Dual Channels of Transmission Using Rectangular Hole Dimers - The

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Dual Channels of Transmission Using Rectangular Hole Dimers Cheng-ping Huang,*,†,§ Yong Zhang,† Qian-jin Wang,‡ Xiao-Gang Yin,|| Guo-dong Wang,‡ Jian-qian Liu,‡ and Yong-yuan Zhu*,‡ †

Department of Applied Physics, Nanjing University of Technology, Nanjing 210009, P.R. China National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, P.R. China § Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China State Key Laboratory of Millimeter Waves, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China

)

‡

ABSTRACT: The optical properties of a plasmonic surface have been engineered using the rectangular nanohole dimers. One or two transmission peak(s), associated with two symmetrical or asymmetrical transmission channels, has (have) been revealed. We found that, similar to the plasmon coupling of a nanorod dimer, a strong coupling effect is also present in a rectangular nanohole dimer. The effect is closely correlated with the surrounding currents of waveguide modes, which mediate, via the magnetic field, an attractive or repulsive interaction between the dimer holes. The resulted low-energy or high-energy mode will couple with the film surface waves, thus producing the transmission peak with a red- or blue-shift. Moreover, the dependence of coupling modes on the sizes and separation of dimer holes has been systematically investigated, and an anticrossing-like coupling behavior has been suggested. We also suggest that, using the rectangular hole dimers with the perpendicular arrangement, the polarization of light can be manipulated at the desired wavelength. Our results may give a supplement to the Babinet principle, considering the correspondence between the underlying plasmonic interactions in the hole dimer and that in its complementary structure, i.e., the particle dimer.

I. INTRODUCTION The metallic nanoholes and nanoparticles are important building blocks for designing various plasmonic materials and realizing novel optical properties. It is well-known that, by drilling periodic hole arrays in a metal film, the transmission of light can be greatly enhanced due to the surface-plasmon polariton (SPP) resonance.1,2 Such effect may find potential applications in developing plasmonic nanolithography, subwavelength light sources, solar energy materials, etc.2
4 Moreover, a metal surface textured with periodic nanoholes forms a two-dimensional SPP crystal, with which highly dispersive photonic elements can be constructed.5 On the other hand, the metallic nanoparticles can support the localized surface-plasmon (LSP) resonance due to collective oscillation of confined conduction electrons. By using the LSP resonance and near-field coupling, the electromagnetic energy can be guided along a linear chain of metallic particles.2 Theoretical and experimental studies also suggest that the metal particles are critical for realizing the optical magnetism, lighttrapping in solar cells, and long-wavelength optical properties of an ionic-type plasmonic crystal.6
8 Recently, the optical properties of metal particle dimers (e.g., a pair of nanospheres, nanodisks, nanoshells, nanorods, etc.) have attracted much research interest.9
14 When two metal particles approach each other, their plasmonic near-fields will overlap and couple strongly, giving rise to a distance-dependent wavelength shift of plasmon mode and a strong field enhancement near the particle junction. This provides a useful tool for trapping the single molecules, enhancing the Raman scattering, measuring the particle distance, etc.15 In addition, the interaction of light with r 2011 American Chemical Society

double holes has also received a lot of attention in recent years.16
21 A frequently studied structure is the double-hole arrays milled in a metal film, where the circular holes overlap with the varying centerto-center distance.16
19 In this structure, the strong field enhancement near the metal apexes has been employed to boost the secondharmonic generation and Raman spectroscopy.16
18 As a complementary structure of particle dimers, the double holes can be termed symmetrically as the hole dimers, especially in the strong coupling regime. In this paper, the optical properties of a metal surface perforated with symmetric and asymmetric rectangular-hole dimers have been studied. Compared with the symmetric dimer which has a single transmission peak, the asymmetric one presents a pair of peaks at the long wavelength. We found that a strong plasmon coupling effect between the dimer holes is present. The resulting attractive or repulsive mode can hybridize with the film surface waves, thus generating the transmission peak. We also show that the rectangular hole dimers with a perpendicular configuration can be employed to manipulate the light polarization in certain wavelength regions.

