Open Access
Add to BibSonomyAbstract
While plasmonic metamaterials find numerous applications in the field of nanophotonic devices, a device may work as a normal or plasmonic device, depending on whether it operates at the resonance mode. In this paper, the extraordinary light transmission through coaxial polygonal aperture arrays, including circle, hexagon, square, and triangle geometries, is studied using FDTD simulation. Circular, hexagonal and squared aperture arrays have similar high transmission rate, while triangular aperture array has considerably lower transmission rate. It is found that the transmission peaks reflect the resonance modes propagating along the direction of neighboring apertures. We hence rearrange the apertures from square lattice to triangle lattice to obtain a uniform resonance mode along the neighboring apertures. This leads to enhanced light transmission. The study gains understanding of new properties of the metamaterials based on plasmonic resonance.
©2009 Optical Society of America
1. Introduction
A plasmonic metamaterial, an artificially metal/dielectric micro/nano-structured material, finds numerous applications in the field of nanophotonics devices [1–3]. When plasmonic devices operate at certain resonance modes [4–6], they show unique properties in terms of light confinement and losses low enough to enable a useful propagation distance. Hence study on light transmission properties in a new metamaterial is of interest.
The extraordinary transmission obtained when light is transmitted through a subwavelength hole on a thin metal film is fundamentally important [7]. A metal film perforated with periodic arrays of subwavelength apertures (holes or slits) can display extraordinary transmission enhancement [8–11]. 90% transmission in the optical regime was demonstrated through a coaxial annular aperture array in a silver thin film [12–15]. A coaxial annular structure shows a larger cut-off wavelength than a circular one. This allows light propagating in a coaxial guide having a smaller transverse width.
In this paper, we consider array of apertures with various geometries (circular, hexagonal, squared and triangular polygons, as shown in Fig. 1 ) to study how geometry influences the optical transmission. We compare transmission peaks in terms of peak shift and peak enhancement and find that the transmission peaks reflect the plasmonic mode resonance along the direction of neighboring apertures. We further demonstrate that the transmission can be enhanced when a more uniform mode resonance is formed in the plasmonic metamaterial by changing the arrangement of apertures from square lattice to triangular lattice.
Fig. 1 Concentric coaxial apertures of various geometries in Ag film of 200 nm in thickness. (a) Circular aperture formed by two concentric circles with outer and inner radii Ro = 125 nm and Ri = 75 nm (slit width w 1 = 50 nm). (b) Hexagon, (c) square, and (d) triangle apertures inscribed in the two circles with width w 2 = 43nm, w 3 = 35 nm, and w 4 = 25 nm respectively.
2. Polygonal apertures and polygonal aperture arrays
Figure 1 shows the coaxial apertures studied. The circular aperture is formed by two concentric circles, and the hexagonal, squared, and triangular apertures are inscribed in the two circles. Triangle represents the polygon with the smallest number of sides and circle may be regarded as a polygon with infinite number of sides. It is noted that the polygons have different interior angles, e.g., 180°(Fig. 1(a)), 120° (Fig. 1(b)), 90° (Fig. 1(c)), and 60° (Fig. 1(d)). The four different apertures are arranged in a 11 × 11 periodic array with fixed period of 400 nm, as illustrated in Fig. 2 , to study their plasmonic modes in light transmission.
Fig. 2 Schematic of a 11 × 11 periodic array of (a) circle, (b) hexagon, (c) square, and (d) triangle with the period Λ = 400 nm and incident with a p-polarized plane wave with its electric field component in the x-direction. The geometric parameters are shown in Fig. 1.
3. Plasmonic modes in transmission through polygonal aperture arrays
With incidence of a p-polarized plane wave, light transmission through the four polygonal aperture arrays is calculated using the finite-difference time-domain (FDTD) simulation with absorption boundary condition assumed [16]. A commercial FDTD software package, FDTD Solutions, provided by Lumerical Solutions Inc [17]. is used. The dispersive data are based on the experimental data on optical constants of noble metals [18]. For example, at the wavelength, λ = 632.8 nm (frequency f = c/λ = 473.76 THz), the dielectric constant of the silver material used in the FDTD is εm = −18.663 + 2.326i. Mesh size in critical metal region is Δx = Δy = 8-10 nm and Δz = 20 nm.
