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Dual resonant bands in UV and the visible range were simultaneously observed in the enhanced optical transmission (EOT) through star-shaped plasmonic structures. EOTs through four types of polygonal bull’s eyes with a star aperture surrounded by the concentric star grooves were analyzed and compared for 3, 4, 5, and 6 corners, using finite difference time domain (FDTD) method. In contrast to plasmonic resonances in the visible range, the UV-band resonance intensity was found to scale with the number of corners, which is related with higher order multipole interactions. Spectral positions and relative intensities of the dual resonances were analyzed parametrically to find optimal conditions to maximize EOT in UV-visible dual bands.
© 2015 Optical Society of America
Introduction
Surface plasmon polaritons (SPPs) have shown a hyper-sensitive response to variations of structural parameters in both reflection and transmission, which has opened new opportunities not only in photonics but also in biological and material science [1–6]. In nano-aperture plasmonic arrays, extraordinary transmission has been observed by Ebbesen nearly a decade ago, which initiated intensive research on plasmonic structures with unique spectral control capability in the optical transmission [7]. However, those nano-aperture arrays in a metallic film have suffered from low transmission efficiency, and concentric grooves around the central aperture have been added form a bull’s eye structure to further maximize enhanced optical transmission (EOT) [8–11]. Bull’s eye structures have shown that the transmitted light can be strongly enhanced via resonant SPP excitation in the periodic corrugations. These enhanced optical transmissions are directly involved in a number of applications, such as refractive index biosensors, optical tweezers, and enhanced Raman scattering sensors, to name a few [12–14]. Recent plasmonic investigations have renewed unique importance of bull’s eye structures and various geometrical modifications from the original circular structure have been attempted. Elliptical aperture surrounded by circular grooves, elliptical aperture surrounded by elliptical grooves, and polygonal aperture surrounded by polygonal grooves have been reported in recent years [15–21]. In previous studies, main concerns have been focused on the single fundamental resonance of surface plasmon polariton, and dual-resonance bands have been far less investigated [22]. It is only very recent that both a relatively weak UV-band resonance and fundamental SP resonance have been observed in EOT through a triangular silver nano-plate [23–25]. Systematic and parametric analyses on this unique dual-band transmission have not been rigorously attempted despite its high potentials in photonic applications.
In this study, we proposed a new type of bull’s eye structure based on a polygonal star-shaped aperture and concentric star-shaped grooves that can consistently provide UV-band response as well as the fundamental SPP resonance in the visible range, by utilizing the nonlinear quadrupole excitation though the narrow edges with an acute internal angle. The UV band was optimized to have a flexibly controlled intensity comparable to that of visible range, for the first time to the best knowledge of the authors. We found that these polygonal star bull’s eyes effectively excited not only the dipole SPP but also the quadrupole SPP, to provide a UV- EOT whose intensity is comparable to that of the visible SPP band. We numerically analyzed EOT characteristics through the star-shaped bull’s eye with 3, 4, 5, and 6-corners on the silver film by using finite-difference time-domain (FDTD) method [26] by varying geometrical parameters systematically. We also studied effects of the incident light polarization on surface plasmons excitation, which can be potentially applicable for lighting and display devices requiring a variable polarization extinction ratio.
Schematic diagrams of the proposed bull’s eyes in this study are summarized in Fig. 1. In comparison to prior bull’s eyes, the proposed structure is based on a star-shaped aperture composed of identical isosceles triangular corners having an acute internal angle attached to an equilateral polygon at the center. The isosceles triangle corners are shown in red and the central equilateral polygons are shown in blue, on the last column of Fig. 1. These isosceles corners were found to efficiently induce a quadrupole to generate an EOT in the UV region and its mechanism is discussed in the latter part of this paper. Here we assumed a silver film with the thickness of 300 nm, which has been used in prior reports to take advantage of its large negative real part and a small imaginary part of dielectric constant in the UV-visible spectral range [27,28].
