We report enhanced optical transmission (EOT) through a hexagonal aperture surrounded by polygonal segmented grooves to explore its unique polarization dependence. Effects of light polarization on EOT through the hexagonal aperture were systematically investigated for three types of grooves: concentric hexagonal grooves, linear segmented grooves and wedge segmented grooves. Significant increase in EOT was observed for the polarization directed along the groove axis compared to the other orthogonal polarization, which can be further applied to polarization dependent photonic devices.
© 2013 Optical Society of America
Surface Plasmons (SPs) have been one of key interests in the sub-wavelength photonics [1–8] and recent investigations have renewed the importance of bull’s eye structures that consist of a circular sub-wavelength aperture and concentric circular grooves on a metal film . This bull’s eye structure generated the enhanced optical transmission (EOT) through the sub-wavelength aperture via surface plasmons excitation in the periodic metallic corrugations, which led to various integrated optoelectronic applications . In prior bull’s eyes studies, detailed parametric investigations have been reported such that the effects of the corrugation period, depth, width, number of the grooves and the aperture diameter on EOT have been well understood under the assumption of the circular symmetry [11–15]. Despite these extensive efforts, there have been only a few reports on the polarization control in bull’s eyes. Earlier polarization studies have been limited only to special geometries such as elliptical and rectangular nano-hole arrays [16–18], single sub-wavelength aperture on a metallic film without any corrugations , nano-hole structures with multiple-grating geometry , and an acicular aperture surrounded by elliptical corrugation . Recently the authors’ group reported the elliptical aperture surrounded by circular corrugations showing a significant improvement in polarization extinction ratio . In addition to these, a slit aperture surrounded by linear grooves  and a circular aperture surrounded by a single channel groove  have shown some potential in polarization control. However, prior bull’s eye studies assumed only highly symmetric structures such as circular/elliptic symmetries or an extreme simplicity as in a liner slit. Impacts of systematic lowering the order of symmetry have not been fully investigated yet, to the best knowledge of the authors. Bull’s eyes with a polygonal aperture and polygonal grooves with a lower order of symmetry might further endow a more fundamental degree of freedom to control the polarization of EOT.
In this study, we investigated polarization dependent EOT, for three types of polygonal bull’s eyes, for the first time. We consider a common hexagonal aperture at the center surrounded by three different grooves: concentric hexagonal groove, linear segmented groove, and wedge segmented grooves. Here we focused on the impacts of the aperture symmetry, and the symmetry of the surrounding grooves over the polarization dependence of EOT by using finite-difference time domain (FDTD) method .
Schematic diagrams of the bull’s eyes in this study are summarized in Figs. 1(a)–1(c), which correspond to the hexagonal, the linear segmented, and the wedge segmented grooves, respectively. The proposed structures shown in Fig. 1 have the common central hexagonal aperture, and their groove structures were designed to share the hexagonal symmetry in part. The grooves in Fig. 1(a) have the complete hexagonal symmetry as the aperture. The linear segmented grooves in Fig. 1(b), and the wedge segmented grooves in Fig. 1(c) are in fact complementary to each other to form the complete hexagonal symmetry. The linear segmented grooves, Fig. 1(b), are parallel to the sides of the hexagonal aperture and extend into a cone with an angle of 60°. The wedge segmented grooves are formed parallel to the corners of the hexagonal aperture and extend into a cone with an angle of 120°. Detailed structural parameters are shown in Fig. 1(d): aperture size (D), distance of aperture center to the first groove (R), groove height (H), width (L), period (P), and 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. In this study, we assumed a silver film with 300 nm thickness, which has been used in prior reports due to its large negative real part and a small imaginary part of dielectric constant in the visible spectral range [25, 26]. We also assumed that the input and output surfaces are 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. Current state of art focused ion beam (FIB) system has realized plasmonic structures with acute angles  to a spatial accuracy sufficiently high enough for the proposed hexagonal structure. Yet the rounding of corners would affect the transmission which are being investigated by the authors.