II. METHODS The plasmonic structure under study is a metal film perforated with a square array of hole dimers, where in each unit cell two rectangular holes are aligned side-by-side (see inset of Figure1). In the experiment, a silver film with the thickness t = 80 nm was Received: September 11, 2011 Revised: November 3, 2011 Published: November 07, 2011 24621

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Figure 1. FIB images of rectangular holes and dimers: (a) monohole array (l = 300 nm), (b) symmetrical dimer array (l = 300 nm), and (c) asymmetrical dimer array (l1 = 300 nm, l2 = 500 nm). Here, a silver film with the thickness 80 nm was deposited on the glass substrate, the lattice period of dimer array is 600 nm, and the width of all rectangular holes is fixed as 100 nm.

deposited on the glass substrate. The hole-dimer array and, for comparison, the monohole array (a unit cell contains a single rectangular hole) were fabricated with the focused-ion-beam (FIB) system (Strata FIB 201, FEI Company, 30 KeV Ga ions, 21pA beam current). Here, the lattice constant is d = 600 nm, the width of rectangular holes is fixed as w = 100 nm, and the hole lengths are set as l = 300, 400, and 500 nm, respectively (the hole separation in a dimer is s = 100 nm). Figure 1 shows the FIB images of the monohole array (a), symmetrical dimer array (b), and asymmetrical dimer array (c). In the measurement, the white light was incident normally upon the sample with the electric field along the short edge of rectangular holes (x-polarization), and the zero-order transmission spectrum (600
1700 nm) was obtained using an optical spectrum analyzer (ANDO AQ6315A). In addition, to confirm the experimental results and systematically study the optical properties of the structure, the finite-difference time-domain (FDTD) simulations have also been carried out using the commercial software CST Microwave Studios. In the numerical simulations, the permittivity of glass substrate is set as 2.25, and the silver is modeled by a lossy Drude dispersion with a plasma frequency of ωp = 1.37  1016 rad/s and a collision frequency of γ = 1.2  1014 Hz.

III. RESULTS AND DISCUSSIONS A. Monohole Arrays. Figure 2a shows the measured transmission spectra of three samples of monohole arrays, where the hole lengths are 300, 400, and 500 nm, respectively (from the left to right). A featured transmission dip appears at around 930 nm, which is independent of the hole size. Note that, using the flatSPP resonance condition,22 this dip can be further predicted with rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi d2 λdip ¼ nd λp 2 þ 2 ð1Þ m þ n2

where nd = 1.5 is the refractive index of glass substrate, λp = 138 nm is the plasma wavelength of silver, and m and n are two integers of reciprocal vectors (the Drude model is used).

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Figure 2. (a) Measured and (b) calculated transmission spectra of monohole arrays. The length of rectangular hole is set as 300 (the black circles or solid line), 400 (the red triangles or dash line), and 500 nm (the blue squares or dot line).

An enhanced transmission peak is present when the wavelength is larger than the dip position (930 nm, here), which depends on the lattice period and hole size significantly.1,22,23 With the increase of hole length, the peak is red-shifted from 1135 nm to around 1350 and 1630 nm. These experimental results agree with the numerical simulations based on the FDTD method (the deviation can be attributed to some errors resulted in the FIB fabrication processes) [see Figure 2b]. Here, an important parameter is the cutoff wavelength of the rectangular hole waveguide. In the plasmonic regime, it has been shown that the cutoff wavelength of rectangular hole can be significantly increased due to the coupling of surface plasmons on the hole walls.24 In the near- and mid-infrared range, the cutoff wavelength of a subwavelength rectangular hole can be determined, based on this surface-plasmon coupling mechanism, as25 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λcut ¼ 2ðl þ 2δÞ 1 þ 2δ=w ð2Þ where δ = 22 nm is the skin depth of silver. The cutoff wavelengths for three hole sizes are calculated respectively to be 826, 1066, and 1306 nm, which, however, is significantly smaller than the peak wavelengths (see Figure 2). This shows, here, the enhanced transmission is not due to the pure waveguide resonance. The dependence of transmission peak on the lattice period as well as hole size suggests that both the film surface waves and hole waveguide modes play an important role. Thus the transmission peaks can be attributed to the coupled excitation (or hybrid-mode) of film surface waves and hole waveguide modes.22,26 B. Symmetrical Hole Dimers. The symmetrical hole dimers consisting of two parallel rectangular-holes in a unit cell may present different optical properties due to the coupling effect. Figure 3a shows the measured (the red circles) and calculated (the blue solid line) transmission spectrum of the symmetrical dimers, which has the hole length l = 300 nm and hole separation s = 100 nm. A reasonable agreement between experiment and simulation can be found. It can be seen the featured transmission dip mentioned above (around 930 nm) is still present in this case, 24622

