- Email: [email protected]
The collective property of enhanced transmission through compound metal periodic arrays of subwavelength apertures
Optics Communications 298–299 (2013) 237–241
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
The collective property of enhanced transmission through compound metal periodic arrays of subwavelength apertures Bo Ni, Lujun Huang, Jiayi Ding, Guanhai Li, Xiaoshuang Chen n, Wei Lu National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 200083 Shanghai, China
a r t i c l e i n f o
abstract
Article history: Received 17 April 2012 Received in revised form 2 February 2013 Accepted 5 February 2013 Available online 13 March 2013
The transmissions through a two-dimensional compound metal periodic hole arrays comprised of rectangle and cross-shaped holes are calculated by the finite-difference-time-domain (FDTD) method. The results show that the transmissions strongly depend on the collective effect of the compound hole cell. Moreover, the comparisons between transmission characteristics corresponding to the asymmetry of the cross-shaped hole in two different directions (vertical and parallel to the light polarization) are also studied. It is found that the 1168 nm peak is split into two peaks when the symmetry of the crossshaped hole in y-axis direction is broken. However, it is shown that there is no obvious change of transmissions with changing the asymmetry in x-axis direction. Thus, it is concluded that the transmissions are more sensitive to the vertical direction asymmetry. The results may be utilized to tune the electromagnetic wave in subwavelength optics. & 2013 Elsevier B.V. All rights reserved.
Keywords: Surface plasmon Compound hole Charge collective effect
1. Introduction The periodically patterned metal films have attracted considerable attention because of their interesting optical properties and potential applications in nanodevices since Ebbesen et al. reported the extraordinary optical transmission (EOT) through metallic films perforated by subwavelength hole arrays [1]. In attempts to understand the underlying physical mechanisms, many experimental [2–10] and theoretical [11–25] studies have been carried out. It is widely accepted that the surface plasmon resonance on the metal film is the main mechanism responsible for light enhancement, and the transmission spectra depend on the metal [6], hole size [4,7], hole depth [2], hole shape [8,9,19,21] and the polarization of incident light [5]. The influence of the hole shape is due to the effect of localized surface plasmon (LSP) around the aperture. In previous works, different hole shapes like circular [1], rectangular [5,19], cross-shaped [8], asymmetric cross-shaped [21] have been studied. On the other hand, the transmissions of light through various complicated structures [26–29], as an important research topic, have been investigated. Some compound structures are utilized to tune the enhanced transmissions of electromagnetic wave. In 2002, by combining thin copper wires and split ring resonators (SRRs) on the same board, Bayindir et al. reported that the transmission measurements exhibit a passband within the stop bands of SRRs and thin wire structures [26]. Later, Yuan et al. showed a dual-band
n
Corresponding author. E-mail address: [email protected] (X. Chen).
0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.02.002
measurement of planar metamaterial with two distinct electric resonances [27]. Li et al. obtained dual-band magnetic resonances by embedding the SRRs within the dielectric holes of the fishnet structure [28]. In addition, the structure of double sets of circular holes has been studied by Wang et al., a redshift of the transmission peak can be seen clearly [29]. However, all the results mentioned above are exhibited in gigahertz or terahertz frequency ranges. It is significant to extend these particular properties to infrared and optical frequency ranges. On the other hand, it is worthy to study the physical mechanism of tuning electromagnetic wave by compound structures. These works have some potential applications for novel nanodevices. In this paper, the transmissions of light through twodimensional compound metal periodic hole arrays, comprised of rectangle and cross-shaped holes, are studied by the finitedifference-time-domain (FDTD) method. It is found that the transmissions strongly depend on the collective effect of the compound cell by comparing to that of the individual rectangle or cross-shaped hole arrays, respectively. In addition, the transmission characteristics are obtained by changing symmetry of the cross-shaped hole in two different directions (vertical and parallel to the light polarization). It is shown that the transmissions are more sensitive to the asymmetry of vertical direction.
