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Enhanced optical transmission (EOT) and its polarization extinction ratio (PER) of a sub-wavelength polygonal aperture surrounded by polygonal grooves are investigated numerically by finite difference time domain (FDTD) method. Effects of light polarization on EOT were analyzed and compared for four types of geometrical structures: triangle aperture surrounded by triangle grooves, square aperture surrounded by square grooves, rhombus aperture surrounded by rhombus grooves, and pentagon aperture surrounded by pentagon grooves. The effects of relative angles between the symmetry axes of polygons and the light polarization were thoroughly analyzed. Among these plasmonic polygonal bull’s eye structures, the rhombus showed a maximum EOT several times larger than others. In contrast to the prior normal incident condition, we further analyzed the impacts of the incident angle and we found a wideband tunability of EOT wavelengths.
© 2014 Optical Society of America
1. Introduction
In the last decades, surface plasmon (SP) has been at the center of nano-scale research and it has been intensively investigated in a wide spectrum of science and technology such as biology, chemistry, physics, and electro-optics [1–7]. SP has played an important role not only in understanding of the fundamental electron-photon interactions, but also in developing novel nano-photonic devices [8,9] that opened a new level of potential to integrate opto-electronic circuits in the nano-scale [10,11]. Various geometries of sub wavelength apertures, differing in shape and size, have been investigated intensively to find the degree of field enhancement as well as its spectral resonance and polarization sensitivity [12–14]. In 1998, enhanced optical transmission (EOT) was firstly observed through a subwavelength metallic circular aperture array [15], which was followed by a circular bull’s eye structure with a single hole surrounded by concentric corrugated metallic grooves [16]. Transmission properties of a single sub-wavelength aperture and sub-wavelength aperture surrounded by periodic surface corrugation by using terahertz (THz) time-domain techniques was investigated [17–19]. Besides those circularly symmetric apertures, non-circular structures have been also reported: C-shaped apertures [20] and hole aperture array surrounded by rectangular shaped Bragg mirrors [21] were studied to understand the role of the dielectric substrates and the light polarization, respectively.
Despite numerous prior studies on bull’s eye structures, only a few have dealt with the impacts of the interaction between the light polarizations and the geometrical symmetry of SP devices. Recently the authors’ group reported the elliptical aperture surrounded by circular corrugations [22] and hexagonal aperture surrounded by segmented corrugations [23], both showing a significant improvement in polarization extinction ratio, which is, we believe, attributed to the interaction between the light polarization and the geometrical symmetry in the plasmonic bull’s eye structures.
In this study, new categories of plasmonic bull’s eyes are introduced, which consist of a polygonal aperture at the center, surrounded by metallic grooves with the same symmetry. The polygonal aperture and grooves were arranged in a concentric manner similar to circular bull’s eyes. In contrast to prior studies on polygonal apertures [24], we focused on the impacts of the geometrical symmetry in the bull’s eye structures. Parametric studies of these polygonal bull’s eyes by varying the number of symmetry axes have not been reported thus far to the best knowledge of the authors. We numerically calculated the normalized transmission through the polygonal plasmonic bull’s eyes using the finite-difference time domain (FDTD) method [25] by varying the angle between the linear light polarization and the symmetry axes of the polygons. We also investigated the impacts of the light incident angle on new tunability of plasmonic resonance, which has not been thoroughly studies in prior reports.
