Strong polarization dependence in the optical transmission through a bull’s eye with a central elliptical aperture in a thin Au film is analyzed numerically by finite difference time domain (FDTD) method. Focusing on the impacts of the structural anisotropy, detailed investigation of polarization dependent enhanced optical transmission (EOT) of light is discussed in terms of the resonance intensity variations caused by the incident light polarization and the geometrical parameters of bull’s eye. We found that the light polarized along the minor axis of the elliptic aperture has significantly larger EOT by more than three orders of magnitude than the other orthogonal polarization, which can be further utilized in polarized EOT devices.
© 2012 OSA
Since the first report of extraordinary optical transmission (EOT) through nano-hole arrays in metal films  the sub-wavelength patterns on metal-dielectric interfaces have generated significant research interests due to their unique optical properties: highly localized and spectrally selective transmission that can find various applications from sensing to opto-electronics devices [2–4]. Driving force of these unique optical properties is known to be surface Plasmon (SP), a form of collective behavior between electromagnetic wave and free electron confined at the metal-dielectric interface. Among the variety of metal aperture structures, bull’s eyes that consisted of a circular aperture surrounded by concentric grooves on thin metal films have drawn much attention. The periodic metal grooves act like an antenna for the incoming light by converting it to SP and enhancing transmission through the aperture by coupling SPs to the incident light. This combination of the central aperture and concentric metal grooves enabled various applications: ultra fast photodetector , vertical-cavity surface-emitting lasers and quantum cascade lasers [6–8], sub-wavelength optical wave plates , plasmonic photon sorter , and sub-wavelength light source for nanolithography .
In prior studies on bull’s eyes, the effects of structural parameters such as the corrugation period, depth, width, number of the grooves and the aperture diameter on EOT have been investigated in detail [12–15]. An anisotropic bowtie aperture with circular grooves has been reported to reduce the divergence of the near-field . Despite these extensive efforts, there have been only a few reports on the polarization dependence. Prior polarization studies have been limited only to elliptical and rectangular nano-hole arrays [17, 18], single sub-wavelength aperture on a metallic film without any corrugations  nano-hole structures with multiple grating geometry , a metallic hole surrounded by double spiral dielectric gratings  and Archimedes’ spiral grooves on a silver film impinged by a circularly polarized light .
In this study, we focus on the fundamental issue in bull’s eyes: how the EOT is affected by the geometrical anisotropy in the central aperture and its interaction with the polarization of incident light in bull’s eye structure, for the first time to the best knowledge of the authors. Polarization dependence in EOT and its controllability in bull’s eye structure would open a new avenue of applications of single polarization photonic devices, and polarization selective sensors.
Schematic diagram for the proposed bull’s eye in this study is shown in Fig. 1(a) . Here we assume a free-standing double side corrugated Au film with an elliptical nano-hole at the center. The elliptical hole is characterized by the diameters on the x and y axes denoted by d1 and d2, respectively. The concentric circular grooves are characterized by geometrical parameters as shown in Fig. 1(b): the film thickness, t, grooves depth, s, grooves width, w, period of grooves, p, and the distance from the center of the hole to the first groove, denoted as a. Figure 1(c) is a schematic diagram of the illumination condition and the EOT outputs corresponding to two orthogonal polarizations, where we assume a uniform plane wave is normally incident on the bull’s eye. The relative EOT for the light polarized along the y axis, or equivalently vertical polarization, shows a significantly stronger EOT than the other polarization. In the following sections, we will discuss in detail how the sub-wavelength scale variations in the geometrical parameters of the proposed elliptic bull’s eye affect the polarization dependence in EOT.
In order to investigate transmission characteristics of the proposed bull’s eye, FDTD method was applied to solve the time dependent Maxwell equations in the vicinity of the proposed bull’s eye structure using a commercially available program . The total simulation size for FDTD analysis was 9 × 9 × 1.5 μm3 and the mesh-grid resolution of 10 nm was chosen to provide numerically converging consistent results. A frequency domain power monitor is located above the upper surface and is used to measure transmission through the aperture. Perfectly matched layer conditions were adopted to absorb parasitic reflections. We assumed double-sided six concentric grooves on Au film and geometrical parameters were t = 300 nm, s = 60 nm, w = 300 nm, a = 600 nm, and p = 600 nm, which are similar to prior circular bull’s eyes . In this study, we introduced the sub-wavelength scale anisotropy in the central aperture such that d1 = 300 nm, and d2 varied from 150 to 300 nm. Note that the range of d2 was chosen, considering the state of art process capability used in bull’s eye fabrication . Using FDTD method, the transmission properties in the far and near field were thoroughly investigated for two orthogonal polarizations; horizontal and vertical polarization as defined in Fig. 1(c). The spectral range of the incident light was 400 to 1000 nm.