Fig. 1 Perspective and top views of the proposed star-shaped bull’s eye structures. (a) 3-corner star aperture surrounded by 3-corner star grooves. (b) 4-corner star aperture surrounded by 4-corner star grooves. (c) 5-corner star aperture surrounded by 5-corner star grooves. (d) 6-corner star aperture surrounded by 6-corner star grooves. (e) comparison of the central polygonal aperture sizes. The silver film with thickness of ‘T’ is structured by ‘n’ grooves with width ‘L’, depth ‘H’, arranged in a periodic pitch of ‘P’, The aperture radius ‘R’ is the radius of a circumscribed circle, and ‘L1’ is the distance between aperture and first groove. Input and output surface structures are identical. (f) Tope and side view of FDTD simulation box.
The structure in Fig. 1(a) is a 3-corner star aperture surrounded by 3-corner star grooves. The aperture includes an equilateral triangle with the side length of ‘b’ at the center and three isosceles triangles with the base of ‘b’ and height ‘h’. In a similar manner, we constructed a 4-corner star aperture surrounded by 4-corner star grooves in Fig. 1(b). The aperture includes a square with the side ‘b’ at the center and four identical isosceles triangles. Figure 1(c) shows a 5-corner star aperture surrounded by 5-corner star grooves. The aperture includes a regular pentagon with the side ‘b’ at the center and five identical isosceles triangles. 6-corner star aperture surrounded by 6-corner star grooves is shown in Fig. 1(d). The aperture includes a regular hexagon with the side ‘b’ and six identical isosceles triangles.
Structural parameters of the metallic grooves are defined in Fig. 1: the distance from the aperture to the first groove (L1), the groove height (H), the width (L), the period (P), and the silver film thickness (T). The first groove is located at the distance of L1 from the aperture and the following grooves were periodically arranged with the spatial periodicity of P. For the systematic and consistent comparison of transmission through these bull’s eyes, we considered two factors. Firstly, we kept the general requirement of sub-wavelength plasmonic condition such that the diameter of the central aperture (2R) should be less than light wavelength (λ), 2R<λ [4]. Secondly, we used the same aperture parameters ‘b’ and ‘h’ for all structures. These conditions are graphically summarized in Fig. 1(e).
A snapshot for FDTD analyses is shown in Fig. 1(f): the simulation cell for the structured metal film, light source, monitor, and mesh box. The light source was assumed to be 100% spatially coherent in the spectral range of 300 nm to 700 nm. We also assumed the light is in the linearly polarized state, whose direction could be varied in reference to the symmetry axes of the polygonal structures. In the normal incidence condition, the z-component of electric field of the light was set to be normal to the metal film plane. The transverse component of electric and magnetic fields were in the x-y plane parallel to the metal film. Our 3-dimensional models include semi-infinite air in both sides of the metal film in the z-direction. We also assumed the incident plane wave entirely covered both the aperture and grooves. Silver was defined as a metal film plan with the “Palik” optical constant [29]. The location and size of simulation area are shown in Fig. 1(f). Since the simulation region must be finite in size, the perfectly matched layer (PML) boundary conditions were assumed along the x, y, and z axes, consistent to prior studies [30]. The smallest mesh step size in our simulations was set to be 5 nm. A monitor was placed on the top of the metal film that allows us to calculate the power intensity. The input and output surfaces were set identical and we carried out analyses on the spectral shift and the relative EOT intensity in both fundamental SP in visible and UV-band resonance, by varying the structural parameters of the proposed bull’s eyes.
2. Results and discussions
In the following sections, we performed parametrical analyses on our proposed star shaped plasmonic bull’s eyes in terms of normalized EOT intensity in dual resonances in UV and visible ranges. We used power transmission in the simulation and defined normalized transmission as the transmission through the proposed structure normalized to that through its aperture without any groove structures, similar to the authors’ prior reports [19].
We considered two linear polarizations, 0ᵒ and 45ᵒ with respect to x-axis for 4-corner star grooves bull’s eye, and 0ᵒ and 90ᵒ with respect to x-axis for the rest in Fig. 1.
In Fig. 2, we presented normalized transmission spectra of our proposed star-shaped bull’s eyes. One of key salient features of our proposed bull’s eye structure is that EOT peak intensities of UV band and visible surface plasmon (SP) band are nearly comparable, and their relative intensity ratio can be controlled by changing the number of corners, as shown in Fig. 2, which has not been reported thus far.