2. Numerical model and simulations We consider a freestanding gold film perforated by an array of two-dimensional compound rectangle and cross-shaped holes, as shown in Fig. 1. The cross-shaped hole are formed by two rectangle
238
B. Ni et al. / Optics Communications 298–299 (2013) 237–241
Fig. 2. The transmission spectra of the compound hole arrays with different crossshaped hole symmetries. The black line is the transmission spectrum corresponding to the symmetrical cross-shaped hole. Two distinct peaks are located at 840 nm and 1168 nm, respectively. The green line is the transmission spectrum corresponding to the x-axis directional asymmetrical cross-shaped hole (Dx ¼30 nm). It is almost the same as the black line. The purple line is the transmission spectrum corresponding to the y-axis directional asymmetrical cross-shaped hole (Dy¼ 30 nm). It has three peaks locating at 840 nm, 1038 nm and 1220 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 1. (a) Side view and (b) top view of the schematic configuration of the studied compound cell comprised of two rectangle and two cross-shaped holes. The crossshaped hole are formed by two rectangle holes (A and B) with the same size as the rectangle hole. L¼ 150 nm, W ¼460 nm, h ¼ 100 nm, and the square array period 2p ¼1200 nm. The compound hole arrays are illuminated normally by a linearly polarized plane wave with electric field vector parallel to x-axis.
holes (A and B), which are parallel and vertical to the light polarization, respectively. A and B are the same size as the rectangle hole. The parameters of the rectangle hole are L¼150 nm and W¼460 nm. The thickness of the metal film is h¼100 nm and the square compound hole cell array has a period of 2p¼1200 nm. The metal hole arrays are illuminated normally by a linearly polarized plane wave with electric field vector parallel to x-axis. The metal is chosen to be gold (Au), with the dielectric function obeying the Drude model as
eðoÞ ¼ e0 f1op 2 =ðo2 þ igoÞg, where e0 is the permittivity of the vacuum, op ¼1.236 1016 rad/s is the plasma frequency, o is the angle frequency of the incident wave, and g ¼1.4 1014 rad/s is the damping rate [30]. To investigate the transmission spectra of the compound hole arrays, the finitedifference-time-domain (FDTD) method is employed [31]. In the calculations, the spatial mesh cell is set to Dx¼ Dy¼ Dz¼ Ds¼ 10 nm and the time step is taken as Dt¼ Ds/2c¼1.66782 10 17 s. Periodic boundary conditions are set in the x and y directions, and an open boundary is defined in the z-direction for the electromagnetic wave incidence and transmission.
3. Results and discussion Fig. 2 presents the transmission spectra of the compound hole arrays with different cross-shaped hole symmetries. The black line is the transmission spectrum corresponding to the compound cell with the symmetrical cross-shaped hole. Two distinct peaks are located at 840 nm and 1168 nm, respectively. It is easily found that the 840 nm peak is resulted from the interaction between rectangle and cross-shaped holes because there is no such a peak in the transmission spectrum of individual rectangle or crossshaped hole arrays. Next, we consider the effect of the asymmetry of cross-shaped hole on the transmission spectrum of compound hole arrays. The asymmetry is obtained by moving the rectangle
hole B of cross-shaped hole. The x-axis directional asymmetry refers to that the rectangle hole B moves along the negative xaxis, and the y-axis directional asymmetry refers to that the hole B moves along the positive y-axis. The transmission spectra (green and purple lines) of the compound structures are shown with the symmetries of cross-shaped hole changing at x-axis direction (Dx¼30 nm) and y-axis direction (Dy¼30 nm). It is obvious that the green line is almost the same as the black one. The result indicates that the transmission spectrum is not sensitive to the asymmetry in x-axis direction. On the other hand, it can be found that the distributions of purple and black lines are different. The purple line has three peaks locating at 840 nm, 1038 nm and 1220 nm, respectively. According to the result in Ref. [21], the 1038 nm and 1220 nm peaks are originated from the split of the 1168 nm peak of the transmission spectrum corresponding to the symmetric cross-shaped hole of the compound cell. These results are also confirmed in the following discussion. In addition, it is necessary to emphasize that the 840 nm peak exists in all the three transmission spectra. For well-recognized