Schematic diagrams of the polygonal bull’s eyes proposed in this study are summarized in Figs. 1(a)–1(d), which correspond to triangle, square, rhombus, and pentagon bulls eye, respectively. The proposed structure shown in Fig. 1(a) is an equilateral triangle aperture surrounded by equilateral triangle grooves. The aperture size of triangle (A) is the normal distance from the aperture center to the base of the triangle. A square aperture surrounded by square grooves is shown in Fig. 1(b). The aperture size of square (A) is the half of the square aperture’s side length. Figure 1(c) shows a rhombus aperture surrounded by rhombus grooves. The size of aperture rhombus is characterized by two parameters: X and Y, which are the distance from the center to the far corner and that from the center to the near corner of the aperture, respectively. The proposed structure shown in Fig. 1(d) is a pentagonal aperture surrounded by pentagonal grooves. The pentagon aperture size (A) corresponds to the distance from the center to the base of the pentagon aperture. Detailed structural parameters are defined in Fig. 1: the distance from the aperture center-to-the first groove (R), the groove height (H), the width (L), the groove period (P), and the silver film thickness (T). The first groove is located at the distance of R from the center and the following grooves were periodically arranged with the spatial periodicity of P. For the systematic comparison of transmission through the polygonal bulls eyes, we considered two factors. Firstly, we kept the general requirement of sub-wavelength plasmonic structure: the diameter of aperture should be less than wavelength (2A<λ) [26]. Secondly we selected aperture sizes that showed the similar transmission level. Considering these two conditions, we selected the aperture sizes for the polygonal bull’s eyes as summarized in Fig. 1(e).
Fig. 1 Perspective and top view of plasmonic polygonal bull’s eye structures. (a) A triangle aperture surrounded by triangle grooves. (b) A square aperture surrounded by square grooves. (c) A rhombus aperture surrounded by rhombus grooves. (d) A pentagon aperture surrounded by pentagon grooves. (e) Aperture sizes for the polygonal bull’s eyes to pursue systematic comparisons. 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 ‘A’ is measured from center to side of the hole, and ‘R’ is the distance between the aperture center and the first groove. Input and output of surfaces are identical.
In this study, we assumed a silver film with 300 nm thickness, to make a consistent comparison with prior silver film plasmonic devices. Silver has been one of preferred metals in plasmonic studies, due to its large negative real part and a small imaginary part of dielectric constant in the visible spectral range [27,28]. The light source was assumed to be 100% spatially coherent in the spectral range of 300 nm to 700 nm and 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 x-component of electric field and y-component of magnetic field were in the xy-plane parallel to the metal film. Our 3D models include a semi-infinite metal film and a semi-infinite air in both side of metal film in the z-direction. The used light source is a plan wave source that covers both the aperture and grooves. We used the perfectly matched layer (PML) boundary conditions along the X, Y, and Z axes. For normal incident condition, we used multiple PML layers to ensure the minimal reflection. We used the Bloch boundary condition [25,29] for the oblique incident light that has been widely used to phase correction in a structure that one period to the next are not exactly periodic. We also assumed that the input and output surfaces were identical. By varying the structural parameters of the proposed bull’s eyes, we investigated the polarization dependence in EOT at the resonance for the incident plane waves.
2. Results and discussions
In the following sections, we summarized the parametrical analyses of the polygonal plasmonic bull’s eyes in terms of normalized EOT intensity, varying all the geometrical parameters shown in Fig. 1. We also investigated the impacts of light polarization to quantify the polarization extinction ratio (PER), which represents polarization dependence in EOT.
2.1 Parametric analyses of enhanced optical transmission through the triangle bull’s eye
Figure 2 shows the variation of the normalized transmission as a function of structural parameters of the triangle plasmonic bull’s eye in Fig. 1(a). Normalized transmission is defined as the transmission through the proposed structure normalized to that through its aperture without any groove structures. Here we have examined the impacts of two linear polarizations: 0°-polarization and the 30°-polarization. These angles are represented in the bottom of Fig. 1(a). Figure 2(a) shows the variation transmission versus the aperture size (A) for two polarisation direction. According to the aperture size requirement for plasmonic resonance, 2A< λ [26], we used A of 150 nm as the aperture size, in the following analyses. Increasing the aperture size increases the output transmission. The normalized EOT versus the number of grooves is summarized in Fig. 2(b). Increasing the number of grooves enhanced the transmission, which is consistent to a prior report [30], we found that this effect was more prominent in the 0°-polarization where the electric field is along the two corners of the triangle aperture than in the 30°-polarization where the electric field is along one corner and a side of the triangle similar to prior reports [31,32]. Note that this is quite a contrast to circular aperture/grooves [33], which did not show any polarization dependence in EOT. We further investigated the impact of the groove width, L, and the results are summarized in Fig. 2(c). We found that the maximum EOT could be obtained for the 0°-polarization with the optimal L of ~250 nm, corresponding to P/2, which is consistent to the prior circular bull’s eye [34]. The impacts of the groove depth, H, are summarized in Fig. 2(d) and we found an optimal value H~40 nm to generate the maximum EOT for the 0°-polarization. We further investigated the impact of R, the distance from the aperture center to the first groove on EOT for three directions of linear polarization and the results are summarized in Fig. 2(e). We found an optimal R of ~400 nm for the 0°-polarization. In triangular plasmonic bull’s eye the maximum PER of 0.64 dB was observed at H = 40 nm as in Fig. 2(d).