Fig. 2 Enhanced optical transmission (EOT) through our proposed star-shaped bull’s eyes with a ‘UV’ band and a surface plasmon ‘SP’ band in the visible spectral range. Here we have: P = 500 nm, n = 3, H = 40 nm, L = 250 nm, T = 300 nm, L1 = 200 nm, b = 150nm, h = 400nm. The light is linearly polarized and it is making 90° with respect to x-axis in Fig. 1.
In the following sections, we reported systematic numerical analyses to understand the impacts of structural parameters over EOT.
2.1. UV-band resonance and visible surface plasmon resonance of the star-shaped bull’s eyes
We started the analyses by varying the number of grooves, ‘n’, from 1 to 5, maintaining other structural parameters. Increasing the number of grooves increased the transmission, which can be attributed to the Bragg reflection effects [31]. The peak intensity of UV band and that of visible SP resonance were plotted as a function of the number of grooves and the results are summarized in Fig. 3.
Fig. 3 Normalized transmission as a function of number of grooves, ‘n’. Here we plotted the peak normalized transmission at UV band and SP resonance in the visible. The incident plane wave’s polarization was 0 °, 45ᵒ, or 90°. Other structural parameters were fixed at P = 500 nm, H = 40 nm, L = 250 nm, T = 300 nm, L1 = 200 nm, b = 150nm, h = 400nm (a) 3-corner star-shaped bull’s eye (b) 4-corner star-shaped bull’s eye (c) 5-corner star-shaped bull’s eye (d) 6-corner star-shaped bull’s eye.
The peaks were located in the range of ~330nm for UV band and 500~550nm for SP band. Here we assumed that the linear polarization of the incident plane wave was either in 0ᵒ, 45ᵒ, or 90° with respect to x-axis in Fig. 1. Figures 2(a)-2(d) show the results for normalized transmission versus the number of grooves, for the star-shaped bull’s eyes with 3, 4, 5, and 6 corners, respectively.
It is noteworthy that UV band and visible SP band did show clearly disparate behavior. Firstly, UV peak intensity monotonically increased with the groove numbers ‘n’, in all structures. In contrast, the visible SP band showed a maximum at either n = 3 or n = 4, depending on the number of corners.
Secondly, the visible SP band showed a certain degree of polarization dependence such that peak EOT intensity had different values for the linear polarizations at 0ᵒ, 45ᵒ, and 90°. In contrast, the UV band resonance showed negligible polarization dependence such that the two polarization directions showed an identical EOT intensity. Polarization dependence in the visible SP bands are well-expected due to the fact that our proposed structure broke the circular symmetry similar to polygonal apertures reported by the authors and other researchers [21]. Yet polarization independent EOT in the UV band was rather unexpected, and this polarization independent EOT in UV band strongly indicates that the physical origin of UV-EOT differed from that of visible SP bands.
Thirdly, the EOT peak intensity in the UV band monotonically increased with the number of corners. The UV band showed a peak normal transmission of~5.3 for the 3-corner star-shaped aperture with the groove number n = 5 as in Fig. 3(a). But the 6-corner star-shaped aperture showed the normal transmission higher than 9.0 in Fig. 3(d), which is a significant increase. In contrast, the visible SP band showed the largest EOT peak of ~6.4 for the 3-corner star-shaped aperture as in Fig. 3(a). Transmission at SP band did not change significantly with the groove numbers for the case of 4, 5, and 6-corner star-shaped bull’s eyes. We found that the relative intensity between UV and visible EOT can be flexibly adjusted by varying the number of grooves and the number of corners. Larger number of corners allowed a larger EOT in UV band.
The impacts of the groove depth, H, are summarized in Fig. 4. In prior reports, a strong transmission peak has been achieved by varying the groove depth near 10% of the groove period [18]. We varied H from 10 to 100nm, and we plotted the EOT peaks for UV and visible SP band. The spectral locations of these two bands were similar as those in Fig. 2. We found contrasting responses of the UV band in comparison to the SP band. The SP band maintained its EOT peak intensity in the entire range of H, however the UV band showed monotonic and nonlinear increase as H increases. At H = 100 nm, the UV band of 3-corner star-shaped bull’s eye showed a normalized transmission over 40 as in Fig. 4(a), and 6-corner star-shaped bull’s eye showed over 110. Note that the UV band intensity was about an order of magnitude larger than that of SP in 6-corner star-shaped bull’s eye at H = 100 nm, and we found the groove depth H had the highest impact on the UV band. Polarization dependence was small in SP bands, and we could confirm that the UV band was polarization-independent.
