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dielectric multilayer films perforated with periodic subwavelength slits
Optics Communications 284 (2011) 471–475
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Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Optical transmission through metal/dielectric multilayer films perforated with periodic subwavelength slits Dong Xiang a,b, Ling-Ling Wang a,⁎, Xiang Zhai a, Liu Wang a, An-Lian Pan a a b
Key Laboratory for Micro-Nano Optoelectronic Devices of Ministry of Education, School of Physics and Microelectronics Science, Hunan University, Changsha 410082, China School of Nuclear Science and Technology, University of South China, Hengyang 421001, China
a r t i c l e
i n f o
Article history: Received 21 December 2009 Received in revised form 5 August 2010 Accepted 10 August 2010 Keywords: Subwavelength slits Multilayer films Extraordinary optical transmission Surface plasmon polaritons
a b s t r a c t The transmission of p-polarized plane wave through Ag/SiO2 multilayer films perforated with periodic subwavelength air slits is investigated by using the finite-difference time-domain (FDTD) method. The results show that the optical transmission property is mediated by the interference among the propagating coupled-SPP modes along the lateral direction inside the SiO2 layers and the conditions of Fabry–Pérot–like resonance along the longitudinal direction together. When some geometric parameters are suitably initialized, the high transmission peaks can split into more peaks as the functional layer (metal/dielectric/metal sandwich stack) number increases, and the wavelength of the same-order transmission peak exhibits a red shift as the grating period increases. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Since the phenomenon of extraordinary optical transmission (EOT) through a thick metal film perforated with a two-dimensional (2D) array of subwavelength holes was first observed in 1998 [1], much effort has been devoted to the EOT through metallic gratings with various subwavelength microstructures, such as one-dimensional (1D) periodic arrays of slits [2–9] and 2D periodic arrays of holes with different shapes [10–16]. To understand the physical origins of the EOT phenomena, many physical models have been established, such as the surface plasmon polariton (SPP) resonant modes model [10,12,17], the Fabry–Pérot–like waveguided-mode resonance model [5,6], the diffracted evanescent wave model [13,16], and so forth. However, most of the reported works in literature focus on the EOT phenomena in the single-layer metallic grating structures so far. Recently, some researchers begin to pay attention to the EOT through multilayer metallic structures with periodic slit or hole arrays. For examples, Ye et al. [18,19] reported experimental results on enhanced light transmission through dual-layer perforated metal films separated by a dielectric layer. They found that enhanced transmission is further increased when two perforated metal films are spaced by a layer of dielectric, and the maximum transmission of the multilayer structure depends on the distance between two metal films. Cheng et al. [20,21] and He et al. [22] numerically investigated light transmission through dual-layer metal films separated by a air layer and perforated with 1D periodic arrays of slits and 2D periodic arrays of
⁎ Corresponding author. E-mail address: [email protected] (L.-L. Wang). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.08.023
holes, respectively. Their results showed that the transmission spectra can be tailored by changing the longitudinal interval and the lateral displacements between the two single-layer metallic gratings. Furthermore, Tang et al. [23] studied optical transmission through metal/ dielectric multilayer films with 2D periodic arrays of subwavelength holes. Their designed multilayer film is constructed by repeating a building block, which contains two layers: one is a perforated metal film and the other is a dielectric film. They demonstrated that the enhancement of optical transmission originates not only from SPP modes but also from the coupling of SPPs in multilayer films, and the coupling of SPPs leads to a blueshift of the transmission modes when the repeating number of building blocks increases. In addition, some researchers [24,25] investigated fishnet structured metamaterials composed of multiple layers of perforated metal/dielectric stacks for achieving optical negative refraction transmission. A metal/dielectric/ metal sandwich stack is being viewed as a functional layer. The stacking up multiple fishnet functional layers leads to a strong magnetoinductive coupling between neighbouring functional layers. In fact, the physics of the optical transmission through 1D arrays of slits is very different from the physics of the optical transmission through 2D arrays of holes [7,12]. Here, we present a metal/dielectric multilayer film perforated with periodic subwavelength slits. The number of metal layers is one more than the number of dielectric layers in a multilayer film and each dielectric layer is sandwiched between two identical metal layers. Similar to the definition of the functional layer in Refs. [24,25], the multilayer structure is regarded as N functional layers. We explore in detail the transmission behavior of the light passing through the multilayer films as we vary the functional layer number N and the grating period in the visible and near infrared region by using the finitedifference time-domain (FDTD) method. It is found that the optical
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transmission can be associated with the Fabry–Pérot–like behavior along the longitudinal direction and the interference among the counter-propagating coupled SPPs along lateral direction inside SiO2 layers. Our results show that the high transmission peaks can split into more peaks as the functional layer number N increases, and these transmission peaks move to larger wavelengths as the grating period increases. The transmission characteristics indicate that we have the ability to open, split, suppress and shift any spectral window by initializing some parameters of metal/dielectric multilayer films. We believe the multilayer structures are promising photonic elements having potential applications in future nanophotonic systems such as frequency selectors or filters. 2. Simulated model and method Fig. 1 shows a schematic diagram for a metal/dielectric multilayer film perforated with periodic subwavelength slits under study. The multilayer film has N functional layers, namely N identical dielectric layers and N + 1 identical metal layers. The thicknesses of the metal and dielectric layers are hm and hd, respectively. Both metal layers and dielectric layers are in fact air slit arrays with the same grating period p and the same width of the slits a. Here, the metal is chosen to be silver (Ag) because of its typical noble metal properties, and the dielectric is chosen to be silicon oxide (SiO2). We will only discuss the results for a fixed slit width a = 50 nm, although the transmission resonances can also depend on the slit width a. The 2D-FDTD method [26,27] is employed to simulate and calculate the transmission of optical waves through multilayer films. In our simulation, the spatial mesh steps are set Δx = Δz = 5 nm and the time step is set Δt = Δx/2c (c is the velocity of light in the vacuum). The calculated region is truncated by using perfectly matched layer (PML) absorbing boundary conditions on the top and bottom boundaries, and the left and right boundaries are treated by periodic boundary conditions due to the periodicity of the structure. Only normally incident p-polarized plane waves are considered here, implying that the magnetic field is parallel to the slits (along the y direction). The frequency-dependent permittivity of Ag εm (which is complex) is described using the tables reported in Ref. [28], and the permittivity of SiO2 is taken as εd = 2.16.