Fig. 2 Variation of the transmission as a function of structural parameters of the triangle plasmonic bull’s eye. (a) transmission (Normalized to the light source) versus A in 0°-polarization and 30°-polarization. (b) Normalized transmission versus number of groove in 0°-polarization and 30°-polarization (P = 500 nm, H = 60 nm, L = 250 nm, T = 300 nm, R = 650 nm, A = 150 nm). (c) Normalized transmission as a function of L in 0°-polarization and 30°-polarization (n = 6, p = 500nm, H = 40nm, R = 650nm, A = 150nm). (d) Normalized transmission as a function of the H in 0°-polarization and 30°-polarization (n = 6, p = 500nm, R = 650nm, A = 150nm, L = 250nm). (e) Normalized transmission versus R in 0°-polarization, 15°-polarization, and 30°-polarization (n = 6, p = 500 nm, H = 40 nm, A = 150 nm, L = 250 nm).
2.2 Parametric analyses of enhanced optical transmission through the square bull’s eye
Figure 3 shows the variation of the normalized transmission as a function of structural parameters for the square plasmonic bull’s eye as in Fig. 1(b). Here we have examined the impacts of two linear polarizations: 0°-polarization and the 45°-polarization. These angles are represented in the bottom of Fig. 1(b). Transmission versus the aperture size (A) of the square bull’s eye is plotted in Fig. 3(a) and we set A = 150 nm in the simulation similar to the triangular bull’s eye. Figure 3(b) shows the normalized transmission versus the number of grooves. The maximum EOT occurred when number of grooves was 6 in both polarizations. We investigated the effect of groove width, L, and the results are summarized in Fig. 3(c). In Fig. 3(d), we summarized the dependence of EOT on the groove depth (H) for both polarizations; we achieved the maximum EOT at the groove depth ~30 nm. Figure 3(e) summarizes the impacts of R on EOT intensity for three polarization states, and we found maximum EOT was at R~500 nm for all the polarizations. In comparison to triangular plasmonic bull’s eyes in Fig. 2, the square bull’s eyes showed very low polarization dependence in EOT acting like a circular bull’s eyes.
Fig. 3 Variation of the transmission as a function of structural parameters of the square plasmonic bull’s eye. (a) transmission (Normalized to the light source) versus A in 0°-polarization and 45°-polarization. (b) Normalized transmission versus number of groove (P = 500 nm, H = 60 nm, L = 200 nm, T = 300 nm, R = 350 nm, A = 150 nm). (c) Normalized transmission as a function of L (n = 6, p = 500nm, R = 350nm, A = 150nm, H = 30nm). (d) Normalized transmission as a function of the H (n = 6, p = 500 nm, R = 350 nm, A = 150 nm, L = 200 nm). (e) Normalized transmission versus R (n = 6, p = 500nm, H = 30nm, L = 200nm, A = 150nm).