Transmission is calculated as the ratio of power transmitted through the structure to the power incident on the structure. The transmission in Fig. 3 shows one peak for circular, hexagonal and triangular aperture arrays and dual peaks for squared aperture array. However, it should be noted that the FDTD simulation is carried out for the optical wavelengths (400-750 nm). When we extend the FDTD simulation to longer wavelength, we find the second transmission peak located between 750 nm and 900 nm for the circular, hexagonal and triangular aperture arrays. The observation is consistent with that of Baida and Labeke [12] that dual modes exist for coaxial circular aperture arrays.
Fig. 3 Plot of transmission as a function of wavelength showing peaks for the four aperture arrays shown in Fig. 2. The shoulder at wavelength λ = 440 nm shows enhanced transmission due to the excitation of SPPs at the array period.
The arrays shown in Fig. 2 are in square lattice. This type of lattice is illustrated in Fig. 4(a) in comparison with a triangle lattice (Fig. 4(b)). The circular shape is used in the illustration, but it represents any of the polygons. For the arrays arranged in square lattice, the propagating surface plasmon polaritons (SPPs) form a resonance along the horizontal (or vertical) and diagonal directions. For the considered aperture P1, SPPs propagate from P1 towards the apertures in its neighborhood, P2, P3 and P4, and the SPPs from P2, P3 and P4 propagate towards P1. The photon oscillation along the horizontal and diagonal directions can form two plasmonic modes, k1,sp and k2,sp.
Fig. 4 (a) Schematic of a 2 × 2 segment in a polygonal aperture array, showing a square lattice. SPPs propagate from aperture P1 towards its neighboring apertures P2, P3, and P4 in the horizontal and diagonal directions, represented by the different modes k1,sp and k2,sp. (b) Schematic of a segment in a rearranged polygonal aperture array, showing a triangle lattice. In that case, a uniform plasmonic mode is observed along the horizontal and 60° directions.
To clarify the point, total-electric-field intensity, |E|2, is simulated through a 2 × 2 segment of squared or triangular apertures using periodic boundary condition and shown in Fig. 5 . At resonance wavelength λ1, the segment is incident by a p-polarized plane wave having the E-field component along the x-direction. In the x-y plane at z = 200 nm away from the exit plane, the resonance modes are observed to propagate largely along the diagonal directions. At resonance wavelength λ2, the |E|2 field through square segment shows mixed resonance modes along both horizontal and diagonal directions (Fig. 6 ). Generally, the transmission peaks reflect the resonance mode propagating along the direction of neighboring apertures.
Fig. 5 At the resonance wavelength λ1, total-electric-field intensity, |E|2, through a 2 × 2 segment of (a) squared and (b) triangular apertures, showing that the resonance mode propagates along the two diagonal directions. The dash lines show location of the apertures.
Fig. 6 At the resonance wavelength λ2, total-electric-field intensity, |E|2, through a squared aperture segment shows the mixed resonance modes along the horizontal and two diagonal directions.
In addition, it is noted from Fig. 3 that enhanced transmission due to excitation of SPPs using the period of 400 nm shows a shoulder peak at 440 nm. The enhancement at 440 nm is much less than that at the resonance modes λ1 and λ2. If one considers different hollow areas of circle, hexagon, square, and triangle in Fig. 1, area ratio (A1:A2:A3:A4)/(Ro2-Ri2) = π:2.6:2:1.3. Area-normalized transmission (Fig. 7 ) shows the almost equal transmission rate for the light transmitted through circular, hexagonal, and squared aperture arrays, while the lowest transmission rate is observed for triangular aperture array. This can be explained as side-to-side effect of plasmonic modes enhances the resonance.
Fig. 7 Area-normalized transmission, showing almost equal transmission rate for the light transmitted through circular, hexagon, and square aperture arrays. Lowest transmission rate is observed for triangle aperture array.
Furthermore, the side-to-side resonance modes are studied using a linearly-polarized plane wave having polarization in different directions (e.g. 30° in comparison with 0°). Figure 8 shows the transmission through hexagon and triangle aperture arrays with incidence of a linearly-polarized plane wave having electric field component in the 30°-direction with respect to the x-direction. The electric field component in the 30°-direction is perpendicular to one side of hexagon or triangle as shown in the insert of Fig. 8. In the figure, the mode at λ1 observed has no shift in comparison with the mode shown in Fig. 7. This shows that the plasmonic resonance forms along the direction perpendicular to one of the aperture sides.
Fig. 8 Transmission through hexagon and triangular aperture arrays with incidence of a linearly-polarized plane wave having electric field component in the 30°-direction with respect to the x-direction. The transmission for circular aperture array is shown as a reference.