2.1 Angular distribution of transmission intensity
Figure 2 shows the angular distribution of transmission through the proposed bull’s eye. The wavelength of the incident wave was set at the structural resonance wavelength λ = 670 nm, which was mainly determined by the metallic groove period p = 600 nm . Here ε denotes the ellipticity of the anisotropic aperture, ε = (d1-d2)/d1, and θ is the collection angle along the x-z plane for the Horizontal polarization and the y-z plane for the Vertical polarization measured from the normal axis as shown in Fig. 1(b). In Fig. 2(a) the EOT of the horizontally polarized light rapidly decreased by increasing the anisotropy in the aperture, or equivalently increasing ε. In contrast, EOT of the vertical polarization increased with the growing ε as in Fig. 2(b). The collection angle for the transmitted light did not change significantly and remained in the range of a full-width at half-maximum (FWHM) divergence of ± 2.5°.
In Fig. 2, we could observe a highly polarization dependent EOT. For example at the ellipticity of ε = 1/2, the EOT peak intensity for the horizontal polarization was two orders of magnitude smaller than that for the vertical polarization, which resulted in the polarization extinction ratio, Iv/Ih of ~187 at θ = 0°. Here, Iv and Ih are the peak EOT intensities for the vertical and horizontal polarization, respectively. The strong polarization dependence of transmission resembles previous reports on transmission through a subwavelength slit surrounded by surface corrugations , and metallic nanowire gratings . In the case of vertical polarization, Fig. 2(b), the peak transmission intensity for ε = 1/2, 1/3, and 1/6 were ~2, 1.75 and 1.3 times greater than that of circular bull’s eye with ε = 0. These results are consistent with prior observations, when the electric field of the incident light is aligned along the minor axis of a single elliptic aperture, as in Fig. 1(c), the electric and magnetic dipoles are excited strongly on the surfaces of the metal film .
2.2 Dependence on the structural parameters of elliptic bull’s eye; s, w, p, and a
In the following analyses, we focused on the peak EOT intensity at θ = 0°. In Fig. 3 , we investigated the effect of groove depth, s, on EOT with other structural parameters set at w = 300 nm, p = 600 nm, a = 600 nm, t = 300 nm. EOT for horizontal and vertical polarization are summarized in Fig. 3(a), (b), respectively. Each data point is the EOT peak intensity at the corresponding resonance wavelengths, which were found by FDTD analyses. The dot-dash lines are fittings. We found that maximum EOT was achieved with s≈50 nm for both polarizations.
Compared with Shuford et al’s report  where the optimum groove depth, sopt, for a circular aperture surrounded by circular groove structures was ~15% of the groove period, p, our result was found to be about ~8% (soptimal = 50 nm for p = 600 nm), which is less by a factor of two. The difference is attributed to the step grooves and an elliptical aperture in the proposed bull’s eye in contrast to sinusoidal grooves and a circular aperture in prior reports. In Fig. 3 we could achieve a high EOT polarization extinction ratio, Iv/Ih = 798 at soptimal = 50 nm and ε = 1/2.
In Fig. 4 , we summarized the dependence of EOT on the groove width w. For both polarizations, we achieved the maximum EOT at the groove width w≈300 nm, which is about a half of the groove period p, consistent to the prior circular bull’s eye s . In the vertical polarization, the maximum EOT peak is observed at ε = 1/2 and w≈300 nm which is 298 times stronger than that of the horizontal polarization.
