), (c) λ = 942 nm (SPP excitation) and (d) λ = 1050 nm. The colour maps shown in Fig. 5 are normalized to the maximum absolute value of E_z at λ = 1050 nm.

 

Fig. 5 Calculated field distributions on y-z plane passing through the centre of a cross-shaped aperture in the array with p = 600 nm, w = 40 nm and l = 250 nm.. (a) λ = 900 nm, (b) λ = 912 nm, (c) λ = 942 nm and (d) λ = 1050 nm. The arrows represent the electric field vectors and colour maps represent the amplitude of field component normal to the metal surface (E_z). The colour maps are normalized to the maximum absolute value of E_z at λ = 1050 nm.

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In Fig. 5(a), the co-existence of LSP resonances and diffracted propagating waves is clearly visible: the LSPs occur on the ridges of the aperture and diffracted field is apparent near the unperforated region on the Au/glass interface. Interference between propagating diffracted orders in the substrate is also apparent. Simulations of field distributions at shorter wavelengths confirm that the co-contribution of LSP excitation and diffraction by periodic apertures gives rise to the additional peak appearing on the short-wavelength side of asymmetric feature in the transmission spectrum of the structure, i.e., the peaks at around 720 nm, 850 nm and 950 nm for structures with a periodicity of 500nm, 600 nm and 700 nm, respectively. This additional peak does not appear in the transmission of the structure with p = 400 nm as it is located outside the spectral range shown in Fig. 3, whereas for the structure with p = 414 nm (green line in Fig. 2) the peak shifts to longer wavelengths and therefore becomes observable in Fig. 2. Nevertheless, the focus of this study is the nature of the asymmetric feature introduced by the periodicity of the structure, which will be revealed in the following discussion.

Figure 5(b) shows that as λ is increased to 912 nm – the wavelength of (0, ± 1) WA excitation, the (0, ± 1) diffracted order grazes the Au/glass interface and E_z exhibits a strong spatial extension away from the Au/glass interface. The E_z amplitudes of the diffracted waves and LSPs imply that WA excitation and LSP resonances do not destructively interfere with each other. In contrast, Fig. 5(c) shows that at λ = 942 nm – the wavelength of (0, ± 1) SPP modes on the Au/glass interface, E_z is noticeable weaker than at other wavelengths (with the field amplitude near the unperforated region of the Au/glass interface is ~1/3 of that at λ = 912 nm). Below the unperforated area E_z decades rapidly away from the glass/Au interface, showing the signature of SPP excitation. The amplitude of the SPP field is relatively low at this wavelength, which seems to contrary to what is generally expected upon SPP excitation – a strong local field enhancement near a metal/dielectric interface. However, it can be seen that the amplitudes of the LSPs existing on the ridges of the aperture are also low, particularly near the Au/glass interface. This implies that the nature of the interference between LSPs and SPPs is destructive, which results in a decrease in the transmission efficiency of the structure at the SPP excitation wavelength. As the wavelength increases further (results not shown here), the strength of SPP excitation decreases rapidly and the strength of the LSPs on the ridges of the aperture increases. At λ = 1050 nm which is the central wavelength of the LSP-related transmission peak, the fields localized on those sites reach the maximum value, as displayed in Fig. 5(d).

A clearer picture of the interference between LSPs and surface waves emerges from studies of local field patterns near the Ag/glass interface. Figure 6 illustrates the E_z profile on x-y planes located at 5 nm above the Au/glass interface in the Au film layer (indicated by z = + 5 nm in the figure) and 5 nm below the interface in the glass substrate layer (indicated as z = −5 nm). Since the aperture geometry affects only the amplitude of the maximum in the asymmetric feature in the spectrum but not its location, we here show the results for a structure with p = 600 nm, l = 350 nm and w = 40 nm, which is the arrangement with a relatively high transmission in the asymmetric feature (as seen in Fig. 2 of Ref 14). The colour scales shown in Fig. 6 are normalized to the maximum absolute value of E_z on z = + 5 nm plane at λ = 942 nm. Figure 6(a) and 6(b) show E_z at λ = 912 nm (peak) and λ = 942 nm (minimum), respectively. For comparison, E_z at the centre wavelength of the LSP peak (λ = 1240 nm) is also displayed in Fig. 6(c), as the field distributions at this wavelength best resemble the profiles of LSPs occurring in an isolated aperture [14].