Fig. 4 Normalized transmission as a function of the groove depth, ‘H’. Here we plotted the peak normalized transmission at UV band and SP resonance in the visible. The incident plane wave’s polarization was 0°, 45ᵒ, or 90°. Other structural parameters were fixed at P = 500 nm, n = 3, L = 250 nm, T = 300 nm, L1 = 200 nm, b = 150nm, h = 400nm (a) 3-corner star-shaped bull’s eye (b) 4-corner star-shaped bull’s eye (c) 5-corner star-shaped bull’s eye (d) 6-corner star-shaped bull’s eye.
We further investigated the impact of L1, the distance from the aperture to the first groove, and the results are summarized in Fig. 5. L1 was varied from 100 to 500 nm and its impacts over EOT in UV and SP bands were analyzed. In prior reports, maximum EOT was found when the distance from the aperture center to the first groove was close to the period of the bull’s eye grooves (L1 + R~P) [18,19]. Impacts of L1 over EOT were very different from those of ‘n’ and ‘H’. The visible SP band intensity showed an oscillatory behavior with decaying amplitude as L1 increased. The maximum visible SP band EOT was observed near L1 = 150nm for 3, 4, and 5-corner star-shaped bull’s eyes as shown in Figs. 5(a)-5(c) respectively. 6-corner star-shaped bull’s eye showed the maximum SP band near L1 = 300nm as in Fig. 5(d). In comparison to nonlinear growth of UV EOT in Figs. 3 and 4, the UV band intensity increased linearly with L1 as shown in Fig. 6. We also observed a consistent trend such that UV band EOT increased with increasing number of corners and 6-corner star-shaped bull’s eyes showed the largest UV EOT.
Fig. 5 Normalized transmission as a function of the distance from the aperture to the first groove, ‘L1’. Here we plotted the peak normalized transmission at UV band and SP resonance in the visible. The incident plane wave’s polarization was 0°, 45ᵒ, or 90°. Other structural parameters were fixed at P = 500 nm, n = 3, H = 50nm, L = 250 nm, T = 300 nm, b = 150nm, h = 400nm (a) 3-corner star-shaped bull’s eye (b) 4-corner star-shaped bull’s eye (c) 5-corner star-shaped bull’s eye (d) 6-corner star-shaped bull’s eye.
Fig. 6 Normalized transmission as a function of the groove width, ‘L’. Here we plotted the peak normalized transmission at UV band and SP resonance in the visible. The incident plane wave’s polarization was either 0°, 45ᵒ, or 90°. Other structural parameters were fixed at P = 500 nm, n = 3, H = 50nm, L1 = 200 nm, T = 300 nm, b = 150nm, h = 400nm (a) 3-corner star-shaped bull’s eye (b) 4-corner star-shaped bull’s eye (c) 5-corner star-shaped bull’s eye (d) 6-corner star-shaped bull’s eye.
Impacts of the groove width, L, were analyzed and the results are summarized in Fig. 6. In prior reports, L close to half the period (L = P/2) has shown a maximum EOT [18]. The response of the visible SP was very different as the number of corners increased such that the bull’s eye with the larger number of corners showed the less dependence in L. For instance, the 3-corner bull’s eye in Fig. 6(a) showed SP band variation in the normalized transmission from 3 to 7 in an oscillatory manner. However 6-corner bull’s eye in Fig. 6(d) showed no oscillatory behavior with a less variation. UV band increased slightly as L varied from 50 to 100nm in all types of bull’s eyes. As L further increased beyond 100nm, UV EOT showed a linear growth with increasing L, similar to Fig. 5 but with a larger slope, which indicates the parameter L is more affecting UV EOT than L1. The largest slope was observed in the 6-cornered bull’s eye along with the largest UV EOT. We could observe slight polarization dependence in SP band but UV band was polarization independent similar to the above discussions.