2. Results and discussions
A snapshot for FDTD analyses is shown in Fig. 2: 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 800 nm and its linear polarization direction was varied. The z-component of electric field was set to be normal to the metal film. The x-component of electric field and y-component of magnetic field were in the xy-plane parallel to metal film. The boundary conditions were perfectly matched layer in the x and y direction with a minimal reflection. 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 electric field intensity.
2.1 Enhanced optical transmission analyses for the hexagonal aperture
For the proposed structures shown in Fig. 1, we calculated the EOT intensity at the resonance as a function of structural parameters. Figure 3 shows the variation of the normalized transmission, as a function of groove numbers. Here we defined normalized transmission as the transmission through the proposed structure normalized to that through the hexagonal aperture without any groove structures. With the increasing the number of grooves, the EOT intensity increases, which can be attributed to the Bragg reflection effects. Figure 3(a) shows the normalized transmission versus number of grooves for the hexagonal aperture surrounded by hexagonal grooves for the x-polarization and the y-polarization. Increasing the number of grooves enhanced the transmission, which is consistent to prior reports , yet we found that this effect was more prominent in the y-polarization where the electric field is along the corners of the hexagonal aperture than in the x-polarization where the electric field is along the sides of the hexagon. Note that this is quite a contrast to circular aperture/grooves , which did not show any polarization dependence in EOT. Figure 3(b) shows the normalized transmission for the hexagonal aperture surrounded by linear segmented grooves, and we found that the polarization dependence in the normalized transmission was significantly increased with increasing number of grooves such that an order of magnitude larger transmission was obtained in the x-polarization than in the y-polarization for 10 grooves. It is also noted that transmission for the y-polarization did not change significantly with the groove numbers in contrast to x-polarization. For the linear grooves, the structure showed a semi-periodic structure in the x-direction. This structure can strongly couple with the incident light with the polarization in the x-direction but weakly with the y-polarization. Consequently the plasmonic resonances will have a high polarization dependence as summarized in Fig. 3(b). Figure 3(c) shows variation of the normalized transmission for the hexagonal aperture surrounded by the wedge segmented grooves. The structure showed a larger transmission in the y-polarization with increasing groove numbers opposite to Fig. 3(b). It is noteworthy that the polarization dependence in EOT in the linear segmented groove and the wedge segmented groove was complementary consistent to their geometrical complementary relation.
In Fig. 3, we found that within the groove number of 10, the wedge segmented groove showed the largest transmission enhancement among three structures. Hexagonal and wedge grooves showed the maximum EOT at groove number of 6. In contrast, the linear segmented groove showed the largest polarization dependence, and EOT in the y-polarization monotonically increased with the groove number.
We further investigated the impact of R, the distance from the aperture center to the first groove, on EOT and the results are summarized in Fig. 4(a). Here the number of grooves was six, which corresponded to the maxima EOT of the hexagonal and wedge grooves as shown in Fig. 3. We found an optimal R of ~350 nm for all structures and the EOT for the wedge segmented grooves showed the largest EOT, which was about factor of two larger than that of linear segmented grooves. The impacts of the groove depth, H, are summarized in Fig. 4(b) and we found an optimal value H~50nm to generate the maximum EOT for all structures and the wedge segmented grooves showed the largest EOT.
We also investigated the impact of the aperture size, D, and the results are summarized in Fig. 5(a). We found that the wedge grooves in the y-polarization showed the largest EOT with the optimal D of ~350nm. We also found that groove width, L, is the most sensitive parameters to control the EOT, and the analyses results are summarized in Fig. 5(b). The maximum EOT could be achieved at L ~200 nm, where its magnitude is more than 6 fold larger than that of minimum value at L~450nm. In this parametric analysis we found that the EOT magnitude was largely affected by the groove width, L, the groove depth, H, as well as the aperture size, D, and the distance to the first groove, R. The absolute optical transmission for hexagonal aperture surrounded by hexagonal grooves, linear segmented grooves, and wedge segmented grooves at optimized conditions (n = 6, p = 500nm, L = 200nm, H = 50nm, R = 350nm, D = 350nm) was 0.2, 0.17, and 0.26, respectively in an arbitrary unit. Corresponding transmission for the conventional circular bull’s eye with the same structural parameters was 0.24. We confirmed that the absolute EOT level of these hexagonal bull’s eyes was comparable to that of conventional circular bull’s eyes.