4. Enhanced transmission through polygonal aperture arrays
When arrangement of the apertures is changed from the square lattice (Fig. 4(a)) to triangle lattice (Fig. 4(b)), the plasmonic resonance mode becomes uniform propagating along the x-direction and the 60°-directions. The uniformity of the plasmonic resonance mode induces enhanced transmission, as shown in Fig. 9 . For example, the rearranged circular aperture array has a higher transmission peak at 564.0 nm (6% increment) in comparison with the array arranged in square lattice. In the hexagon case, the transmission rate at 569.5 nm increases by 6% also. In addition, a broader transmission peak is observed at 569.5 nm in the square case. In particular, the almost same plasmonic mode is observed at 569.5 nm for the arrays of different polygons. Thus we found that the transmission can be enhanced when a more uniform mode resonance is formed by changing the arrangement of apertures from square lattice to triangle lattice.
Fig. 9 When the polygonal apertures are arranged in triangle lattice, enhanced transmission is obtained. For circular, hexagonal, and squared aperture arrays, the same plasmonic mode is observed at 569.5 nm, but two broad shoulder peaks are observed at 623.5 and 658.2 nm for triangular aperture array. As in Fig. 8, transmission for circular aperture array arranged in square lattice is shown as a reference.
While our approach is suitable to explain the modes in a coaxial guide using circular, hexagonal, and squared geometries, the triangular case shows a difference. For example, the low transmission rate is observed at the optical wavelengths (Fig. 3) and, in particular, the mode has two shoulder peaks observed at the wavelengths of 623.5 and 658.2 nm (Fig. 7). It indicates that not only side-to-side resonance mode but also the mode at side-to-corner or even corner-to-corner may play a role in light transmission.
5. Conclusion
This study compares extraordinary transmission through different polygonal aperture arrays at the optical wavelengths. Calculation of the area-normalized transmission shows that the transmission rate is comparable for circular, hexagonal, and squared aperture arrays but considerably lower for the triangular aperture array. Transmission peaks are located at different wavelengths for the four types of apertures arranged in square lattice. The plasmonic resonance mode is shown to propagate along the direction of neighboring apertures. It is interesting to find almost the same resonance wavelength at 569.5 nm for circular, hexagonal and squared aperture arrays, when we rearrange the arrays from square lattice to triangle lattice. In the case of triangle lattice, the transmission is enhanced due to a uniform mode resonance along horizontal and 60° directions.
Acknowledgements
We thank A*Star, Singapore for financial support through SERC Grant No. 072 101 0023.
References and links
1. I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007). [CrossRef] [PubMed]
2. I. I. Smolyaninov, “Two-dimensional plasmonic metamaterials,” Appl. Phys., A Mater. Sci. Process. 87(2), 227–234 (2007). [CrossRef]
3. I. Smolyaninov, “Nanophotonic devices based on plasmonic metamaterials,” J. Mod. Opt. 55(19), 3187–3192 (2008). [CrossRef]
4. J. Wang and W. Zhou, “Subwavelength beaming using depth-tuned annular nanostructures,” J. Mod. Opt. 56(7), 919–926 (2009). [CrossRef]
5. J. Wang, W. Zhou, and A. K. Asundi, “Effect of polarization on symmetry of focal spot of a plasmonic lens,” Opt. Express 17(10), 8137–8143 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-10-8137. [CrossRef] [PubMed]
6. I. Ahmed, C. E. Png, E. P. Li, and R. Vahldieck, “Electromagnetic wave propagation in a Ag nanoparticle-based plasmonic power divider,” Opt. Express 17(1), 337–345 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-1-337. [CrossRef] [PubMed]
7. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
8. 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]
9. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]
10. J. A. Porto, F. J. Garcia-Vidal, and P. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999). [CrossRef]
11. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001). [CrossRef] [PubMed]
12. F. I. Baida and D. V. Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209(1-3), 17–22 (2002). [CrossRef]
13. F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67(15), 155314 (2003). [CrossRef]
14. F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006). [CrossRef]
15. Y. Poujet, J. Salvi, and F. I. Baida, “90% Extraordinary optical transmission in the visible range through annular aperture metallic arrays,” Opt. Lett. 32(20), 2942–2944 (2007). [CrossRef] [PubMed]
16. A. Taflove, and S. C. Hagness, Computational electrodynamics: the finite difference time-domain method (Artech House, Boston, 2005).
17. F. D. T. D. Solutions, from Lumerical Solutions Inc., http://www.lumerical.com.
18. D. R. Lide, ed., CRC handbook of chemistry and physics (89th Edition, CRC Press/Taylor and Francis, Boca Raton, FL, Internet Version 2009).