2.3 Parametric analyses of enhanced optical transmission through the rhombus bull’s eye
Figure 4 shows the variation of the normalized transmission as a function of structural parameters of the rhombus plasmonic bull’s eye in Fig. 1(c). Figure 4(a) shows the variation transmission versus the aperture size (x) for two polarisation direction. Figure 4(b) shows the normalized transmission versus the major axis length ‘X’. Here we have examined the impacts of two linear polarizations: 0°-polarization and the 90°-polarization. These angles are represented in the bottom of Fig. 1(c). The maximum EOT occurred at X = 360 nm for the 90°-polarisation with Y was maintained at 200 nm. In this case, we could observe very high polarization dependent EOT with PER of ~8.86 dB. We further analyzed the normalized transmission as a function of the number of grooves in Fig. 4(c). The EOT showed maxima at 7 grooves for the 90°-polarization, and the PER was about ~7.5 dB. In Fig. 4(d), we investigated the effects of groove depth, H, on EOT with other structural parameters set at n = 7, p = 500 nm, R = 450 nm, L = 200 nm, x = 360 nm, y = 200 nm. The maximum EOT occurred at H ~30 nm for the 90°-polarization, with the PER of ~7.6 dB. The maximum EOT was observed at L = 150 nm for the 90°-polarization as summarized in Fig. 4(e). In contrast, the transmission for the 0°-polarization did not change significantly with the groove width, L and the PER at L = 150 nm was about ~7.84 dB. We further investigated the impact of R, the distance from the aperture center to the first groove, on EOT in four different polarization directions and the results are summarized in Fig. 4(f). We found the maximum EOT at R ~350 nm for the 90°-polarisation and we observed the PER~6.22 dB. Among structural parameters of rhombus bull’s eye, we found that the major axis length, X, of the aperture, and the groove width, L, in the metallic grooves were the most sensitive parameters to affect the polarization dependence in EOT.
Fig. 4 Variation of the transmission as a function of structural parameters of the rhombus plasmonic bull’s eye. (a) transmission (Normalized to the light source) versus x in 0°-polarization and 90°-polarization. (b) Normalized transmission versus X in 0°-polarization and 90°-polarization (n = 6, P = 500 nm, H = 30 nm, L = 200 nm, T = 300 nm). (c) Normalized transmission versus number of groove in 0°-polarization and 90°-polarization (P = 500 nm, H = 30 nm, L = 200 nm, T = 300 nm, R = 450 nm, x = 360 nm, y = 200 nm). (d) Normalized transmission as a function of H in 0°-polarization and 90°-polarization (n = 7, p = 500 nm, R = 450 nm, L = 200 nm, x = 360 nm, y = 200 nm). (e) Normalized transmission as a function of the L in 0°-polarization and 90°-polarization (n = 7, p = 500nm, R = 450nm, H = 30nm, x = 360 nm, y = 200 nm). (f) Normalized transmission versus R in 0°-polarization, 32°-polarization, 69°-polarization, and 90°-polarization (n = 7, p = 500nm, H = 30nm, L = 200nm, x = 360 nm, y = 200 nm).
2.4 Parametric analyses of enhanced optical transmission through the pentagon bull’s eye
Finally, we investigated the pentagon plasmonic bull’s eyes as in Fig. 1(d). Transmission versus the aperture size (A) of pentagon is shown in Fig. 5(a). Increasing the aperture size increases the output transmission. Normalized transmission versus number of grooves in 0°-polarization and 54°-polarization are shown in Fig. 5(b). These polarization angles are represented in the bottom of Fig. 1(d). In comparison to other polygonal bull’s eyes, the transmission intensity was found to monotonically increase with the groove number in the pentagon bull’s eye. Especially for 54°-polarization the transmission showed a saturation behavior in the range of 8-10 grooves. In the following numerical analyses, therefore, we have assumed 8 grooves. The impacts of the groove width, L, are summarized in Fig. 4(c) for 0°-polarization and 54°-polarization and we found an optimal value of L~250nm to maximize EOT, which is about a half of the groove period, P, consistent to the prior circular bull’s eye results [30]. In Fig. 4(d), we plotted normalized transmission versus the groove depth, H, and we found the maximum EOT at H~30 nm. We also investigated the impact of R for three polarization directions and the results are summarized in Fig. 5(e). In comparison to rhombus bull’s eye, the polarization dependence of pentagon bull’s eye was significantly lower.