 

Fig. 6 E_z profiles on x-y planes situating at 5 nm above the Au/glass interface in the Ag film (z = + 5 nm) and 5 nm below the interface in the glass substrate (z = −5 nm). Structure geometry: p = 600 nm, w = 40 nm and l = 350 nm. (a) λ = 912 nm, (b) λ = 942 nm and (c) λ = 1240 nm. The colour scales are normalized to the maximum absolute value of E_z on z = + 5 nm plane at λ = 942 nm.

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We see that for y-polarized incident light, LSPs are excited along the ridges of the x-oriented arm of the cross-shaped aperture. At λ = 1240 nm the maximum field amplitude occurs near the intersection of two arms, with a large spatial extension into the y-oriented arm of the aperture is clearly visible on z = + 5 nm plane. The phases of the LSP fields are maintained across the interface at this wavelength. The field patterns suggest that LSPs excited at the ridges of the aperture act as an efficient dipole scatterer re-emitting the incident light in the z-direction. In contrast, at the shorter wavelengths where periodicity-related responses exist, E_z in the vicinity of the aperture shows different characteristics. The degree of modification of the LSP profile in the presence of surface wave excitation is determined by the relative strength of two fields. As illustrated in the z = + 5 nm plane plots in Fig. 6(a) and 6(b), in the regions where the LSP excitation is relatively weak, i.e., near the two ends of the y-oriented arm of the cross, a reversal of the phase of the E_z component (with respect to that at λ = 1240 nm) is clearly visible. Near the vicinity of the x-oriented arm, E_z profiles are rather different at WA excitation and SPP resonance wavelengths. At λ = 912 nm, E_z in these regions remains similar to that shown in Fig. 6(c). Furthermore, E_z propagating along the interface tends to avoid the structured area on the metal film while still maintaining its profile. Therefore, the total response of the structure at this wavelength is the sum of two excitation processes. The increase in E_z leads to enhancement of the total electric field on the output interface of the structure, which results in the transmission peak observed at WA excitation wavelength. On the other hand, at λ = 942 nm (Fig. 6(b)) E_z distributions around the x-oriented arm of the cross are noticeably different from that shown in Fig. 6(c), that is, on the z = + 5 nm plane the local field maximum occurs in the metallic side of the aperture sidewalls rather than in the air gap. Furthermore, it can be seen from the z = −5 nm plane plot that the excited SPP field is drawn towards the x-oriented arm of the aperture at the interface. The dramatic modification of the field distribution in the vicinity of the aperture upon the excitation of the SPP resonances suggests that the initial amplitude of SPP field on Au/glass interface is significantly larger than that of LSPs. Owing to the presence of the aperture in the metal film, the collective electron oscillation near the metal surface upon SPP excitation is interrupted by the discontinuity in the metal film, resulting in charge accumulation on the Au side of aperture sidewalls, which leads to the spread of the SPP fields towards the x-oriented arm of the aperture observed on the z = −5 nm plane. The electric field arising from the charge accumulation interacts with the LSP field of the aperture and causes the reversal of the phases of E_z near the ridges of the x-oriented arm of the aperture across the Au/glass interface. This distorts the LSP dipole emitter of the aperture and leads to zero transmission of the structure at SPP resonance wavelength. The overall weak E_z field strength observed at this wavelength is a consequence of the destructive interference between two SP modes.

4. Conclusion

We have shown that EOT through cross-shaped aperture arrays in thin metal films is attributable to LSP resonances of the apertures. The overall optical response of the array structure involves mainly surface excitations on the Au/glass interface rather than elsewhere in the structure. The periodicity-related optical phenomena, including WA and SPP excitation, interfere with LSP resonances occurring within the cross-shaped apertures and generate a distinct asymmetric Fano line-shape in the transmission spectra of the structures. The simulations of field distributions show that at the wavelength of WA excitation, the total response of the structure is the sum of LSP excitation and the (0, ± 1) diffracted order grazing the Au/glass interface. Therefore, the transmission maximum of the Fano profile, which appears at the WA excitation wavelength, is a result of the constructive interference between LSPs and the diffracted light propagating on the output interface of the structure. In contrast, at the wavelength corresponding to SPP excitation the field amplitudes of both LSPs and SPPs are weak, suggesting that the transmission minimum of the Fano profile, which appears at the wavelength of SPP excitation, is a consequence of the destructive interference between LSPs and SPPs. The findings of this study clarify the effects of WA, SPP and LSP resonances on the transmission properties of metallic films perforated with subwavelength aperture arrays and confirm the negative role of SPP resonances in the EOT phenomenon.