properties of the different transmission peaks, Figs. 3 and 4 indicate the time-averaged density distributions of the electric field 9Ez9 of different peaks over a period cell at the position z ¼100þnm (‘‘ þ’’ denotes the position being away from the exit surface of metal film along the positive direction of the z-axis). Fig. 3(a)–(c) is the electric field distributions of the 840 nm peak corresponding to symmetrical, x-axis and y-axis directional asymmetrical cross-shaped hole, respectively. It is known that the metal surface charges (surface plasmon) can be deduced out from the electric field distribution [21]. The charges among the hole edges are oscillated with the incident electric field and emit photons at the same time, and the interference between the photons leads to the EOT [32]. Therefore, Fig. 3 reveals that the surface charges are distributed among the rectangle and cross-shaped hole edges at the 840 nm transmission peak. The two type holes in one compound cell have an interaction with each other, in consistent with the discussion mentioned before. Note that the interaction intensity of Fig. 3(a) is almost the same as that of Fig. 3(b). However, the interaction intensity is a little weaker in Fig. 3(c). The result can be used to understand why the amplitude of the 840 nm peak corresponding to y-axis directional asymmetry is smaller, as
B. Ni et al. / Optics Communications 298–299 (2013) 237–241
239
Fig. 3. The electric field distributions of 9Ez9 of the 840 nm peak corresponding to (a) the symmetrical cross-shaped hole, (b) asymmetrical cross-shaped hole in x-direction (Dx¼ 30 nm) and (c) in y direction (Dy¼30 nm). The electric field are distributed among the rectangle and cross-shaped hole edges and the two type holes have an interaction with each other. The interaction intensity in (a) is almost the same as that in (b), however, it is a little weaker in (c).
shown in Fig. 1. Hence, it is clear that the 840 nm peak is resulted from the collective effect of the compound cell no matter whether the symmetry of cross-shaped hole changes. The electric field distributions of 9Ez9 of the 1168 nm peak corresponding to symmetrical cross-shaped hole and asymmetrical cross-shaped hole in x-direction (Dx ¼30 nm) is shown in Fig. 4(a) and (b), respectively. It is found that surface charges are only distributed at the edges of the cross-shaped hole, and the cross-shaped hole possesses the axial symmetry along the incident light polarization in the two cases. Moreover, there is not a great deal of difference of the electric field distributions between Fig. 4(a) and (b). On the other hand, Fig. 4(c) and (d) presents the electric field distributions of 1038 nm and 1220 nm peaks, respectively. The peak at 1038 nm mainly benefits from the resonance of LSP modes on the lower part edges of the asymmetric cross-shaped hole, while the other peak at 1220 nm mainly results from the resonance of the LSP modes on the upper part edges. Because the upper section of asymmetric cross-shaped hole is longer than the lower section, the amplitude of the 1220 nm peak is higher than that of the 1038 nm peak. Thus, we can see that the transmission spectra are not influenced by the asymmetry of the cross-shaped hole at x-axis direction, but strongly depend on the asymmetry at y-axis direction. We also have studied the transmission spectra as a function of the asymmetry (Dx and Dy), as shown in Fig. 5(a) and (b). It is seen that the transmission peaks almost do not move with the increase
of Dx. Although the 1168 nm peak exhibits little redshift after Dx4110 nm, it exhibits only 51 nm redshift even the asymmetric cross-shaped hole becomes a horizontal T-shaped hole (Dx¼155 nm). On the other hand, for Dy40, the 1168 nm peak has split into two peaks. The two peaks are located at shorter and longer wavelengths than that of 1168 nm peak, respectively. With the increase of Dy, the ‘‘shorter peak’’ and ‘‘longer peak’’ positions exhibit blueshift and redshift, respectively. When Dy4120 nm, the ‘‘shorter peak’’ does not exist anymore. It is because the peak is resulted from the resonance of LSP modes on the lower part edges of asymmetric cross-shaped hole, and the lower part edges is nearly zero in this case. When the asymmetric cross-shaped hole becomes an inverted T-shaped hole (Dy¼155 nm), the 1168 nm peak exhibits large redshift of 344 nm. In all cases, the 840 nm peak does not move. It can be clearly seen that the transmission spectra are more sensitive to the asymmetry of y-axis direction.