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Figure 3. (a) Measured (the red circles) and calculated (the blue line) transmission spectra of symmetrical hole dimers with the length l = 300 nm and hole separation s = 100 nm. The green dash line represents the spectrum of mono- hole array with l = 300 nm. Panels b and c show the electric-field pattern and current distributions at the transmission peak 1017 nm, respectively.

Figure 4. Transmission spectra of symmetrical hole dimers: (a) The hole length is set as 300 (the red circles), 350 (the green triangles), and 400 nm (the blue squares); the hole separation is s = 100 nm. The inset shows the dependence of peak positions of dimer-hole (the solid circles) and monohole (the open circles) on the hole length. (b) The hole separation is set as 150 (the red circles), 100 (the green triangles), and 50 nm (the blue squares); the hole length is l = 300 nm. The inset shows the peak position as a function of hole separation.

with the spectral width becomes narrower (due to the blueshift of transmission peak). Moreover, a dominant transmission peak appears at the long wavelength (around 1017 nm, theoretically). Compared to the spectrum of monohole array with the same hole size (the peak locates at 1135 nm, see the green dash line), the dimer peak shows a significant blueshift of 118 nm. Here, the electric- field pattern and current distribution for the transmission peak of dimer (1017 nm) are plotted in Figure 3, panels b and c, respectively. We can see that the two rectangular holes are strongly and equally excited due to the dimer symmetry. Furthermore, the results suggest that the electromagnetic fields in the rectangular holes (the waveguide modes) are accompanied by a surrounding current simultaneously. Thus, via the interaction of these currents, two rectangular holes (or waveguide modes) can be coupled. To understand the above effect, we may employ the Babinet principle and the plasmon coupling of parallel-nanorod dimer. According to the Babinet principle,27 the spectral response of a structure for a given light polarization corresponds to that of its complement for the orthogonal polarization. In principle, the Babinet principle is exactly true for the infinitely thin and perfectly conducting planar screen. It has been shown that,28 for the plasmonic metamaterials in the optical frequencies, the principle still qualitatively holds despite the deviation of system from the ideal physical conditions. Moreover, besides the transmission and reflection response, the resonant field modal profiles of a screen and its complement can also be related to each other.28 Thus, we believe, the underlying plasmonic interactions in the rectangular hole dimers may be correlated with that in the metallic nanorod dimers. Imaging the plasmon coupling in a nanorod dimer (the electric field is along the rod axis), the parallel currents can be excited in the two nanorods and the charges of the opposite sign accumulate on the two ends of either nanorod. The charged nanorods

behave as two parallel electric dipoles, which induce a repulsive interaction via the electric field, thus shifting the coupling mode to a high energy or shorter wavelength. Correspondingly, as can be seen from Figure 3c, the resonant excitation of rectangular holes (the electric field is along the short edge) causes the current of the same direction circulating around the two upper (or lower) ends of the holes. The upper (or lower) circulating currents behave as two parallel magnetic dipoles, which can also induce a repulsive interaction via the magnetic field and shift the coupling mode to a shorter wavelength. The coupling mode of hole dimer (the coupled waveguide modes) will mix with the film surface waves, thus generating a transmission peak. This explains the blueshift as observed for the symmetrical hole dimers. Figure 4a presents the transmission spectra of symmetrical hole dimers with the varying hole length (the hole separation is fixed as s = 100 nm, the hole length is l = 300, 350, and 400 nm, respectively). With the increase of hole length, the dominant transmission peak shifts to the longer wavelength significantly. A detailed dependence of peak position on the hole length is depicted in the inset of Figure 4a (the solid circles). Note that, in the whole range of study, the peak position of hole dimers is shorter than that of the corresponding monohole array (the open circles). In addition, Figure 4b presents the spectra of symmetrical dimers with the varying hole separation (the hole length is fixed as l = 300 nm, the hole separation is s = 150, 100, and 50 nm, respectively). Surprisingly, the transmission peak exhibits a moderate redshift with the decrease of hole separation. A detailed dependence of peak position on the separation is presented in the inset of Figure 4b. Generally, for the parallel nanorods (or its complement) with the small rod radius, the approach of nanorods will lead to a blueshift of resonance mode,11 due to the increased repulsive 24623