calculated transmission spectra of four kinds of Ag/SiO2 multilayer films with different N = 1, 2, 3 and 4, respectively. By comparison of Fig. 2(a)–(d), we find some main features. First, the transmission peaks can be grouped into two types. Type-1 is the transmission peaks at A1, B1, C1 and D1 shown in Fig. 2. Type-2 includes all of other transmission peaks (A2, B2–B3, C2–C4 and D2–D5 shown in Fig. 2). The two types of peaks have different features. For the transmission peaks of Type-1, in all cases (N = 1, 2, 3, and 4), there is a relatively fixed transmission feature at 490 nm. For the transmission peaks of Type-2, they can split into more peaks as the functional layer number N is increased by 1. For instance, the high transmission peak at 680 nm [as shown in Fig. 2(a)] for N = 1 splits from one single peak into two peaks located at different sides of 680 nm as N is increased by 1 (N = 2). One is at 630 nm, and the other is at 730 nm [as shown in Fig. 2(b)]. These transmission peaks at 630 nm and 730 nm for N = 2 split from two peaks into three peaks [610 nm, 690 nm and 750 nm as shown in Fig. 2(c)] as N is increased by 1 (N = 3). For N = 4, four transmission peaks are observed at wavelengths of 600 nm, 650 nm, 720 nm and 760 nm [as shown in Figure 2(d)], respectively. Moreover, the position (680 nm) of the transmission maximum for N = 1 becomes the position of the transmission minimum for N = 2, and the position (690 nm) of the transmission maximum for N = 3 becomes the position of the transmission minimum for N = 4. Additionally, whenever N = 1, 2, 3 or 4, the intensities of the transmission at certain wavelength range are close to zeroes. Specifically, the suppressed transmission is over a very broad wavelength range from 790 nm to 1600 nm (is not displayed from 1000 nm to 1600 nm). Finally, the intensity of transmission peak decreases as the functional layer number N increases. In order to understand the physical mechanism behind the transmission phenomena, we calculate spatial distributions of the
3. Results and discussion We first initialize hm = 100 nm, hd = 100 nm and p = 400 nm, and study the effect of different functional layer number N on transmission spectrum of Ag/SiO2 multilayer films. Fig. 2 displays the
x
y
incident light
air slit
z
hM
Ag
hD
SiO2
hM
Ag
hD
2
hM
SiO2 Ag
hD
SiO2
3
hM
Ag
p
a
1
N=3
Fig. 1. (Color online) a schematic diagram for a Ag/SiO2 multilayer film with periodic subwavelength slits.
Fig. 2. The calculated transmission spectra of the Ag/SiO2 multilayer films with different numbers of functional layers (a) N = 1, (b) N = 2, (c) N = 3 and (d) N = 4, respectively. The other parameters are hm = 100 nm, hd = 100 nm and p = 400 nm, respectively.
D. Xiang et al. / Optics Communications 284 (2011) 471–475
z (nm)
0 300 600 900 (A1) 0 300 600 900 (B1) 0 300 600 900 (C1) 0 300 600 900
N=2 z (nm)
magnetic field |Hy| at some of the wavelengths of transmission maxima and minima for N = 1, 2, 3 and 4, respectively. Fig. 3(A1)–(A2), (B1)– (B3), (C1)–(C4) and (D1)–(D5) show the calculated field distributions of |Hy| at A1–A2, B1–B3, C1–C4 and D1–D5 as shown in Fig. 2, respectively. From the field distribution of |Hy| in Fig. 3, we can see standing wave patterns inside each slit in these Ag/SiO2 multilayer films formed along the longitudinal direction. So the optical transmission can also be associated with Fabry–Pérot–like resonances. Similar to the Fabry–Pérot–like guided-mode resonance of coupled-SPP modes inside the slit in single-layer metallic grating, the transmission peaks in the Ag/SiO2 multilayer films can be indexed with orders. For instance, the transmission peaks at 490 nm and 680 nm for N = 1 are attributed to the first- and zeroth-order Fabry–Pérot–like resonant modes, respectively [as shown in Fig. 3 (A1) and (A2)]. The transmission peaks at 490 nm, 620 nm and 730 nm for N = 2 attribute to the second-, first- and zeroth-order Fabry–Pérot–like resonant modes, respectively [as shown in Fig. 3 (B1)–(B3)], the transmission peaks at 490 nm, 610 nm, 690 nm and 750 nm for N = 3 attribute to the third-, second-, first- and zerothorder Fabry–Pérot–like resonant modes, respectively [as shown in Fig. 3(C1)–(C4)], and so forth. On the contrary, as shown in Figs. 4 (a) and 3(d), the transmission minima (which has been labeled by E, F, G, and H respectively as shown in Fig. 2) for N = 1, 2, 3 or 4 are associated with maxima of the reflections and destructive conditions of Fabry–Pérot–like resonance. Moreover, Fig. 3 shows that the features of the distributions of |Hy| between the Type-1 and Type-2 transmission peaks are different. For the Type-1 transmission peak, the magnetic field is very weak in all SiO2 layers, and it is mostly centralized inside every slit of Ag layers. In contrast, for the Type-2 transmission peak, the magnetic field is relatively strong inside SiO2 layers, and the magnetic-field distribution shows the standing-wave patterns along lateral direction inside SiO2 layers, which indicates there are electromagnetic waves propagating along + x and−x direction inside SiO2 layers.
473
N=3
N=3
N=4 2
0 300 600 900
1
(a)
(c)
(b)
(d)
0
-200 0 200 -200 0 200 -200 0 200 -200 0 200
x (nm) Fig. 4. (Color online) The calculated field distributions of |Hy| at the wavelengths λ of transmission minima for the numbers of functional layers N = 1, 2, 3 and 4, respectively. (a), (b), (c) and (d) are the field distributions of |Hy| at E, F, G and H shown in Fig. 2, respectively.