We further investigated the impact of thickness of silver film, T, and the results are summarized in Fig. 7. Silver film thickness was varied from 200 to 350 nm. UV-EOT showed a very different behavior in comparison to visible SP band as T increased. EOT in SP band showed slight variation as a function of T, but UV-EOT monotonically decreased and became negligibly small beyond T~330nm in 3, 4, and 5-corner star-shaped bull’s eye as in Figs. 7(a)-7(c), respectively. In the case of 6 corner bull’s eye, UV-EOT deceased and became equivalent to EOT at SP band as in Fig. 7(d). We found that incident light polarization on EOT at different direction has small variation with the change in the thickness of silver film. Then in the Fig. 7, EOT for SP and UV bad are shown only for 0ᵒ polarization with respect to x-axis in the Fig. 1.
Fig. 7 Normalized transmission as a function of the silver film thickness, ‘T’. Here we plotted the peak normalized transmission at UV band and SP resonance in the visible. The incident plane wave’s polarization was 0°. Other structural parameters were fixed at P = 500 nm, n = 3, H = 50nm, L = 300 nm, L1 = 200 nm,, b = 150nm, h = 400nm (a) 3-corner star-shaped bull’s eye (b) 4-corner star-shaped bull’s eye (c) 5-corner star-shaped bull’s eye (d) 6-corner star-shaped bull’s eye.
2.2. Comparison of UV and visible EOT
In our study, we found that we can flexibly vary the relative intensity ratio of UV and visible bands by adjusting structural parameters. In Figs. 8(a)-8(c), we showed three different types of EOT spectra from our structure: UV dominant EOT, comparable intensity ratio of UV-Visible EOT, Visible dominant EOT.
Fig. 8 Transmission spectra of 3, 4, 5, and 6-corner star-shaped grooves bull’s eyes in the 0°-polarization. (a) UV dominant EOT. (b) UV-Visible equally distributed EOT. (c) Visible dominant EOT. (d) Transmission spectra of the 3-corner star shape bull’s eye in the 90°-polarization versus wavelength (P = 500 nm, n = 5, H = 40 nm, L = 250 nm, T = 300 nm, L1 = 200 nm, b = 150nm, h = 400nm) for silver, gold, copper, and aluminium.
UV dominant EOT spectrum was demonstrated in Fig. 8(a). Note that visible band was intentionally suppressed and the UV band had the intensity an order of magnitude larger than that of the visible band. Increasing the number of corners we obtained a larger UV-band resonance. In Fig. 8(b), we showed UV-Visible band with a comparable intensity ratio. In Fig. 8(c) we have the spectra where the visible band was dominant over UV band by several folds. These results confirmed that the proposed star-shaped bull's eyes can provide tunable dual band EOT at UV and visible bands, which was not possible in prior studies. We further investigated material aspects and Fig. 8(d) shows EOT spectra for silver, gold, copper, and aluminium. We found that only the silver film could excite dual band EOT consistent to prior reports [32]. The wavelength of EOT Peak is sifted into the near-IR wavelength ranges in metal-dielectric substrate plasmonic structures [33]. Table 1 shows the structural parameters of Figs. 8(a)-8(d).
Table 1. Corresponding Structural Parameters in Figs. 8(a)-8(d)
In addition to commonly observed light-electric dipole interactions, quadrupole can also interact with the incident light in higher modes of plasmon excitation [34]. In order to understand UV EOT band, we calculated the dipole moment distribution within our bull’s eyes by the discrete dipole approximation (DDA), and further expanded it to the quadrupole moments [35]. In the DDA method, the object of interest is represented as a cubic lattice of N polarizable points with the arbitrary lattice position [36]. With this condition, DDA method can be used for an object or multiple objects with any shape and composition. Dipole polarization in the electric field can be determined by
where is the local electric field, is the polarizability, and ri is the location of the ith dipole. The local field for each dipole iswhere E0 and are the amplitude and wave vector of the incident field, respectively. is the interaction matrix of dipole-dipole.here, and . Then, and are 3N-dimensional vectors, and A is a 3N × 3N matrix. For getting the polarization P, 3N complex linear Eq. should be solved. The extinction cross-section can beQuadrupole moment tensor Q ishere, rk,i is the ith component of the position of the kth charge. We can expand first term with supposing that each dipole include 2 opposite point charges at the position of and .Quadrupole moment include of the dipole array can beThe response of dipole arrays with applying electromagnetic field is caused by self-consistently that is determined by the induced dipole moment of each element [25]. Far-field radiation light of a quadrupole from the metal iswhere is the unit vector in the direction of x, y, and z in cartesian coordinate system and vector includes the components of . From this Eq., we can determine far-field properties such as extinction efficiencies. Then, the extinction cross-section of the quadrupole is given byIn Eq. (9), let us assume that the incident light propagates along the z-axis with the polarized electric field along the x-axis (See Ref [36]. for details). Assuming that the quadrupole is defined on the xy plane, the would have the same value for x and y polarizations. Note that this picture can qualitatively explain why the UV EOT was polarization-independent as observed in the previous sections.