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Figure 5. Measured (the red circles) and calculated (the blue line) transmission spectra of asymmetrical hole dimers. Here, the hole separation is s = 100 nm, the length of hole dimer is set as (a) l1 = 300 nm and l2 = 400 nm and (b) l1 = 300 nm and l2 = 500 nm. The short and long arrows indicate the peak positions of mono- hole array with l = 300 nm and l = 400 nm (or 500 nm), respectively.

Figure 6. Simulated electric-field patterns (a and c) and current distributions (b and d) of the asymmetrical hole dimer, for the peak wavelength (a and b) 1060 nm and (c and d) 1440 nm. Here, the dimer sizes are set as l1 = 300 nm and l2 = 400 nm and the hole separation is s = 100 nm.

interaction. Here, the use of larger hole width (100 nm) will make a significant difference. Still considering the wide nanorod dimer, the increased repulsive interaction due to the approach of nanorods will lead to the departure of charges on the two upper (or lower) ends of nanorods. This departure effect can reduce the coupling energy moderately. Correspondingly, when the two rectangular holes become very close to each other, the current and charges in the metallic interlayer (between the two holes) will be partly canceled (see Figure 3c). Therefore, the current on the two upper (or lower) ends of holes as well as the fields in the two rectangular holes (see Figure 3b) seem to be departed from each other. This may be responsible for the anomalous redshift mentioned above. C. Asymmetrical Hole Dimers. The asymmetrical hole dimer studied here consists of two parallel rectangular-holes (in a unit cell) with different hole length. Figure 5a shows the measured (the red circles) and simulated (the blue line) transmission spectra of the asymmetrical dimers, where the dimer sizes are l1 = 300 nm and l2 = 400 nm, and the separation is s = 100 nm. It can be seen that the experimental result is in accordance with the simulation. After comparison to the symmetrical dimer with one peak, here two transmission peaks around 1060 and 1440 nm can be observed at the long wavelength. Moreover, in contrast to the monohole array with l = 300 nm (peak 1135 nm) and l = 400 nm (peak 1350 nm), these two peaks show obvious blueshift and redshift, respectively. To identify the origin of two transmission peaks, we have simulated the electric -field pattern and current distribution for the asymmetric dimer. Figure 6, panels a and c, plotted, respectively, the electric-field profiles (Ex at half thickness of the silver film) corresponding to the peak wavelength 1060 and 1440 nm. One can see that at 1060 nm the field is strongly concentrated in the small hole of dimer and the field in the large hole is weak (the fields in the two holes are parallel and their transmission will interfere constructively). Nonetheless, at 1440 nm, the result is just contrary: the large hole is strongly excited with the small one being weak (the fields in the two holes are antiparallel and their

transmission will interfere destructively). The corresponding current distributions for the two peaks are shown in Figure 6, panels b and d, respectively, where a strong (weak) current circulating around the small (large) or large (small) hole is available. These results suggest that there are two dominant channels for the transmission and each channel corresponds to a transmission peak. That also means the photons will “choose” one of the dimer holes as the main transmission channel when passing through the metal film. To understand these effects, we resort to the plasmon coupling of the asymmetrical nanorod dimer. In an asymmetric nanorod dimer (with the electric field along the rod axis), the plasmon coupling causes two plasmon modes:12 one is the attractive lowenergy mode with the fields mainly concentrated in the long nanorod, and the other is the repulsive high-energy mode with the fields largely focused in the short one, instead. Compared with the resonance of individual nanorods, the former shows a redshift and the latter a blueshift. Note that when the nanorod dimer is symmetric, one plasmon mode (here, the repulsive one) survives and the other mode will not be optically active due to the structural symmetry.11 Correspondingly, for the present hole dimer, the strong coupling of two closely spaced rectangular holes can also induce two hole-dimer modes. At the peak wavelength 1440 nm (the low-energy mode), the larger hole is strongly excited and its current drives a weak one of opposite direction circulating around the small hole (see Figure 6d; note that the small hole is mainly driven by the larger one but not by the incident field). The oppositely circulating currents around the upper (or lower) hole ends will behave as two anti- parallel magnetic dipoles, which are attractive and lower the energy of coupling mode. Nonetheless, for the peak wavelength 1060 nm (the high-energy mode), a strong current near the small hole is excited and a weak one of the same direction is induced around the large hole (see Figure 6b; note that, here, the large hole is mainly driven by the small one, but the motion of free electrons around the large hole cannot keep up with that of small hole because of the lower eigen-frequency). As a consequence, the 24624