4. Conclusions We have calculated the transmissions of light through a compound metal periodic hole arrays comprised of rectangle and cross-shaped holes. It is found that a new transmission peak originates from the collective effect of the compound periodic hole arrays. In addition, the calculated results show that the transmission spectra are more sensitive to the asymmetry of the
240
B. Ni et al. / Optics Communications 298–299 (2013) 237–241
Fig. 4. The electric field distributions of 9Ez9 of the 1168 nm peak corresponding to (a) the symmetrical and (b) asymmetrical cross-shaped hole in x-direction (Dx ¼ 30 nm), respectively. The electric fields are only distributed at the edges of cross-shaped hole and possess the axial symmetry along the incident light polarization in these two cases. (c) and (d) are the electric field distributions of the 1038 nm peak and 1220 nm peak, respectively. The two peaks correspond to y-axis directional asymmetrical cross-shaped hole (Dy ¼30 nm). The electric field of the 1038 nm peak is only distributed at the lower part edges of the asymmetric cross-shaped hole, while the electric field of the 1220 nm peak is only distributed at the upper part edges.
Fig. 5. The transmission spectra as a function of the asymmetry (Dx and Dy). (a) While Dx increasing, the 840 nm peak almost does not move and the 1168 nm peak exhibits little redshift after Dx4110 nm. (b) While Dy increasing, the 840 nm peak also almost does not move and the 1168 nm peak splits into two peaks which are located at shorter and longer wavelengths than that of 1168 nm peak, respectively. The ‘‘shorter peak’’ exhibits blueshift and disappears after Dy4120 nm. The ‘‘longer peak’’ exhibits redshift. When Dy¼ 155 nm, the 1168 nm peak exhibits large redshift of 344 nm.
B. Ni et al. / Optics Communications 298–299 (2013) 237–241
cross-shaped hole in the direction vertical to the light polarization than in the direction that parallel to the light polarization. The 1168 nm peak is split into two peaks when the cross-shaped hole symmetry in y-axis direction is broken. However, it is found that there is no obvious change of transmissions with changing the asymmetry in x-axis direction. The results may be utilized to tune the electromagnetic wave in subwavelength optics.
Acknowledgment This work was supported in part by the State Key Program for Basic Research of China Grants (2011CB922004, 2013CB632705), the National Natural Science Foundation of China Grants (10990104, 60976092 and 61290301); the Fund of Shanghai Science and Technology Foundation Grant (10JC1416100). References [1] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Nature 391 (1998) 667. [2] A. Degiron, H.J. Lezec, W.L. Barnes, T.W. Ebbesen, Applied Physics Letters 81 (2002) 4327. [3] A. Degiron, T.W. Ebbesen, Journal of Optics A: Pure and Applied Optics 7 (2005) S90. [4] S.M. Williams, A.D. Stafford, T.M. Rogers, S.R. Bishop, J.V. Coe, Applied Physics Letters 85 (2004) 1472. [5] K.L. van der Molen, K.J. Klein Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, L. Kuipers, Physical Review B 72 (2005) 045421. [6] F. Przybilla, A. Degiron, J.Y. Laluet, C. Genet, T.W. Ebbesen, Journal of Optics A: Pure and Applied Optics 8 (2006) 458. [7] M.W. Tsai, T.H. Chuang, H.Y. Chang, S.C. Lee, Applied Physics Letters 88 (2006) 213112. [8] C.Y. Chen, M.W. Tsai, T.H. Chuang, Y.T. Chang, S.C. Lee, Applied Physics Letters 91 (2007) 063108. [9] J.Y. Li, Y.L. Hua, J.X. Fu, Z.Y. Li, Journal of Applied Physics 107 (2010) 073101.