Fig. 5 Variation of the transmission as a function of structural parameters of the pentagon plasmonic bull’s eye. (a) transmission (Normalized to the light source) versus A in 0°-polarization and 54°-polarization. (b) Normalized transmission versus number of groove in 0°-polarization and 54°-polarization (P = 500 nm, H = 40 nm, L = 250 nm, R = 400 nm, A = 200 nm). (c) Normalized transmission as a function of L in 0°-polarization and 54°-polarization (n = 8, p = 500 nm, H = 40 nm, A = 200 nm, R = 400 nm). (d) Normalized transmission as a function of the H in 0°-polarization and 54°-polarization (n = 8, p = 500nm, R = 400nm, A = 200nm, L = 250nm). (e) Normalized transmission versus R in 0°-polarization, 18°-polarization, and 54°-polarization (n = 8, p = 500nm, H = 40nm, L = 250nm, A = 200nm).
Transmission spectra of these polygonal bull’s eyes were calculated and they were compared in Fig. 6(a). Here we chose geometrical parameters to maximize EOT of individual plasmonic structures: triangle bull’s eyes in the 0°-polarization and 30°-polarization, square bull’s eyes in the 45°-polarization, rhombus bull’s eyes in the 0°-polarization and 90°-polarization, and pentagonal bull’s eyes in the 0°-polarization. Figure 6(a) shows the results of optimized parameters of structures for the max of EOT. We found that the rhombus bull’s eye provided the largest EOT and the square the lowest among four types of polygonal bull’s eyes. It is noteworthy to find that the EOT peak wavelength consistently shifted to a longer wavelength as the geometry of the plasmonic bull’s eyes changes from triangle, rhombus, square, and pentagon as shown in the inset of Fig. 6(a). The EOT peaks were at λmax = 529, 548, 550 and 569 nm for triangle, rhombus, square, and pentagonal bull’s eye, respectively. All of these plasmonic resonance wavelengths of polygonal bull’s eyes were found to satisfy a relationship . P is the periodicity of the grooves and the effective refractive index is given by, where and are the dielectric constants of the metal and the dielectric, respectively [35,36]. In contrast, the circular bull’s eyes satisfies [37,38]. As we can find in the inset of Fig. 6(a), the resonance wavelength of the polygonal bull’s eyes increase with the number of sides and symmetry axes of the polygon, and it converged to the value of circular bull’s eyes. Therefore, we can have a new degree of freedom to tune the resonance wavelength and control the polarization dependence in EOT by polygonal bull’s eyes. Pick spectral positions of the waveguide modes [39] for triangle, square, rhombus, and pentagonal aperture without bull’s eye structure for A = 125nm are λmax = 501, 503, 508, and 510 nm, respectively. In comparison, the pick spectral positions of the waveguide modes for triangle, square, rhombus, and pentagonal bulls eye for A = 125nm are λmax = 531, 546, 550 and 565 nm, respectively.
Fig. 6 (a) Transmission (normalized to the source) spectra of the triangle bull’s eye in the 0°-polarization and 30°-polarization versus wavelength (n = 6, p = 500nm, L = 250nm, H = 30nm, R = 400nm, A = 150nm), transmission spectra versus wavelength of the square bull’s eye in the 45°-polarization (n = 6, p = 500nm, L = 200nm, H = 30nm, R = 500nm, A = 150nm), transmission spectra versus wavelength of the rhombus bull’s eye in the 0°-polarization and 90°-polarization (n = 7, p = 500nm, L = 200nm, H = 30nm, R = 350nm, X = 360nm, Y = 200nm), and transmission spectra versus wavelength of the pentagonal bull’s eye in the 54°-polarization (n = 8, p = 500nm, L = 250nm, H = 40nm, R = 250nm, A = 200nm). (insetted to a) EOT peak wavelength versus geometrical structures for triangle, rhombus, square, and pentagon. (b) Polarization extinction ratio (PER) of square bulls eye at (n = 6, p = 500nm, L = 200nm, H = 30nm, R = 500nm, A = 150nm) and rhombus bulls eye at (n = 7, p = 500nm, L = 200nm, H = 30nm, R = 350nm, X = 360nm, Y = 200nm).