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Figure 7. (a) Anticrossing-like coupling behavior of asymmetrical hole dimer, where one hole is fixed as l1 = 350 nm and the other hole length is changed from 200 to 500 nm. Here, the squares and triangles represent the peak modes of monohole array with the hole lengths l1 and l2, respectively, and the circles represent the two coupled modes of the hole dimers. (b) Transmission spectra of the asymmetrical dimer with the varying hole separations s = 150 (the red circles), 75 (the green triangles), and 15 nm (the blue squares). The dimer sizes are set as l1 = 300 nm and l2 = 400 nm. The inset shows the positions of the two dominant peaks as a function of hole separation.

parallel magnetic dipoles are resulted, which are repulsive and increase the coupling energy. For an array of asymmetrical dimers, the two hole-dimer modes will couple, respectively, to the film surface waves, thus giving rise to two transmission peaks as observed in the spectrum. Figure 5b also presents the measured (the red circles) and simulated (the blue line) transmission spectra of another array of asymmetrical dimers, where the dimer sizes are l1 = 300 nm and l2 = 500 nm. We can see by comparing to Figure 5a that, with the increase of dimer asymmetry, one transmission peak redshifts slightly from 1060 to 1080 nm and the other peak redshifts significantly from 1440 to 1690 nm. We note that, by continually tune the length of an asymmetrical nanorod dimer, an anticrossing behavior in the plasmon coupling energy diagrams can be obtained.29,30 To explore this effect in the hole dimer, we kept the length of one rectangular hole as l1 = 350 nm and change the length of another hole from l2 = 200 to 500 nm (the hole separation is fixed as s = 100 nm). The results extracted from the numerical simulations are presented in Figure 7a, where the squares and triangles indicate, respectively, the resonant modes of monohole array with the hole length l1 and l2, and the circles represent the coupled mode of the hole dimers. An anticrossinglike coupling behavior can be seen clearly. Nonetheless, when the lengths of two rectangular holes approach each other, the attractive low-energy mode will be very weak (the efficiency of the longest transmission peak is small). When the hole dimer becomes completely symmetrical, the low-energy mode will disappear in the diagram. This character in anticrossing makes a difference from the case of polariton excitation.8

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Figure 8. (a) Simulated transmission spectra of the asymmetrical hole dimers with the perpendicular arrangement. Here, the dimer sizes are l1 = 300 nm and l2 = 400 nm, the hole separation is 100 nm, and the open and solid circles correspond to the x and y polarization, respectively. The electric-field distributions for the peak wavelength (b) 1140 (x polarization) and (c) 1360 nm (y polarization).