241
[10] M. Najiminaini, F. Vasefi, B. Kaminska, J.L. Carson, Optics Express 18 (2010) 22255. [11] E. Popov, M. Nevie0 re, S. Enoch, R. Reinisch, Physical Review B 62 (16) (2000) 100. [12] L. Salomon, F. Grillot, A.V. Zayats, F. de Fornel, Physical Review Letters 86 (2001) 1110. [13] L. Martı´n-Moreno, F.J. Garcı´a-Vidal, H.J. Lezec, K.M. Pellerin, T. Thio, J.B. Pendry, T.W. Ebbesen, Physical Review Letters 86 (2001) 1114. [14] S. Enoch, E. Popov, M. Neviere, R. Reinisch, Journal of Optics A: Pure and Applied Optics 4 (2002) S83. [15] P. Lalanne, C. Sauvan, J.P. Hugonin, J.C. Rodier, P. Chavel, Physical Review B 68 (2003) 125404. [16] K.L. van der Molen, K.J. Klein Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, L. Kuipers, Physical Review B 72 (2005) 045421. [17] R. Gordon, A.G. Brolo, Optics Express 13 (2005) 1933. [18] K.J. Webb, J. Li, Physical Review B 73 (2006) 033401. [19] A. Mary, G. Rodrigo, L. Martı´n-Moreno, F.J. Garcı´a-Vidal1, Physical Review B 76 (2007) 195414. [20] M. Zhang, C.P. Huang, G.D. Wang, Y.Y. Zhu, Journal of Optics—IOP Science 12 (2010) 015004. [21] M.D. He, J.Q. Liu, Z.Q. Gong, Y.F. Luo, X.S. Chen, Solid State Communications 150 (2010) 104. [22] Y.M. Strelniker, Physical Review B 76 (2007) 085409. [23] X.Y. He, X.N. Fu, Y.W. Luo, Journal of Modern Optics 56 (15) (2009) 1698. [24] X.Y. He, Optics Express 17 (17) (2009) 15359. [25] X.Y. He, Q.J. Wang, S.F. Yu, IEEE Journal of Quantum Electronics 48 (12) (2012) 1554. [26] M. Bayindir, K. Aydin, E. Ozbay, P. Markoˇs, C.M. Soukoulis, Applied Physics Letters 81 (2002) 120. [27] Y. Yuan, C. Bingham, T. Tyler, S. Palit, T.H. Hand, W.J. Padilla, D.R. Smith, N.M. Jokerst, S.A. Cummer, Optics Express 16 (2008) 9746. [28] M. Li, Z.C. Wen, J.X. Fu, X. Fang, Y.M. Dai, R.J. Liu, X.F. Han, X.G. Qiu, Journal of Physics D: Applied Physics 42 (2009) 115420. [29] K.J. Wang, L. Ding, J.S. Liu, J. Zhang, X.M. Yang, J.Y. Chin, T.J. Cui, Optics Express 19 (2011) 11375. [30] Y.G. Chen, Y.H. Wang, Y. Zhang, S.T. Liu, Optics Communications 274 (2007) 236. [31] EastFDTD v2.0, DONGJUN Science and Technology Co. China. [32] X.R. Huang, R.W. Peng, Z. Wang, F. Gao, S.S. Jiang, Physical Review A 76 (2007) 035802.
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
The collective property of enhanced transmission through compound metal periodic arrays of subwavelength apertures Bo Ni, Lujun Huang, Jiayi Ding, Guanhai Li, Xiaoshuang Chen n, Wei Lu National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 200083 Shanghai, China
a r t i c l e i n f o
abstract
Article history: Received 17 April 2012 Received in revised form 2 February 2013 Accepted 5 February 2013 Available online 13 March 2013
The transmissions through a two-dimensional compound metal periodic hole arrays comprised of rectangle and cross-shaped holes are calculated by the finite-difference-time-domain (FDTD) method. The results show that the transmissions strongly depend on the collective effect of the compound hole cell. Moreover, the comparisons between transmission characteristics corresponding to the asymmetry of the cross-shaped hole in two different directions (vertical and parallel to the light polarization) are also studied. It is found that the 1168 nm peak is split into two peaks when the symmetry of the crossshaped hole in y-axis direction is broken. However, it is shown that there is no obvious change of transmissions with changing the asymmetry in x-axis direction. Thus, it is concluded that the transmissions are more sensitive to the vertical direction asymmetry. The results may be utilized to tune the electromagnetic wave in subwavelength optics. & 2013 Elsevier B.V. All rights reserved.