Among structural parameters, the groove periodicity, p, defines not only the dimension of the structure but also the resonance wavelength . The periodic metallic corrugation has the role of coupling the incident light to SPs which focus the electromagnetic fields in the aperture to provide EOT. Figure 5 summarizes the impacts of the groove period, p, on EOT intensity. The maximum EOT occurred when p≈2w (w = 300 nm), which is consistent to previous studies [13, 14]. In the vertical polarization, the maximum EOT intensity was observed at ε = 1/2, with p≈650 nm, and the polarization extinction ratio, Iv/Ih, was 563.
We then investigated the effect of the distance from the aperture center to the center of the first groove, a, and the results are summarized in Fig. 6 . The maximum EOT occurred at a≈550 nm for both polarizations, which is close to the period of the groove, p, in good agreement with the previous results . Similar to discussion on other parameters, we observed highly polarization dependent EOT such that vertical polarization showed a dominant peak whose intensity is 284 times larger at ε = 1/2.
In Fig. 7 , we summarized transmission spectra for various ellipticities, ε, in horizontal and vertical polarizations. As shown in the inset of Fig. 7(a), the spectral at ε = 0 composed of two peaks. The peak near 490 nm is related to interplay between the real part of the conduction electron dielectric function and the imaginary part of the d-electron dielectric function  and it didn’t change with the structural parameter variations. The stronger transmission peak due to the SP excitation was observed near 675 nm, which was affected by the ellipticity as in Fig. 7(b).
The near field intensity profiles were obtained in the log scale in Fig. 8(a), and (b) . Here we assumed s = 60 nm, w = 300 nm, p = a = 600 nm, t = 300 nm, d1 = 300 nm and d2 = 150 nm, with ε = 1/2. A plane wave was incident normal to the proposed bull’s eye at the resonance wavelength λ = 670 nm. When the structure is illuminated in the horizontal polarization, Fig. 8(a), the induced electric dipole is relatively weak and the primary source of radiation is the induced magnetic quadruple . In general, quadrapolar sources are weak radiators, thus accounting for the weakness of transmission through an elliptical aperture illuminated by a plane wave. In the case of vertical polarization, Fig. 8(b), we can expect more electrical charges and stronger surface currents and also a greater separation of the two magnetic dipoles to provide higher EOT . Furthermore, the periodic grooves which act as a resonant antenna further enhanced the polarization dependent EOT at the wavelengths determined by the periodic corrugations, efficiently coupling to SPs.
In Fig. 8(c), we plotted the EOT spectra for the vertical and horizontal polarizations for the optimal structural parameters (w = 300 nm, p = 650 nm, a = 550 nm, t = 300nm, s = 50 nm). The proposed device provided a unique optical characteristics with a high polarization extinction ratio over 1000, along with a highly directive beaming property as shown in Fig. 2. We summarized the polarization extinction ratio, Iv/Ih, as a function of the aperture ellipticity, ε, in Fig. 8(d) for the optimal parameters. We found monotonic and rapid increase of the polarization extinction ratio with increasing ellipticity, ε. The light polarized along the minor axis of the elliptic aperture had an EOT significantly larger by more than three orders of magnitude than the other orthogonal polarization. These results are consistent with prior observations in a single elliptic aperture without concentric grooves . When the electric field of the incident light is aligned along the minor axis of the aperture, the electric and magnetic dipoles are excited strongly on the upper surface of the metal film, which produces even stronger dipoles on the lower facet of the film . In our proposed device, the metallic grooves further enhance EOT to produce higher polarization dependence.
By introducing sub-wavelength scale anisotropy in the central aperture of a metallic bull’s eye structure, we were able to demonstrate that the polarization dependence in the EOT could be flexibly controlled. When the polarization of the incident plane was along the minor axis of the aperture with an ellipticty of ε = 1/2, we observed the EOT larger by over ~1000 times than that of the other orthogonal polarization. The proposed elliptic bull’s eye could provide unique highly polarization selective transmission, which was not demonstrated in prior circularly symmetric bull’s eye structures. Polarization dependence in EOT and its flexible control in bull’s eye structure would open new EOT applications such as single polarization photonic devices, and polarization selective plasmonic sensors.
This work was supported in part by the Brain Korea 21 Project, in part by the National Research Foundation of Korea (NRF) and grant funded by the Korea government (MEST) (No. 2011-00181613 and 2012M3A7B4049800), in part by the Seoul R&BD Program (No.PA110081M0212351), and in part by the LG Display (2011-8-2160).
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