Figure 6(b) shows the polarization extinction ratio of square bulls eye at (n = 6, p = 500nm, L = 200nm, H = 30nm, R = 500nm, A = 150nm) and rhombus bulls eye at (n = 7, p = 500nm, L = 200nm, H = 30nm, R = 350nm, X = 360nm, Y = 200nm). Figure 6(b) shows the results of optimized parameters of structures for the max of EOT for square and rhombus. PER of square was calculated for max of EOT (45°-polarization) and min of EOT (0°-polarization) and PER of square was calculated for max of EOT (90°-polarization) and min of EOT (0°-polarization). The polarization extinction ratio (PER) was calculated in the spectral range of 510 to 650 nm.
2.5. Tuning EOT wavelength by varying the light incident angle
In this part, we simulated the effect of the light incident angle on the EOT wavelength. Figure 7 shows the perspective view of the plane wave incident on the polygonal bull’s eye structure. The geometrical parameters include: the incident angle (θ) measured from the zenith direction, and the azimuth angle (φ) of its orthogonal projection on the bull’s eye structure plane to the X direction. We can define the TM and TE states of the incident light polarization shown in Figs. 7(a) and 7(b), respectively. We varied incident angle (θ) from 0 to 48 degree at various azimuth angle (φ) for the TE and TM polarizations.
Fig. 7 Perspective view of linear polarized light at polygonal bull’s eye structure. Incident light tilted θ degree to the normal of surface of the silver plane and the azimuth angle (φ) of its orthogonal projection on a silver plane that passes through the origin. (a) Linear polarisation at TM state. (b) Linear polarisation at TE state.
Figure 8(a) summarizes the variation of EOT wavelength versus the incident angle for the triangle bull’s eye. TE and TM polarizations showed very contrasting properties such that the EOT wavelength tuning range for the TE polarization was significantly narrower than TM cases. In the TM polarization with the azimuth angle of φ = 90°, the EOT wavelength was tuned from 450 to 670 nm by varying the incident angle θ. In contrast, the TE polarization with the same conditions, gave the spectral tuning range from 450 to 550nm. We also carried out the similar investigations for the square bull’s eye, and the results are shown in Fig. 8(b). We also observed the TM polarization provided a wider tuning range of EOT than TE.
Fig. 8 (a) Wavelength versus incident angle for triangle bulls eye at φ = 0, 30, and 90 degree for TE and TM polarisation state. (b) Wavelength versus incident angle for square bulls eye at φ = 0 and 45 degree for TE and TM polarisation state. (c) Wavelength versus incident angle for rhombus bulls eye at φ = 0 and 90 degree for TE and TM polarisation state. (d) Wavelength versus incident angle for pentagonal bulls eye at φ = 0, 54, and 90 degree for TE and TM polarisation state.
The TM polarization with φ = 45° provided a EOT tuning range from 440 to 670nm, which covers almost whole visible spectral range. In Fig. 8(c), we summarized the analyses for the rhombus bull’s eye, which showed a consistent behavior as Figs. 8(a) and 8(b).
Figure 8(d) shows the pentagon bull’s eye analyses, where TM polarization also provided a wider tuning spectral range than TE polarization. This unique wavelength tenability controlled by the incident angle could be further utilized as rotational sensor applications [40,41].
4. Conclusion
Effects of incident light polarization on the enhanced transmission (EOT) through polygonal aperture surrounded by polygonal silver grooves were parametrically analyzed. For four types of polygonal bull’s eyes, triangle, square, rhombus, and pentagon, we found that the rhombus bull’s eye showed the largest polarization dependence in EOT, which is an order of magnitude larger than other structures. The rhombus bull’s eye polarization showed a polarization extinction ratio of 8.86 dB in EOT. As the number of symmetry axes increased from triangle to pentagon in the polygonal bull’s eyes, we found a new consistent feature such that the plasmonic resonance wavelength red-shifted approaching toward that of circular bull’s eyes, which provides a new spectral tuning method. We also found a very wide spectral tuning capability of EOT by changing the incident angle such that the TM polarization could provide a wide tuning range over 200nm.
Acknowledgments
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 MEST (2012M3A7B4049800). by a grant funded by the Korea government (MSIP) (2012M3A7B4049800), by the Seoul R&BD Program (PA110081), by the Doosan DST (2013-8-0202), by the Samsung Electronics (2013-8-0483), by the Samsung Electro-mechanics (2013-8-1221), and by the LG Display (2013-8-0662).