Keywords: Surface plasmon Compound hole Charge collective effect
1. Introduction The periodically patterned metal films have attracted considerable attention because of their interesting optical properties and potential applications in nanodevices since Ebbesen et al. reported the extraordinary optical transmission (EOT) through metallic films perforated by subwavelength hole arrays [1]. In attempts to understand the underlying physical mechanisms, many experimental [2–10] and theoretical [11–25] studies have been carried out. It is widely accepted that the surface plasmon resonance on the metal film is the main mechanism responsible for light enhancement, and the transmission spectra depend on the metal [6], hole size [4,7], hole depth [2], hole shape [8,9,19,21] and the polarization of incident light [5]. The influence of the hole shape is due to the effect of localized surface plasmon (LSP) around the aperture. In previous works, different hole shapes like circular [1], rectangular [5,19], cross-shaped [8], asymmetric cross-shaped [21] have been studied. On the other hand, the transmissions of light through various complicated structures [26–29], as an important research topic, have been investigated. Some compound structures are utilized to tune the enhanced transmissions of electromagnetic wave. In 2002, by combining thin copper wires and split ring resonators (SRRs) on the same board, Bayindir et al. reported that the transmission measurements exhibit a passband within the stop bands of SRRs and thin wire structures [26]. Later, Yuan et al. showed a dual-band
n
Corresponding author. E-mail address: [email protected] (X. Chen).
0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.02.002
measurement of planar metamaterial with two distinct electric resonances [27]. Li et al. obtained dual-band magnetic resonances by embedding the SRRs within the dielectric holes of the fishnet structure [28]. In addition, the structure of double sets of circular holes has been studied by Wang et al., a redshift of the transmission peak can be seen clearly [29]. However, all the results mentioned above are exhibited in gigahertz or terahertz frequency ranges. It is significant to extend these particular properties to infrared and optical frequency ranges. On the other hand, it is worthy to study the physical mechanism of tuning electromagnetic wave by compound structures. These works have some potential applications for novel nanodevices. In this paper, the transmissions of light through twodimensional compound metal periodic hole arrays, comprised of rectangle and cross-shaped holes, are studied by the finitedifference-time-domain (FDTD) method. It is found that the transmissions strongly depend on the collective effect of the compound cell by comparing to that of the individual rectangle or cross-shaped hole arrays, respectively. In addition, the transmission characteristics are obtained by changing symmetry of the cross-shaped hole in two different directions (vertical and parallel to the light polarization). It is shown that the transmissions are more sensitive to the asymmetry of vertical direction.
2. Numerical model and simulations We consider a freestanding gold film perforated by an array of two-dimensional compound rectangle and cross-shaped holes, as shown in Fig. 1. The cross-shaped hole are formed by two rectangle
238
B. Ni et al. / Optics Communications 298–299 (2013) 237–241
Fig. 2. The transmission spectra of the compound hole arrays with different crossshaped hole symmetries. The black line is the transmission spectrum corresponding to the symmetrical cross-shaped hole. Two distinct peaks are located at 840 nm and 1168 nm, respectively. The green line is the transmission spectrum corresponding to the x-axis directional asymmetrical cross-shaped hole (Dx ¼30 nm). It is almost the same as the black line. The purple line is the transmission spectrum corresponding to the y-axis directional asymmetrical cross-shaped hole (Dy¼ 30 nm). It has three peaks locating at 840 nm, 1038 nm and 1220 nm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 1. (a) Side view and (b) top view of the schematic configuration of the studied compound cell comprised of two rectangle and two cross-shaped holes. The crossshaped hole are formed by two rectangle holes (A and B) with the same size as the rectangle hole. L¼ 150 nm, W ¼460 nm, h ¼ 100 nm, and the square array period 2p ¼1200 nm. The compound hole arrays are illuminated normally by a linearly polarized plane wave with electric field vector parallel to x-axis.