We believe that any slit of Ag layers of a multilayer film can be considered as a metal–dielectric–metal waveguide. In the metallic slit, the SPPs of each metal–dielectric surface will be coupled and propagate in the form of a coupled-SPP (waveguide) mode for p-polarized case. The complex effective wave vector βs in the z direction inside the slit can be approximately calculated by the following [29,30]: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1−exp a β2s −ε1 k20 β2s −εm k20 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi = εm β2s −ε1 k20 1 + exp a β2s −ε1 k20 ε1
ð1Þ
where ε1 is the permittivity of the dielectric (air), k0 = 2π/λ is the wave vector of light in vacuum, and λ is the wavelength of the incident light in vacuum, respectively. The calculated results show that the effective refractive index ns = βs/k0 is dependent on the wavelength of the incident light λ, the permittivity of the dielectric ε1 and the slit width a; when ε1 and a are fixed, ns has a decreasing
4 2
(A2)
N=1
0 4 2
(B2)
(B3)
N=2
0 4 2
(C2)
(C3)
(C4)
N=3
0 4 2
(D1)
(D2)
(D3)
(D4)
(D5)
N=4
0
-200 0 200 -200 0 200 -200 0 200 -200 0 200 -200 0 200
x (nm) Fig. 3. (Color online) the calculated field distributions of |Hy| at the wavelengths λ of transmission maxima for the numbers of functional layers N = 1, 2, 3 and 4, respectively. (A1)– (A2), (B1)–(B3), (C1)–(C4) and (D1)–(D5) are the field distributions of |Hy| at A1–A2, B1–B3, C1–C4 and D1–D5 shown in Fig. 2, respectively.
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tendency as λ increases; and when ε1 and λ are fixed, ns also has a decreasing tendency as a increases [29]. At the same time, a functional layer can also be considered as a metal–dielectric–metal waveguide. If βs, ε1 and a in Eq. (1) are replaced by βd (the complex effective wave vector in the x direction inside the SiO2 layer sandwiched by two Ag layers), εd and hd, respectively, then βd and n′d (=βd/k0, the effective refractive index inside the SiO2 layer) can also be approximately calculated by Eq. (1). In fact, the two Ag–air–Ag waveguides of any functional layer are separated by a SiO2 layer. The optical transmission phenomena observed in the multilayer films can be understood by the interaction of evanescent waves from the subwavelength slits of every Ag layer [21]. The exit of every slit in the front Ag layer can be regarded as a source of the evanescent field. The emitted evanescent waves from those sources propagate not only along the z direction but also along the x direction. In the two Ag–SiO2 surfaces of a function layer, the SPP modes can also be supported, respectively. When hd is very narrow, the two SPP modes will couple to form a coupled-SPP mode. The coupled-SPP mode can propagate along + x or −x direction inside the SiO2 layer and interfere with each other. Based on the coupling effect, the electromagnetic radiation from the front Ag layer can tunnel into the rear Ag layer through the SiO2 layer sandwiched by the two Ag layers. According to interference principle, the strongest coupling effect is approximately determined by the following equation: Reðn′d Þ⋅k0 ⋅p = m⋅2π
Fig. 5. (Color online) the calculated transmission spectra of the Ag/SiO2 multilayer films with different grating period p for the numbers of functional layers (a) N = 1 and (b) N = 2, respectively. The other parameters are hm = 100 nm and hd = 100 nm, respectively.
ð2Þ
where m is a relative integer. For the case above, m in Eq. (2) can take m = 1 only. Therefore, the high transmissions through the Ag/SiO2 multilayer films are mediated by the coupling effect between the two Ag layers of a functional layer and the conditions of Fabry–Pérot–like resonance along the z direction inside the slits together. For the Type-1 transmission peak, the magnetic field is very weak in all SiO2 layers while relatively strong in every slit of Ag layers, and the intensity of the transmission peak exponentially decreases as the functional layer number N increases (as shown in Fig. 2). These results indicate that the emitted evanescent wave from front Ag layers propagates along the z direction through the slits of SiO2 layers into rear Ag layers, and the coupled-SPP transmission process (βshm) obeys the Fabry–Pérot–like resonance condition. It can explain why there is relatively fixed transmission peak at 490 nm in all cases (N = 1, 2, 3, and 4). On the contrary, for the Type-2 transmission peak, the magnetic field distribution shows the coupling effect between the two Ag layers of a functional layer is very strong, and these wavelengths of the Type-2 transmission modes are in a range from 570 nm to 790 nm, which is in good agreement with Eqs. (1) and (2). At the same time, the Type-2 transmission modes are also mediated by Fabry–Pérot–like resonance condition along the z direction. Consequently, as shown in Fig. 3(A2) and Fig. 4(a), the transmission peak at 680 nm for N = 1 is the zerothorder Fabry–Pérot–like resonant peak, whereas the transmission minimum corresponding to destructive conditions of Fabry–Pérot–like resonance appears at nearly the same position for N = 2. Analogously, as shown in Fig. 3(C3) and Fig. 4(d), the transmission peak at 690 nm for N = 3 is the first-order Fabry–Pérot–like resonant peak, whereas destructive conditions of Fabry–Pérot–like resonance also appear at the almost same position for N = 4. Next, we investigate the situation when the grating period p is changed. We fix hm = 100 nm, hd = 100 nm all the same, and investigate the transmission spectra of the Ag/SiO2 multilayer films with different grating period p = 500 nm, 600 nm and 700 nm as shown in Fig. 5, respectively. It is obvious that the transmission peaks of these Type-2 transmission modes move to larger wavelengths as p increases, whereas their intensities decrease gradually. This result can also be explained in terms of Eqs. (1) and (2). According to Eq. (1), when εd and hd is fixed, n′d changes little as λ increases in the longer wavelength region. So the relation in Eq. (2) requires that λ also increases as p increases. At the
same time, transmission behavior in the shorter wavelength region becomes complex due to the coupling effect of coupled SPPs modes between the two Ag layers of a functional layer. In the shorter wavelength region, n′d has a relatively notable decrease as λ increases, and when p N 500 nm, m in Eq. (2) can take m = 2 or more, which can lead to the appearance of more peaks. Moreover, from Fig. 5(a) we can also find that a distinct SPP resonant peak appears at 540 nm when N = 1 and p = 500 nm. It is well known that the wavelength of transmission peak λspp for the 1D metallic grating structure due to SPP resonant mode in the case of normal incidence can be given by the following: rffiffiffiffiffiffiffiffiffiffiffiffiffi p εm ; λspp = Re n
1 + εm
qffiffiffiffiffiffiffiffiffiffiffiffiffi εm is [6] where n is a integer (for this case, n = 1) and Re 1 + εm slightly greater than 1. Finally, we calculate the transmission spectra of the Ag/SiO2 multilayer films at different hd from 50 nm to 200 nm, with hm = 100 nm and p = 400 nm for N = 1, 2 and 3, respectively. Fig. 6 only displays the calculated transmission spectra of these films at hd = 50 nm and 150 nm. By comparison of Figs. 2 and 6, we find that the Type-2 transmission modes at hd = 50 nm and 150 nm exhibit the redshift and blueshift, respectively. We can also explain the phenomena in terms of Eqs. (1) and (2). According to Eq. (1), when εd is fixed, in the wavelength region, n′d does not decrease much as λ increases, but n′d has a relatively notable increase as hd decreases. Consequently, λ will increase as hd decrease in terms of Eq. (2). As shown in Fig. 6, the main features of the transmission spectra at hd = 50 nm resemble those at hd = 100 nm, while those at hd = 150 nm do not. Therefore, the significant properties of the transmission spectra as shown in Fig. 2 can be gained only if both hm and hd are suitably initialized. 4. Summary In conclusion, we investigated the transmission characteristics of the electromagnetic radiation in visible and near infrared frequencies passing through Ag/SiO2 multilayer films perforated with periodic subwavelength slits by using the FDTD method. In the nanostructured Ag/SiO2 multilayer film, where each Ag layer and SiO2 layer has same
D. Xiang et al. / Optics Communications 284 (2011) 471–475
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National Natural Science Foundation of China (Grant No. 11074069, 90606001, 10874042, 90923014, 10974050), Natural Science Foundation of Hunan Province, China (Grant No. 09JJ1009), the Science Research Program of Educational Department of Hunan Province, China (Grant No. 09C851), the China Postdoctoral Science Foundation funded project (Grant No. 20100471310), the Scientific Project of Jiangxi Education Departments of China (Grant No. GJJ10263), and Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province.