In Figs. 4 and 5, we found that the wedge segmented structure showed the highest EOT in all cases. The polarization extinction ratio (PER), which is represented by the ratio of the larger EOT to the smaller EOT in two orthogonal polarizations, was found to be very sensitive to structural parameters, especially L in Fig. 5(b) and H as in Fig. 4(b). The PER was found to be significantly higher in the hexagonal aperture in the linear segmented grooves PER = 13.4 dB than the wedge segmented grooves PER = 10.5 dB in L = 200 nm. This result shows that the hexagonal aperture surrounded by linear segmented grooves would give highest polarization dependence in EOT among three structures. The simulations in this paper were done at normal incident angle. With changing the angle of incident light, the central frequency shifts that depend on the incident light angle. Another effect of changing the structure parameters can be explained by phase shift between incident light and out coming light that mostly depend on groove depth and grooves width . There are some papers that the experimentally measured phase shift equals between the incident light and surface waves launched by holes surrounded by grooves [31, 32].
The resonant wavelength of EOT was found to be dominantly affected by the groove periodicity, P, and the results are summarized in Fig. 6(a). As the period increased from 400 to 650nm, the resonance wavelength of hexagonal aperture surrounded by hexagonal grooves monotonically increased, which is consistent to prior circular bull’s eyes . For linear segmented grooves and wedge segmented grooves structures, the resonance wavelength and the groove periodicity showed a nonlinear relation that can be well-fitted by a cubic function. Note that the linear segmented groove [the red curve in Fig. 6(a)] can provide the widest range of resonance wavelength for the given range of P. In circular bull’s eyes  and square bull’s eyes  the resonance wavelength (λr) showed a linear increase with the groove periodicity (P). In our study, we also found a similar linear relationship for the hexagonal grooves as in Fig. 6(a). In contrast, the linear segmented grooves and wedge segmented grooves structures showed a nonlinear relationship. The nonlinear fitting analyses showed a cubic response: linear segmented grooves (λr ~2.9x10−5P3 −0.044 P2 + 21.82P-3076.6) and wedge segmented grooves (λr ~1.2x10−5 P3 −0.044 P2 + 10.54P-1335.5). The basis of this nonlinearity could be attributed to the lower symmetry and the authors are investigating related effects in other polygonal structures, which will be reported in a separate article. Transmission spectra of EOT from the hexagonal bull’s eyes in the x-polarization and y-polarization, linear segmented grooves in the x-polarization and y-polarization, and wedge segmented grooves in the x-polarization and y-polarization were also calculated and the results are summarized in Fig. 6(b). Figure 6(c) shows PER versus wavelength for hexagonal grooves, linear segmented grooves, and wedge segmented grooves. The green line in Fig. 6(c) shows the wavelength of peak of EOT in Fig. 6(b). Our studies assumed the normal incident light, which has been widely accepted in prior reports. In contrast to conventional circular bull’s eyes, the polygonal structure provides distinctive axes of rotation depending on the symmetry of the polygons. The authors are in fact investigating this angular dependence on the resonance wavelength shift, which has not been a critical issue in conventional circular bull’s eyes.
We calculated the near-field electric field intensity distribution at the EOT peaks and the results are summarized in Fig. 7. It is noted that a higher electric field intensity is distributed around the corners of the hexagonal structures than along the sides, which is consistent to previous structures consisted of sharp corners and edges [34–37]. In Fig. 7(a), the electric field intensity is significantly higher along the y direction parallel to the corners of hexagonal aperture and grooves. The unexpected polarization dependent EOT in the hexagonal grooves in Fig. 3(a) is attributed to this asymmetric distribution of electric field in Fig. 7(a). When we compare the wedge segmented grooves in Fig. 7(c) with Figs. 7(a) and 7(b), we can qualitatively understand why the highest EOT was achieved in the wedge segmented grooves. For the y-polarization, the electric field in the wedge segmented grooves is well aligned to the corners but in the hexagonal grooves there are electric field intensity distributions along the sides of hexagonal in the x-direction with a lower intensity that does not contribute to EOT [34, 35] to result in a lower EOT. For the linear segmented grooves, the overall electric field intensity in the direction of sides of the hexagonal aperture for the x-polarization light is lower than that of wedge segmented grooves, which accounts for the lower EOT in the linear segmented grooves. The results show that the out-put light at the far field showed a typical diffraction pattern.