In addition, we also simulated the transmission spectra of the asymmetrical dimer with the varying hole separation. Here, the structure sizes are set as l1 = 300 nm and l2 = 400 nm and s = 150, 75, and 15 nm. The results are shown in Figure 7b. We found, with the decrease of hole separation, the high-energy mode shifts to the longer wavelength; and the low-energy mode is almost immovable at first and then redshifts when the hole separation is down to about 45 nm (twice the skin depth). A detailed dependence of the two resonance modes on the hole separation is mapped in the inset of Figure 7b. Here, the redshift of the highenergy mode shares the similar mechanism as that of symmetrical hole dimer, where the current and charges in the metal interlayer (between the two holes) are partly canceled because the upper (or lower) currents are of the same circulating direction (see Figure 6b). However, the evolution of the low-energy mode may correlate with a competition between the attractive and additional repulsive interactions. The former originates from the oppositely circulating currents or antiparallel magnetic dipoles, and the latter is due to the crowd of charges of the same sign in the metallic interlayer (see Figure 6d). When the hole separation is extremely small, the latter effect will be greatly suppressed, as the import of charges into the narrow metallic interlayer is limited. This may account for the redshift of the low-energy mode at the small hole separations. D. Perpendicular Hole Dimers. The rectangular hole dimers can also be employed to manipulate the light polarization in certain wavelength regions. For the purpose, the inset of Figure 8a gives a design of dimer configuration, where two rectangular holes with the lengths l1 = 300 nm and l2 = 400 nm are arranged perpendicular to each other. The transmission spectra for the x (the open circles) and y (the solid circles) polarization are simulated respectively, with the results shown in Figure 8a. One can see that there is an x-polarized transmission peak around the wavelength 1140 nm and a y-polarized peak around 1360 nm. The corresponding field distributions for the two transmission peaks are plotted in Figure 8, panels b and c, 24625

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The Journal of Physical Chemistry C showing that the small and large holes can be excited respectively (the hole coupling is weak in this case). The results also indicate that, with the unpolarized incident light, a dominant x polarization can be obtained near 1140 nm and y polarization obtained around 1360 nm. Note that the weak y-polarized transmission at 1140 nm can be suppressed by increasing the y period to 750 nm, according to the eq 1. It is worth noticing that the transmission peak with the desired working wavelength and polarization can be controlled freely by varying the structure parameters, such as the lattice period and hole sizes. This provides the opportunity for manipulating the light polarization at the desired wavelengths.

IV. CONCLUSION In summary, a metal surface perforated with rectangular hole dimers have been studied, which presents dual transmission channels in a unit cell. The symmetrical hole dimer owns a single transmission peak at the long wavelength, whereas the asymmetric one exhibits double peaks with the fields concentrated in different transmission channels. We found that a strong plasmon coupling effect exists in the rectangular nanohole dimer due to the excitation of surrounding currents. The resulted low-energy and high-energy dimer modes will hybridize, respectively, with the film surface waves, thus generating the double transmission peaks. Moreover, by tuning the sizes (or configuration) of rectangular hole dimers, an anticrossing-like coupling behavior (or polarization filtering effect) has been revealed. Interestingly, our results also suggest that the underlying plasmonic interactions in the hole dimer and that in its complement (i.e., the particle dimer) can be related closely to each other. This may give a supplement to the Babinet principle and thus provide convenience for studying the interactions in various plasmonic hole dimers or trimers.

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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]; [email protected].

’ ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (Grant Nos. 10804051 and 10874079), by the State Key Program for Basic Research of China (Grant No. 2010CB630703). ’ REFERENCES (1) Ebbesen, T. W.; Lezec, H. J.; Ghaemi, H. F.; Thio, T.; Wolff, P. A. Nature 1998, 391, 667. (2) Ozbay, E. Science 2006, 311, 189. (3) Liu, Z. W.; Wei, Q. H.; Zhang, X. Nano Lett. 2005, 5, 957. (4) Granqvist, C. G. Solar Energy Mater. Solar Cells 2007, 91, 1529. (5) Mikhailov, V.; Wurtz, G. A.; Elliott, J.; Bayvel, P.; Zayats, A. V. Phys. Rev. Lett. 2007, 99, 083901. (6) Shalaev, V. M. Nat. Photon. 2007, 1, 41. (7) Mokkapati, S.; Beck, F. J.; Polman, A.; Catchpole, K. R. Appl. Phys. Lett. 2009, 95, 053115. (8) Huang, C. P.; Yin, X. G.; Wang, Q. J.; Huang, H.; Zhu, Y. Y. Phys. Rev. Lett. 2010, 104, 016402. (9) Su, K. H.; Wei, Q. H.; Zhang, X.; Mock, J. J.; Smith, D. R.; Schultz, S. Nano Lett. 2003, 3, 1087. (10) Kravets, V. G.; Schedin, F.; Grigorenko, A. N. Phys. Rev. Lett. 2008, 101, 087403. (11) Funston, A. M.; Novo, C.; Davis, T. J.; Mulvaney, P. Nano Lett. 2009, 9, 1651. 24626

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