References
Fig. 6. (Color online) the calculated transmission spectra of the Ag/SiO2 multilayer films with the different functional layer number N for the thicknesses of the SiO2 layers (a) hd = 50 nm and (b) hd = 150 nm, respectively. The other parameters are hm = 100 nm, and p = 400 nm, respectively.
periodic arrays of subwavelength air slits. If geometrical parameters of multilayer films are suitably selected, the high transmission peaks somewhere can split into more peaks and the original positions of the transmission maxima almost become the positions of transmission minima when the functional layer number N is increased by 1. The wavelength of the same-order transmission peak exhibits a redshift as the grating period p increases. We consider that the optical transmission property is mediated by the interference among the propagating coupled-SPP modes along the lateral direction inside the SiO2 layers and the conditions of Fabry–Pérot–like resonance along the longitudinal direction together. Our results indicate that the Ag/SiO2 multilayer films may have potential applications in future nanophtonic systems where spectral control is desired. Acknowledgments This work was supported by the “973” National Key Basic Research Program of China (Grant No. 2007CB310502-2, 2007CB310403), the
[1] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Nature (London) 391 (1998) 667. [2] J.A. Porto, F.J. Garcia-Vidal, J.B. Pendry, Phys. Rev. Lett. 83 (1999) 2845. [3] K.G. Lee, Q.H. Park, Phys. Rev. Lett. 95 (2005) 103902. [4] Y. Xie, A.R. Zakharian, J.V. Moloney, M. Mansuripur, Opt. Express 13 (2005) 4485. [5] S. Astilean, P. Lalanne, M. Palamaru, Opt. Commun. 175 (2000) 265. [6] X. Jiao, P. Wang, L. Tang, Y. Lu, Q. Li, D. Zhang, P. Yao, H. Ming, J. Xie, Appl. Phys. B 80 (2005) 301. [7] Q. Cao, P. Lalanne, Phys. Rev. Lett. 88 (2002) 057403. [8] D. Pacifici, H.J. Lezec, Harry A. Atwater, J. Weiner, Phys. Rev. B 77 (2008) 115411. [9] Hu. Bin, Gu. Ben-Yuan, Bi-Zhen Dong, Yan Zhang, Opt. Commun. 281 (2008) 6120. [10] H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, H.J. Lezec, Phys. Rev. B 58 (1998) 6779. [11] K.J.K. Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, L. Kuipers, Phys. Rev. Lett. 92 (2004) 183901. [12] W.L. Barnes, W.A. Murray, J. Dintinger, E. Devaux, T.W. Ebbesen, Phys. Rev. Lett. 92 (2004) 107401. [13] Henri J. Lezec, Tineke Thio, Opt. Express 12 (2004) 3629. [14] Z. Ruan, M. Qiu, Phys. Rev. Lett. 96 (2006) 233901. [15] A. Mary, S.G. Rodrigo, L. Martín-Moreno, F.J. García-Vidal, Phys. Rev. B 76 (2007) 195414. [16] Zhiyuan Fan, Li. Zhan, Hu. Xiao, Yuxing Xia, Opt. Commun. 281 (2008) 5467. [17] H. Liu, P. Lalanne, Nature(London) 452 (2008) 728. [18] Y.H. Ye, J.Y. Zhang, Opt. Lett. 30 (2005) 1521. [19] Y.H. Ye, Z.B. Wang, D.S. Yan, J.Y. Zhang, Appl. Phys. Lett. 89 (2006) 221108. [20] C. Cheng, J. Chen, Q.Y. Wu, F.F. Ren, J. Xu, Y.X. Fan, H.T. Wang, Appl. Phys. Lett. 91 (2007) 111111. [21] C. Cheng, J. Chen, D.J. Shi, Q.Y. Wu, F.F. Ren, J. Xu, Y.X. Fan, J.P. Ding, H.T. Wang, Phys. Rev. B 78 (2008) 075406. [22] M.D. He, L.L. Wang, J.Q. Liu, X. Zhai, Q. Wan, X.S. Chen, B.S. Zou, Appl. Phys. Lett. 93 (2008) 221909. [23] Z.H. Tang, R.W. Peng, Z. Wang, X. Wu, Y.J. Bao, Q.J. Wang, Z.J. Zhang, W.H. Sun, M. Wang, Phys. Rev. B 76 (2007) 195405. [24] Jason Valentine, Shuang Zhang, Thomas Zentgraf, Erick Ulin-Avila, Dentcho A. Genov, Guy Bartal, Xiang Zhang, Nature(London) 455 (2008) 376. [25] Zahyun Ku, Jingyu Zhang, S.R.J. Brueck, Opt. Express 17 (2009) 6782. [26] A. Taflove, S.C. Hagness, Computational Electrodynamics. The Finite-Difference Time-Domain Method, 2nd ed., Artech House, Boston, 2000. [27] Stephen K. Gray, Teobald Kupka, Phys. Rev. B 68 (2003) 045415. [28] E.D. Palik, Handbook of Optical Constants and Solids, Academic, New York, 1985. [29] J.Q. Liu, L.L. Wang, M.D. He, W.Q. Huang, D.Y. Wang, B.S. Zou, S.C. Wen, Opt. Express 16 (2008) 4888. [30] E.N. Economou, Phys. Rev. 182 (1969) 539.