2.2 Further control of polarization dependence in EOT
Polarization dependence can be further controlled by elongating the aperture in either along the corners or the sides. Schematic diagrams of this approach are shown in Fig. 8 for the linear segmented grooves. Figure 8(a) shows the elongation of the aperture along the corners in the y-direction. Figure 8(b) shows the elongation of the hexagonal aperture along the sides in the x-direction. Here we introduce additional structural parameters h1 in Fig. 8(a) and h2 (angle ) in Fig. 8(b).
Normalized transmission was calculated for these elongated apertures by varying h1 and h2 and the results are summarized in Figs. 9(a) and 9(b), respectively. In both cases the EOT along the corners or equivalently in the y-direction did not change with the additional structural parameters, h1 and h2. However, in Fig. 9(a) the EOT for the x-polarization grew monotonically with h1, to reach the PER of ~19.5 dB at h1 = 1 μm. In Fig. 9(b), the EOT for the x-polarization was about 10 times larger than EOT for the y-polarization but it was almost independent of h2 parameter.
Effects of incident light polarization on the enhanced transmission (EOT) through a hexagonal aperture were parametrically analyzed for hexagonal, linear segmented, and wedge segmented grooves on a silver film. Our results show that, high EOT is assisted by the hexagonal aperture surrounded by wedge segmented grooves in the y-polarization, which was about factor of two larger than that of linear segmented grooves. However, hexagonal aperture surrounded by linear segmented grooves in the x-polarization would give highest polarization dependence with the polarization extinction ratio of 13.4 dB compared to the hexagonal aperture surrounded by wedge segmented grooves in the y-polarization with the polarization extinction ratio of 10.5 dB in the groove width (L = 200 nm). Elongated aperture surrounded by linear segmented grooves in the x-polarization shows high sensitivity to the polarization state with the polarization extinction ratio of 19.5 dB compared to the hexagonal aperture surrounded by linear segmented grooves in the x-polarization.
This work was supported in part by the National Research Foundation of Korea (NRF), 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. Heng, X. Cui, D. W. Knapp, J. Wu, Z. Yaqoob, E. J. McDowell, D. Psaltis, and C. Yang, “Characterization of light collection through a subwavelength aperture from a point source,” Opt. Express 14(22), 10410–10425 (2006). [CrossRef] [PubMed]
2. S. Carretero-Palacios, O. Mahboub, F. J. Garcia-Vidal, L. Martin-Moreno, S. G. Rodrigo, C. Genet, and T. W. Ebbesen, “Mechanisms for extraordinary optical transmission through bull’s eye structures,” Opt. Express 19(11), 10429–10442 (2011). [CrossRef] [PubMed]
4. D. W. Kim, Y. C. Kim, O. Suwal, V. Jha, M. J. Park, and S. S. Choi, “Optimization of light-surface plasmon coupling by periodicity regulation for a pyramidal probe,” Mater. Sci. Eng. B 149(3), 242–246 (2008).
5. N. Bonod, E. Popov, D. Gérard, J. Wenger, and H. Rigneault, “Field enhancement in a circular aperture surrounded by a single channel groove,” Opt. Express 16(3), 2276–2287 (2008). [CrossRef] [PubMed]
6. K. Y. Kim, A. V. Goncharenko, J. S. Hong, and K. R. Chen, “Near-field characterization on light emanated from subwavelength plasmonic double slit of finite length,” J. Opt. Soc. Korea 15, 196–201 (2011).