References and links
1. X. Y. Yao, B. Yi, J. Xiao, and Z. Li, “Surface plasmon resonance biosensors and its application,” in 1st International Conference on Bioinformatics and Biomedical Engineering, IEEE (2007), pp. 1043–1046.
2. B. Guo, G. Song, and L. Chen, “Plasmonic very-small-aperture lasers,” Appl. Phys. Lett. 91(2), 021103 (2007). [CrossRef]
3. E. Popov, M. Nevière, A. L. Fehrembach, and N. Bonod, “Enhanced transmission of light through a circularly structured aperture,” Appl. Opt. 44, 6898–6904 (2005).
4. J. M. Luther, P. K. Jain, T. Ewers, and A. P. Alivisatos, “Localized surface plasmon resonances arising from free carriers in doped quantum dots,” Nat. Mater. 10(5), 361–366 (2011). [CrossRef] [PubMed]
5. H. E. Arabi, H. E. Joe, T. Nazari, B. K. Min, and K. Oh, “A high throughput supra-wavelength plasmonic bull’s eye photon sorter spatially and spectrally multiplexed on silica optical fiber facet,” Opt. Express 21(23), 28083–28094 (2013). [CrossRef] [PubMed]
6. H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express 13(3), 763–769 (2005). [CrossRef] [PubMed]
7. K. Toma, J. Dostalek, and W. Knoll, “Long range surface plasmon-coupled fluorescence emission for biosensor applications,” Opt. Express 19(12), 11090–11099 (2011). [CrossRef] [PubMed]
8. L. Aigouy, P. Lalanne, H. Liu, G. Julié, V. Mathet, and M. Mortier, “Near-field scattered by a single nanoslit in a metal film,” Appl. Opt. 46, 8573–8577 (2007).
9. S. S. Akarca-Biyikli, I. Bulu, and E. Ozbay, “Resonant excitation of surface plasmons in one-dimensional metallic grating structures at microwave frequencies,” J. Opt. A, Pure Appl. Opt. 7(2), 159–164 (2005). [CrossRef]
10. K. Tanaka, K. Katayama, and M. Tanaka, “Nanofocusing of surface plasmon polaritons by a pyramidal structure on an aperture,” Opt. Express 18(2), 787–798 (2010). [CrossRef] [PubMed]
11. T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,” Phys. Today 61(5), 44–50 (2008). [CrossRef]
12. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
13. W. Hou and S. B. Cronin, “A review of surface plasmon resonance-enhanced photocatalysis,” Adv. Funct. Mater. 23(13), 1612–1619 (2013). [CrossRef]
14. H. L. Liu, N. Wang, Y. H. Liu, and X. J. Wu, “Influence of vertex angles on the extraordinary optical transmission characteristics of triangular and bow-tie-shaped apertures,” Solid State Commun. 150(37–38), 1822–1826 (2010). [CrossRef]
15. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
16. B. Huang, F. Yu, and R. N. Zare, “Surface plasmon resonance imaging using a high numerical aperture microscope objective,” Anal. Chem. 79(7), 2979–2983 (2007). [CrossRef] [PubMed]
17. A. Agrawal, H. Cao, and A. Nahata, “Excitation and scattering of surface plasmon-polaritons on structured metal films and their application to pulse shaping and enhanced transmission,” New J. Phys. 7, 249–261 (2005). [CrossRef]
18. A. Agrawal, H. Cao, and A. Nahata, “Time-domain analysis of enhanced transmission through a single subwavelength aperture,” Opt. Express 13(9), 3535–3542 (2005). [CrossRef] [PubMed]
19. A. Agrawal and A. Nahata, “Time-domain radiative properties of a single subwavelength aperture surrounded by an exit side surface corrugation,” Opt. Express 14(5), 1973–1981 (2006). [CrossRef] [PubMed]
20. O. Lopatiuk-Tirpak and S. Fathpour, “Effects of the surrounding medium on the optical properties of a subwavelength aperture,” Opt. Express 17(26), 23861–23866 (2009). [CrossRef] [PubMed]