Figures 9(a)-9(d) show the electric field intensity distribution in near field for 3-corner star-shaped aperture at UV range (λ = 324 nm), 3-corner star-shaped aperture at visible range (λ = 540 nm), 3-corner star-shaped bulls eye at UV range (λ = 324 nm), and 3-corner star-shaped bulls eye at visible range (λ = 540 nm), respectively. Figures 9(a) and 9(b) show clearly the quadrupole and dipole field distributions were dominant in UV and visible, respectively, which is consistent to the prior investigations [34,37–39]. Quadrupole resonances are generally narrower than the broad dipole resonances [40,41] and we could confirm narrower full width half maximum width of UV band than that of the visible band. See Fig. 8. The wavelength of EOT Peak would shift as a function of dielectric constants of the external surrounding media [33]. However, the UV band peak wavelength does not change significantly with the external dielectric constants [22,23].
Fig. 9 (a) Electric field intensity distribution in near field for 3-corner aperture (b = 150nm, h = 400nm) at UV range (λ = 324 nm) (b) Electric field intensity distribution in near field for 3-corner aperture (b = 150nm, h = 400nm) at visible range (λ = 540 nm) (c) Electric field intensity distribution in near field for 3-corner bulls eye (P = 500 nm, n = 3, H = 40 nm, L = 250 nm, T = 300 nm, L1 = 200 nm, b = 150nm, h = 400nm) at UV range (λ = 324 nm) (d) Electric field intensity distribution in near field for 3-corner bulls eye (P = 500 nm, n = 3, H = 40 nm, L = 250 nm, T = 300 nm, L1 = 200 nm, b = 150nm, h = 400nm) at visible range (λ = 540 nm) in the 90°-polarization
3. Conclusion
We proposed a new type of plasmonic bull’s eye structure that consisted of a polygonal star-shaped aperture surrounded by concentric star-shaped silver grooves. For four types of star- shaped bull’s eyes with 3, 4, 5, and 6-corners, we found dual enhanced optical transmission (EOT) bands, a UV-band resonance band (300~350nm) in addition to the well-known fundamental surface plasmon resonance in the visible range (600~700nm). By changing the number of corners, and adjusting structural parameters of the aperture and the grooves, we could observe a very flexible controllability of the relative EOT intensity between UV and visible, which was not possible in prior techniques. Thickness of the silver film was found to affect only the UV-band to result in a UV EOT with 4~10 times larger intensity than the visible counterpart. In contrast to the visible EOT band, the UV-band showed a very negligible dependence on the incident light polarization. Unique characteristics of the UV EOT were attributed to the light-quadrupole surface plasmons interaction, whilst the visible EOT was consistent to well-known dipole surface plasmons excitation. This quadrupole model explained polarization independence, narrower spectral width, and electric filed intensity distribution of the UV EOT band. This dual band EOT from our proposed bull’s eyes can extend the application of bull’s eyes into UV in a very systematic manner, and applications of these structures in optical sensing in both UV and visible range are being pursued by the authors. It is also noteworthy that unique polarization dependence of the proposed bull’s eyes can also find applications spectrally selective polarization filter and switch, which is also being investigated by the authors.
Acknowledgment
This work was supported in part by Institute of Physics and Applied Physics, Yonsei University, in part by ICT R&D Program of MSIP/IITP (2014-044-014-002), in part by Nano Material Technology Development Program through NRF funded by the MSIP (NRF-2012M3A7B4049800).
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