7. H. Nasari and M. S. Abrishamian, “Active focusing of light in plasmonic lens via Kerr effect,” J. Opt. Soc. Korea 16, 305–312 (2012).
8. J. H. Lee, S. K. Hong, and S. W. Nam, “Cooperative spontaneous emission from nanocrystals to a surface plasmon polariton in a metallic nanowire,” J. Opt. Soc. Korea 15, 407–414 (2011).
9. 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]
10. F.-F. Ren, K.-W. Ang, J. Ye, M. Yu, G.-Q. Lo, and D.-L. Kwong, “Split bull’s eye shaped aluminum antenna for plasmon-enhanced nanometer scale germanium photodetector,” Nano Lett. 11(3), 1289–1293 (2011). [CrossRef] [PubMed]
11. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90(16), 167401 (2003). [CrossRef] [PubMed]
12. M. Pournoury, H. E. Arabi, and K. Oh, “Strong polarization dependence in the optical transmission through a bull’s eye with an elliptical sub-wavelength aperture,” Opt. Express 20(24), 26798–26805 (2012). [CrossRef] [PubMed]
13. 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]
14. F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90(21), 213901 (2003). [CrossRef] [PubMed]
15. K. L. Shuford, M. A. Ratner, S. K. Gray, and G. C. Schatz, “Finite-difference time-domain studies of light transmission through nanohole structures,” Appl. Phys. B 84(1–2), 11–18 (2006). [CrossRef]
16. R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92(3), 037401 (2004). [CrossRef] [PubMed]
17. K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004). [CrossRef] [PubMed]
18. C. K. Chang, D. Z. Lin, C. S. Yeh, C. K. Lee, Y. C. Chang, M. W. Lin, J. T. Yeh, and J. M. Liu, “Similarities and differences for light-induced surface plasmons in one- and two-dimensional symmetrical metallic nanostructures,” Opt. Lett. 31(15), 2341–2343 (2006). [CrossRef] [PubMed]
19. A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239(1-3), 61–66 (2004). [CrossRef]
20. N. Sedoglavich, J. C. Sharpe, R. Künnemeyer, and S. Rubanov, “Polarisation and wavelength selective transmission through nanohole structures with multiple grating geometry,” Opt. Express 16(8), 5832–5837 (2008). [CrossRef] [PubMed]
22. 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]
23. N. Bonod, E. Popov, D. Gérard, J. Wenger, and H. Rigneault, “Field enhancement in a circular aperture surrounded by a single channel groove,” Opt. Express 16(3), 2276–2287 (2008). [CrossRef] [PubMed]
24. FDTD Lumerical Solutions Inc, www.lumerical.com.
25. 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]
26. J. R. Sambles, G. W. Bradbery, and F. Yang, “Optical excitation of surface plasmons: an introduction,” Contemp. Phys. 32, 173–183 (1991).
27. S. Park, J. W. Hahn, and J. Y. Lee, “Doubly resonant metallic nanostructure for high conversion efficiency of second harmonic generation,” Opt. Express 20(5), 4856–4870 (2012). [CrossRef] [PubMed]
28. T. Ishi, J. Fujikata, and K. Ohashi, “Large optical transmission through a single subwavelength hole associated with a sharp-apex grating,” Jpn. J. Appl. Phys. 44(4), L170–L172 (2005). [CrossRef]
30. P. Lalanne and J. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006). [CrossRef]
31. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004). [CrossRef] [PubMed]
32. G. Gay, O. Alloschery, B. V. de Lesegno, J. Weiner, and H. Lezec, “Surface wave generation and propagation on metallic subwavelength structures measured by far-field interferometry,” Phys. Rev. Lett. 96, 213901 (2006).
33. N. C. Lindquist, A. Lesuffleur, and S. 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]
35. 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]
36. Z. Zhang, S. Zhang, and Z. Xiong, “Optical properties of silver hollow triangular nanoprisms,” Plasmonics 5(4), 411–416 (2010). [CrossRef]
37. X. Jiao and S. Blair, “Polarization multiplexed optical bullseye antennas,” Plasmonics 7(1), 39–46 (2012). [CrossRef]