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Optical transmission through metal/dielectric multilayer films perforated with periodic subwavelength slits Dong Xiang a,b, Ling-Ling Wang a,⁎, Xiang Zhai a, Liu Wang a, An-Lian Pan a a b
Key Laboratory for Micro-Nano Optoelectronic Devices of Ministry of Education, School of Physics and Microelectronics Science, Hunan University, Changsha 410082, China School of Nuclear Science and Technology, University of South China, Hengyang 421001, China
a r t i c l e
i n f o
Article history: Received 21 December 2009 Received in revised form 5 August 2010 Accepted 10 August 2010 Keywords: Subwavelength slits Multilayer films Extraordinary optical transmission Surface plasmon polaritons
a b s t r a c t The transmission of p-polarized plane wave through Ag/SiO2 multilayer films perforated with periodic subwavelength air slits is investigated by using the finite-difference time-domain (FDTD) method. The results show that the optical transmission property is mediated by the interference among the propagating coupled-SPP modes along the lateral direction inside the SiO2 layers and the conditions of Fabry–Pérot–like resonance along the longitudinal direction together. When some geometric parameters are suitably initialized, the high transmission peaks can split into more peaks as the functional layer (metal/dielectric/metal sandwich stack) number increases, and the wavelength of the same-order transmission peak exhibits a red shift as the grating period increases. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Since the phenomenon of extraordinary optical transmission (EOT) through a thick metal film perforated with a two-dimensional (2D) array of subwavelength holes was first observed in 1998 [1], much effort has been devoted to the EOT through metallic gratings with various subwavelength microstructures, such as one-dimensional (1D) periodic arrays of slits [2–9] and 2D periodic arrays of holes with different shapes [10–16]. To understand the physical origins of the EOT phenomena, many physical models have been established, such as the surface plasmon polariton (SPP) resonant modes model [10,12,17], the Fabry–Pérot–like waveguided-mode resonance model [5,6], the diffracted evanescent wave model [13,16], and so forth. However, most of the reported works in literature focus on the EOT phenomena in the single-layer metallic grating structures so far. Recently, some researchers begin to pay attention to the EOT through multilayer metallic structures with periodic slit or hole arrays. For examples, Ye et al. [18,19] reported experimental results on enhanced light transmission through dual-layer perforated metal films separated by a dielectric layer. They found that enhanced transmission is further increased when two perforated metal films are spaced by a layer of dielectric, and the maximum transmission of the multilayer structure depends on the distance between two metal films. Cheng et al. [20,21] and He et al. [22] numerically investigated light transmission through dual-layer metal films separated by a air layer and perforated with 1D periodic arrays of slits and 2D periodic arrays of
⁎ Corresponding author. E-mail address: [email protected] (L.-L. Wang). 0030-4018/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2010.08.023
holes, respectively. Their results showed that the transmission spectra can be tailored by changing the longitudinal interval and the lateral displacements between the two single-layer metallic gratings. Furthermore, Tang et al. [23] studied optical transmission through metal/ dielectric multilayer films with 2D periodic arrays of subwavelength holes. Their designed multilayer film is constructed by repeating a building block, which contains two layers: one is a perforated metal film and the other is a dielectric film. They demonstrated that the enhancement of optical transmission originates not only from SPP modes but also from the coupling of SPPs in multilayer films, and the coupling of SPPs leads to a blueshift of the transmission modes when the repeating number of building blocks increases. In addition, some researchers [24,25] investigated fishnet structured metamaterials composed of multiple layers of perforated metal/dielectric stacks for achieving optical negative refraction transmission. A metal/dielectric/ metal sandwich stack is being viewed as a functional layer. The stacking up multiple fishnet functional layers leads to a strong magnetoinductive coupling between neighbouring functional layers. In fact, the physics of the optical transmission through 1D arrays of slits is very different from the physics of the optical transmission through 2D arrays of holes [7,12]. Here, we present a metal/dielectric multilayer film perforated with periodic subwavelength slits. The number of metal layers is one more than the number of dielectric layers in a multilayer film and each dielectric layer is sandwiched between two identical metal layers. Similar to the definition of the functional layer in Refs. [24,25], the multilayer structure is regarded as N functional layers. We explore in detail the transmission behavior of the light passing through the multilayer films as we vary the functional layer number N and the grating period in the visible and near infrared region by using the finitedifference time-domain (FDTD) method. It is found that the optical
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transmission can be associated with the Fabry–Pérot–like behavior along the longitudinal direction and the interference among the counter-propagating coupled SPPs along lateral direction inside SiO2 layers. Our results show that the high transmission peaks can split into more peaks as the functional layer number N increases, and these transmission peaks move to larger wavelengths as the grating period increases. The transmission characteristics indicate that we have the ability to open, split, suppress and shift any spectral window by initializing some parameters of metal/dielectric multilayer films. We believe the multilayer structures are promising photonic elements having potential applications in future nanophotonic systems such as frequency selectors or filters. 2. Simulated model and method Fig. 1 shows a schematic diagram for a metal/dielectric multilayer film perforated with periodic subwavelength slits under study. The multilayer film has N functional layers, namely N identical dielectric layers and N + 1 identical metal layers. The thicknesses of the metal and dielectric layers are hm and hd, respectively. Both metal layers and dielectric layers are in fact air slit arrays with the same grating period p and the same width of the slits a. Here, the metal is chosen to be silver (Ag) because of its typical noble metal properties, and the dielectric is chosen to be silicon oxide (SiO2). We will only discuss the results for a fixed slit width a = 50 nm, although the transmission resonances can also depend on the slit width a. The 2D-FDTD method [26,27] is employed to simulate and calculate the transmission of optical waves through multilayer films. In our simulation, the spatial mesh steps are set Δx = Δz = 5 nm and the time step is set Δt = Δx/2c (c is the velocity of light in the vacuum). The calculated region is truncated by using perfectly matched layer (PML) absorbing boundary conditions on the top and bottom boundaries, and the left and right boundaries are treated by periodic boundary conditions due to the periodicity of the structure. Only normally incident p-polarized plane waves are considered here, implying that the magnetic field is parallel to the slits (along the y direction). The frequency-dependent permittivity of Ag εm (which is complex) is described using the tables reported in Ref. [28], and the permittivity of SiO2 is taken as εd = 2.16.