21. N. C. Lindquist, A. Lesuffleur, and S. H. Oh, “Lateral confinement of surface plasmons and polarization-dependent optical transmission using nanohole arrays with a surrounding rectangular Bragg resonator,” Appl. Phys. Lett. 91(25), 253105 (2007). [CrossRef]
22. M. Pournoury, H. E. Joe, J. H. Park, T. Nazari, Y. M. Sung, B. K. Min, S. Im, D. Kim, and K. Oh, “Polarization-dependent transmission through a bull’s eye with an elliptical aperture,” Opt. Commun. 316, 1–4 (2014). [CrossRef]
23. T. Nazari, S. H. Kassani, R. Khazaeinezhad, and K. Oh, “Polarization dependent transmission through a sub-wavelength hexagonal aperture surrounded by segmented polygonal grooves,” Opt. Express 21(26), 32668–32679 (2013). [PubMed]
24. Z. Rao, L. Hesselink, and J. S. Harris, “High transmission through ridge nano-apertures on Vertical-Cavity Surface-Emitting Lasers,” Opt. Express 15(16), 10427–10438 (2007). [CrossRef] [PubMed]
25. FDTD Lumerical Solutions Inc, www.lumerical.com.
26. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002). [CrossRef] [PubMed]
27. T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13(3), 429–432 (2002). [CrossRef]
28. J. R. Sambles, G. W. Bradbery, and F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemp. Phys. 32, 173–183 (1991).
29. Q. Chen, Y. Z. Huang, W. H. Guo, and L. J. Yu, “Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Pade´ approximation,” Opt. Commun. 248(4–6), 309–315 (2005). [CrossRef]
30. E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photon. 2(3), 161–164 (2008). [CrossRef]
31. Z. Zhang, S. Zhang, and Z. Xiong, “Optical properties of silver hollow triangular nanoprisms,” Plasmonics 5(4), 411–416 (2010). [CrossRef]
32. E. X. Jin and X. Xu, “Obtaining super resolution light spot using surface plasmon assisted sharp ridge nanoaperture,” Appl. Phys. Lett. 86(11), 111106 (2005). [CrossRef]
33. E. Popov, M. Nevière, A. L. Fehrembach, and N. Bonod, “Enhanced transmission of light through a circularly structured aperture,” Appl. Opt. 44(32), 6898–6904 (2005). [CrossRef] [PubMed]
34. O. Mahboub, S. C. Palacios, C. Genet, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and T. W. Ebbesen, “Optimization of bull’s eye structures for transmission enhancement,” Opt. Express 18(11), 11292–11299 (2010). [CrossRef] [PubMed]
35. Y. Cui and S. He, “A theoretical re-examination of giant transmission of light through a metallic nano-slit surrounded with periodic grooves,” Opt. Express 17(16), 13995–14000 (2009). [CrossRef] [PubMed]
36. T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” IOPP 13, 429–432 (2002).
37. S. Shinada, J. Hashizume, and F. Koyama, “Surface plasmon resonance on microaperture vertical-cavity surface-emitting laser with metal grating,” Appl. Phys. Lett. 83(5), 836–838 (2003). [CrossRef]
38. T. Ishi, J. i. Fujikata, and K. Ohashi, “Large optical transmission through a single subwavelength hole associated with a sharp-apex grating,” Jpn. J. Appl. Phys. 44(4), 170–172 (2005). [CrossRef]
39. A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A, Pure Appl. Opt. 7(2), 90–96 (2005). [CrossRef]
40. H. S. Leong, J. Guo, R. G. Lindquist, and Q. H. Liu, “Surface plasmon resonance in nanostructured metal films under the Kretschmann configuration,” J. Appl. Phys. 106(12), 124314 (2009). [CrossRef]
41. W. M. Mukhtar, P. S. Menon, S. Shaari, M. Z. A. Malek, and A. M. Abdullah, “Angle shifting in surface plasmon resonance: experimental and theoretical verification,” J. Phys. Conf. Ser. 431, 012028 (2013). [CrossRef]