calculated transmission spectra of four kinds of Ag/SiO2 multilayer films with different N = 1, 2, 3 and 4, respectively. By comparison of Fig. 2(a)–(d), we find some main features. First, the transmission peaks can be grouped into two types. Type-1 is the transmission peaks at A1, B1, C1 and D1 shown in Fig. 2. Type-2 includes all of other transmission peaks (A2, B2–B3, C2–C4 and D2–D5 shown in Fig. 2). The two types of peaks have different features. For the transmission peaks of Type-1, in all cases (N = 1, 2, 3, and 4), there is a relatively fixed transmission feature at 490 nm. For the transmission peaks of Type-2, they can split into more peaks as the functional layer number N is increased by 1. For instance, the high transmission peak at 680 nm [as shown in Fig. 2(a)] for N = 1 splits from one single peak into two peaks located at different sides of 680 nm as N is increased by 1 (N = 2). One is at 630 nm, and the other is at 730 nm [as shown in Fig. 2(b)]. These transmission peaks at 630 nm and 730 nm for N = 2 split from two peaks into three peaks [610 nm, 690 nm and 750 nm as shown in Fig. 2(c)] as N is increased by 1 (N = 3). For N = 4, four transmission peaks are observed at wavelengths of 600 nm, 650 nm, 720 nm and 760 nm [as shown in Figure 2(d)], respectively. Moreover, the position (680 nm) of the transmission maximum for N = 1 becomes the position of the transmission minimum for N = 2, and the position (690 nm) of the transmission maximum for N = 3 becomes the position of the transmission minimum for N = 4. Additionally, whenever N = 1, 2, 3 or 4, the intensities of the transmission at certain wavelength range are close to zeroes. Specifically, the suppressed transmission is over a very broad wavelength range from 790 nm to 1600 nm (is not displayed from 1000 nm to 1600 nm). Finally, the intensity of transmission peak decreases as the functional layer number N increases. In order to understand the physical mechanism behind the transmission phenomena, we calculate spatial distributions of the
3. Results and discussion We first initialize hm = 100 nm, hd = 100 nm and p = 400 nm, and study the effect of different functional layer number N on transmission spectrum of Ag/SiO2 multilayer films. Fig. 2 displays the
x
y
incident light
air slit
z
hM
Ag
hD
SiO2
hM
Ag
hD
2
hM
SiO2 Ag
hD
SiO2
3
hM
Ag
p
a
1
N=3
Fig. 1. (Color online) a schematic diagram for a Ag/SiO2 multilayer film with periodic subwavelength slits.
Fig. 2. The calculated transmission spectra of the Ag/SiO2 multilayer films with different numbers of functional layers (a) N = 1, (b) N = 2, (c) N = 3 and (d) N = 4, respectively. The other parameters are hm = 100 nm, hd = 100 nm and p = 400 nm, respectively.
D. Xiang et al. / Optics Communications 284 (2011) 471–475
z (nm)
0 300 600 900 (A1) 0 300 600 900 (B1) 0 300 600 900 (C1) 0 300 600 900
N=2 z (nm)
magnetic field |Hy| at some of the wavelengths of transmission maxima and minima for N = 1, 2, 3 and 4, respectively. Fig. 3(A1)–(A2), (B1)– (B3), (C1)–(C4) and (D1)–(D5) show the calculated field distributions of |Hy| at A1–A2, B1–B3, C1–C4 and D1–D5 as shown in Fig. 2, respectively. From the field distribution of |Hy| in Fig. 3, we can see standing wave patterns inside each slit in these Ag/SiO2 multilayer films formed along the longitudinal direction. So the optical transmission can also be associated with Fabry–Pérot–like resonances. Similar to the Fabry–Pérot–like guided-mode resonance of coupled-SPP modes inside the slit in single-layer metallic grating, the transmission peaks in the Ag/SiO2 multilayer films can be indexed with orders. For instance, the transmission peaks at 490 nm and 680 nm for N = 1 are attributed to the first- and zeroth-order Fabry–Pérot–like resonant modes, respectively [as shown in Fig. 3 (A1) and (A2)]. The transmission peaks at 490 nm, 620 nm and 730 nm for N = 2 attribute to the second-, first- and zeroth-order Fabry–Pérot–like resonant modes, respectively [as shown in Fig. 3 (B1)–(B3)], the transmission peaks at 490 nm, 610 nm, 690 nm and 750 nm for N = 3 attribute to the third-, second-, first- and zerothorder Fabry–Pérot–like resonant modes, respectively [as shown in Fig. 3(C1)–(C4)], and so forth. On the contrary, as shown in Figs. 4 (a) and 3(d), the transmission minima (which has been labeled by E, F, G, and H respectively as shown in Fig. 2) for N = 1, 2, 3 or 4 are associated with maxima of the reflections and destructive conditions of Fabry–Pérot–like resonance. Moreover, Fig. 3 shows that the features of the distributions of |Hy| between the Type-1 and Type-2 transmission peaks are different. For the Type-1 transmission peak, the magnetic field is very weak in all SiO2 layers, and it is mostly centralized inside every slit of Ag layers. In contrast, for the Type-2 transmission peak, the magnetic field is relatively strong inside SiO2 layers, and the magnetic-field distribution shows the standing-wave patterns along lateral direction inside SiO2 layers, which indicates there are electromagnetic waves propagating along + x and−x direction inside SiO2 layers.
473
N=3
N=3
N=4 2
0 300 600 900
1
(a)
(c)
(b)
(d)
0
-200 0 200 -200 0 200 -200 0 200 -200 0 200
x (nm) Fig. 4. (Color online) The calculated field distributions of |Hy| at the wavelengths λ of transmission minima for the numbers of functional layers N = 1, 2, 3 and 4, respectively. (a), (b), (c) and (d) are the field distributions of |Hy| at E, F, G and H shown in Fig. 2, respectively.
We believe that any slit of Ag layers of a multilayer film can be considered as a metal–dielectric–metal waveguide. In the metallic slit, the SPPs of each metal–dielectric surface will be coupled and propagate in the form of a coupled-SPP (waveguide) mode for p-polarized case. The complex effective wave vector βs in the z direction inside the slit can be approximately calculated by the following [29,30]: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1−exp a β2s −ε1 k20 β2s −εm k20 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi = εm β2s −ε1 k20 1 + exp a β2s −ε1 k20 ε1
ð1Þ
where ε1 is the permittivity of the dielectric (air), k0 = 2π/λ is the wave vector of light in vacuum, and λ is the wavelength of the incident light in vacuum, respectively. The calculated results show that the effective refractive index ns = βs/k0 is dependent on the wavelength of the incident light λ, the permittivity of the dielectric ε1 and the slit width a; when ε1 and a are fixed, ns has a decreasing
4 2
(A2)
N=1
0 4 2
(B2)
(B3)
N=2
0 4 2
(C2)
(C3)
(C4)
N=3
0 4 2
(D1)
(D2)
(D3)
(D4)
(D5)
N=4
0
-200 0 200 -200 0 200 -200 0 200 -200 0 200 -200 0 200
x (nm) Fig. 3. (Color online) the calculated field distributions of |Hy| at the wavelengths λ of transmission maxima for the numbers of functional layers N = 1, 2, 3 and 4, respectively. (A1)– (A2), (B1)–(B3), (C1)–(C4) and (D1)–(D5) are the field distributions of |Hy| at A1–A2, B1–B3, C1–C4 and D1–D5 shown in Fig. 2, respectively.
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tendency as λ increases; and when ε1 and λ are fixed, ns also has a decreasing tendency as a increases [29]. At the same time, a functional layer can also be considered as a metal–dielectric–metal waveguide. If βs, ε1 and a in Eq. (1) are replaced by βd (the complex effective wave vector in the x direction inside the SiO2 layer sandwiched by two Ag layers), εd and hd, respectively, then βd and n′d (=βd/k0, the effective refractive index inside the SiO2 layer) can also be approximately calculated by Eq. (1). In fact, the two Ag–air–Ag waveguides of any functional layer are separated by a SiO2 layer. The optical transmission phenomena observed in the multilayer films can be understood by the interaction of evanescent waves from the subwavelength slits of every Ag layer [21]. The exit of every slit in the front Ag layer can be regarded as a source of the evanescent field. The emitted evanescent waves from those sources propagate not only along the z direction but also along the x direction. In the two Ag–SiO2 surfaces of a function layer, the SPP modes can also be supported, respectively. When hd is very narrow, the two SPP modes will couple to form a coupled-SPP mode. The coupled-SPP mode can propagate along + x or −x direction inside the SiO2 layer and interfere with each other. Based on the coupling effect, the electromagnetic radiation from the front Ag layer can tunnel into the rear Ag layer through the SiO2 layer sandwiched by the two Ag layers. According to interference principle, the strongest coupling effect is approximately determined by the following equation: Reðn′d Þ⋅k0 ⋅p = m⋅2π
Fig. 5. (Color online) the calculated transmission spectra of the Ag/SiO2 multilayer films with different grating period p for the numbers of functional layers (a) N = 1 and (b) N = 2, respectively. The other parameters are hm = 100 nm and hd = 100 nm, respectively.
ð2Þ
where m is a relative integer. For the case above, m in Eq. (2) can take m = 1 only. Therefore, the high transmissions through the Ag/SiO2 multilayer films are mediated by the coupling effect between the two Ag layers of a functional layer and the conditions of Fabry–Pérot–like resonance along the z direction inside the slits together. For the Type-1 transmission peak, the magnetic field is very weak in all SiO2 layers while relatively strong in every slit of Ag layers, and the intensity of the transmission peak exponentially decreases as the functional layer number N increases (as shown in Fig. 2). These results indicate that the emitted evanescent wave from front Ag layers propagates along the z direction through the slits of SiO2 layers into rear Ag layers, and the coupled-SPP transmission process (βshm) obeys the Fabry–Pérot–like resonance condition. It can explain why there is relatively fixed transmission peak at 490 nm in all cases (N = 1, 2, 3, and 4). On the contrary, for the Type-2 transmission peak, the magnetic field distribution shows the coupling effect between the two Ag layers of a functional layer is very strong, and these wavelengths of the Type-2 transmission modes are in a range from 570 nm to 790 nm, which is in good agreement with Eqs. (1) and (2). At the same time, the Type-2 transmission modes are also mediated by Fabry–Pérot–like resonance condition along the z direction. Consequently, as shown in Fig. 3(A2) and Fig. 4(a), the transmission peak at 680 nm for N = 1 is the zerothorder Fabry–Pérot–like resonant peak, whereas the transmission minimum corresponding to destructive conditions of Fabry–Pérot–like resonance appears at nearly the same position for N = 2. Analogously, as shown in Fig. 3(C3) and Fig. 4(d), the transmission peak at 690 nm for N = 3 is the first-order Fabry–Pérot–like resonant peak, whereas destructive conditions of Fabry–Pérot–like resonance also appear at the almost same position for N = 4. Next, we investigate the situation when the grating period p is changed. We fix hm = 100 nm, hd = 100 nm all the same, and investigate the transmission spectra of the Ag/SiO2 multilayer films with different grating period p = 500 nm, 600 nm and 700 nm as shown in Fig. 5, respectively. It is obvious that the transmission peaks of these Type-2 transmission modes move to larger wavelengths as p increases, whereas their intensities decrease gradually. This result can also be explained in terms of Eqs. (1) and (2). According to Eq. (1), when εd and hd is fixed, n′d changes little as λ increases in the longer wavelength region. So the relation in Eq. (2) requires that λ also increases as p increases. At the
same time, transmission behavior in the shorter wavelength region becomes complex due to the coupling effect of coupled SPPs modes between the two Ag layers of a functional layer. In the shorter wavelength region, n′d has a relatively notable decrease as λ increases, and when p N 500 nm, m in Eq. (2) can take m = 2 or more, which can lead to the appearance of more peaks. Moreover, from Fig. 5(a) we can also find that a distinct SPP resonant peak appears at 540 nm when N = 1 and p = 500 nm. It is well known that the wavelength of transmission peak λspp for the 1D metallic grating structure due to SPP resonant mode in the case of normal incidence can be given by the following: rffiffiffiffiffiffiffiffiffiffiffiffiffi p εm ; λspp = Re n
1 + εm
qffiffiffiffiffiffiffiffiffiffiffiffiffi εm is [6] where n is a integer (for this case, n = 1) and Re 1 + εm slightly greater than 1. Finally, we calculate the transmission spectra of the Ag/SiO2 multilayer films at different hd from 50 nm to 200 nm, with hm = 100 nm and p = 400 nm for N = 1, 2 and 3, respectively. Fig. 6 only displays the calculated transmission spectra of these films at hd = 50 nm and 150 nm. By comparison of Figs. 2 and 6, we find that the Type-2 transmission modes at hd = 50 nm and 150 nm exhibit the redshift and blueshift, respectively. We can also explain the phenomena in terms of Eqs. (1) and (2). According to Eq. (1), when εd is fixed, in the wavelength region, n′d does not decrease much as λ increases, but n′d has a relatively notable increase as hd decreases. Consequently, λ will increase as hd decrease in terms of Eq. (2). As shown in Fig. 6, the main features of the transmission spectra at hd = 50 nm resemble those at hd = 100 nm, while those at hd = 150 nm do not. Therefore, the significant properties of the transmission spectra as shown in Fig. 2 can be gained only if both hm and hd are suitably initialized. 4. Summary In conclusion, we investigated the transmission characteristics of the electromagnetic radiation in visible and near infrared frequencies passing through Ag/SiO2 multilayer films perforated with periodic subwavelength slits by using the FDTD method. In the nanostructured Ag/SiO2 multilayer film, where each Ag layer and SiO2 layer has same
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National Natural Science Foundation of China (Grant No. 11074069, 90606001, 10874042, 90923014, 10974050), Natural Science Foundation of Hunan Province, China (Grant No. 09JJ1009), the Science Research Program of Educational Department of Hunan Province, China (Grant No. 09C851), the China Postdoctoral Science Foundation funded project (Grant No. 20100471310), the Scientific Project of Jiangxi Education Departments of China (Grant No. GJJ10263), and Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province.
References
Fig. 6. (Color online) the calculated transmission spectra of the Ag/SiO2 multilayer films with the different functional layer number N for the thicknesses of the SiO2 layers (a) hd = 50 nm and (b) hd = 150 nm, respectively. The other parameters are hm = 100 nm, and p = 400 nm, respectively.
periodic arrays of subwavelength air slits. If geometrical parameters of multilayer films are suitably selected, the high transmission peaks somewhere can split into more peaks and the original positions of the transmission maxima almost become the positions of transmission minima when the functional layer number N is increased by 1. The wavelength of the same-order transmission peak exhibits a redshift as the grating period p increases. We consider that the optical transmission property is mediated by the interference among the propagating coupled-SPP modes along the lateral direction inside the SiO2 layers and the conditions of Fabry–Pérot–like resonance along the longitudinal direction together. Our results indicate that the Ag/SiO2 multilayer films may have potential applications in future nanophtonic systems where spectral control is desired. Acknowledgments This work was supported by the “973” National Key Basic Research Program of China (Grant No. 2007CB310502-2, 2007CB310403), the
[1] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Nature (London) 391 (1998) 667. [2] J.A. Porto, F.J. Garcia-Vidal, J.B. Pendry, Phys. Rev. Lett. 83 (1999) 2845. [3] K.G. Lee, Q.H. Park, Phys. Rev. Lett. 95 (2005) 103902. [4] Y. Xie, A.R. Zakharian, J.V. Moloney, M. Mansuripur, Opt. Express 13 (2005) 4485. [5] S. Astilean, P. Lalanne, M. Palamaru, Opt. Commun. 175 (2000) 265. [6] X. Jiao, P. Wang, L. Tang, Y. Lu, Q. Li, D. Zhang, P. Yao, H. Ming, J. Xie, Appl. Phys. B 80 (2005) 301. [7] Q. Cao, P. Lalanne, Phys. Rev. Lett. 88 (2002) 057403. [8] D. Pacifici, H.J. Lezec, Harry A. Atwater, J. Weiner, Phys. Rev. B 77 (2008) 115411. [9] Hu. Bin, Gu. Ben-Yuan, Bi-Zhen Dong, Yan Zhang, Opt. Commun. 281 (2008) 6120. [10] H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, H.J. Lezec, Phys. Rev. B 58 (1998) 6779. [11] K.J.K. Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, L. Kuipers, Phys. Rev. Lett. 92 (2004) 183901. [12] W.L. Barnes, W.A. Murray, J. Dintinger, E. Devaux, T.W. Ebbesen, Phys. Rev. Lett. 92 (2004) 107401. [13] Henri J. Lezec, Tineke Thio, Opt. Express 12 (2004) 3629. [14] Z. Ruan, M. Qiu, Phys. Rev. Lett. 96 (2006) 233901. [15] A. Mary, S.G. Rodrigo, L. Martín-Moreno, F.J. García-Vidal, Phys. Rev. B 76 (2007) 195414. [16] Zhiyuan Fan, Li. Zhan, Hu. Xiao, Yuxing Xia, Opt. Commun. 281 (2008) 5467. [17] H. Liu, P. Lalanne, Nature(London) 452 (2008) 728. [18] Y.H. Ye, J.Y. Zhang, Opt. Lett. 30 (2005) 1521. [19] Y.H. Ye, Z.B. Wang, D.S. Yan, J.Y. Zhang, Appl. Phys. Lett. 89 (2006) 221108. [20] C. Cheng, J. Chen, Q.Y. Wu, F.F. Ren, J. Xu, Y.X. Fan, H.T. Wang, Appl. Phys. Lett. 91 (2007) 111111. [21] C. Cheng, J. Chen, D.J. Shi, Q.Y. Wu, F.F. Ren, J. Xu, Y.X. Fan, J.P. Ding, H.T. Wang, Phys. Rev. B 78 (2008) 075406. [22] M.D. He, L.L. Wang, J.Q. Liu, X. Zhai, Q. Wan, X.S. Chen, B.S. Zou, Appl. Phys. Lett. 93 (2008) 221909. [23] Z.H. Tang, R.W. Peng, Z. Wang, X. Wu, Y.J. Bao, Q.J. Wang, Z.J. Zhang, W.H. Sun, M. Wang, Phys. Rev. B 76 (2007) 195405. [24] Jason Valentine, Shuang Zhang, Thomas Zentgraf, Erick Ulin-Avila, Dentcho A. Genov, Guy Bartal, Xiang Zhang, Nature(London) 455 (2008) 376. [25] Zahyun Ku, Jingyu Zhang, S.R.J. Brueck, Opt. Express 17 (2009) 6782. [26] A. Taflove, S.C. Hagness, Computational Electrodynamics. The Finite-Difference Time-Domain Method, 2nd ed., Artech House, Boston, 2000. [27] Stephen K. Gray, Teobald Kupka, Phys. Rev. B 68 (2003) 045415. [28] E.D. Palik, Handbook of Optical Constants and Solids, Academic, New York, 1985. [29] J.Q. Liu, L.L. Wang, M.D. He, W.Q. Huang, D.Y. Wang, B.S. Zou, S.C. Wen, Opt. Express 16 (2008) 4888. [30] E.N. Economou, Phys. Rev. 182 (1969) 539.