holes (A and B), which are parallel and vertical to the light polarization, respectively. A and B are the same size as the rectangle hole. The parameters of the rectangle hole are L¼150 nm and W¼460 nm. The thickness of the metal film is h¼100 nm and the square compound hole cell array has a period of 2p¼1200 nm. The metal hole arrays are illuminated normally by a linearly polarized plane wave with electric field vector parallel to x-axis. The metal is chosen to be gold (Au), with the dielectric function obeying the Drude model as
eðoÞ ¼ e0 f1op 2 =ðo2 þ igoÞg, where e0 is the permittivity of the vacuum, op ¼1.236 1016 rad/s is the plasma frequency, o is the angle frequency of the incident wave, and g ¼1.4 1014 rad/s is the damping rate [30]. To investigate the transmission spectra of the compound hole arrays, the finitedifference-time-domain (FDTD) method is employed [31]. In the calculations, the spatial mesh cell is set to Dx¼ Dy¼ Dz¼ Ds¼ 10 nm and the time step is taken as Dt¼ Ds/2c¼1.66782 10 17 s. Periodic boundary conditions are set in the x and y directions, and an open boundary is defined in the z-direction for the electromagnetic wave incidence and transmission.
3. Results and discussion Fig. 2 presents the transmission spectra of the compound hole arrays with different cross-shaped hole symmetries. The black line is the transmission spectrum corresponding to the compound cell with the symmetrical cross-shaped hole. Two distinct peaks are located at 840 nm and 1168 nm, respectively. It is easily found that the 840 nm peak is resulted from the interaction between rectangle and cross-shaped holes because there is no such a peak in the transmission spectrum of individual rectangle or crossshaped hole arrays. Next, we consider the effect of the asymmetry of cross-shaped hole on the transmission spectrum of compound hole arrays. The asymmetry is obtained by moving the rectangle
hole B of cross-shaped hole. The x-axis directional asymmetry refers to that the rectangle hole B moves along the negative xaxis, and the y-axis directional asymmetry refers to that the hole B moves along the positive y-axis. The transmission spectra (green and purple lines) of the compound structures are shown with the symmetries of cross-shaped hole changing at x-axis direction (Dx¼30 nm) and y-axis direction (Dy¼30 nm). It is obvious that the green line is almost the same as the black one. The result indicates that the transmission spectrum is not sensitive to the asymmetry in x-axis direction. On the other hand, it can be found that the distributions of purple and black lines are different. The purple line has three peaks locating at 840 nm, 1038 nm and 1220 nm, respectively. According to the result in Ref. [21], the 1038 nm and 1220 nm peaks are originated from the split of the 1168 nm peak of the transmission spectrum corresponding to the symmetric cross-shaped hole of the compound cell. These results are also confirmed in the following discussion. In addition, it is necessary to emphasize that the 840 nm peak exists in all the three transmission spectra. For well-recognized properties of the different transmission peaks, Figs. 3 and 4 indicate the time-averaged density distributions of the electric field 9Ez9 of different peaks over a period cell at the position z ¼100þnm (‘‘ þ’’ denotes the position being away from the exit surface of metal film along the positive direction of the z-axis). Fig. 3(a)–(c) is the electric field distributions of the 840 nm peak corresponding to symmetrical, x-axis and y-axis directional asymmetrical cross-shaped hole, respectively. It is known that the metal surface charges (surface plasmon) can be deduced out from the electric field distribution [21]. The charges among the hole edges are oscillated with the incident electric field and emit photons at the same time, and the interference between the photons leads to the EOT [32]. Therefore, Fig. 3 reveals that the surface charges are distributed among the rectangle and cross-shaped hole edges at the 840 nm transmission peak. The two type holes in one compound cell have an interaction with each other, in consistent with the discussion mentioned before. Note that the interaction intensity of Fig. 3(a) is almost the same as that of Fig. 3(b). However, the interaction intensity is a little weaker in Fig. 3(c). The result can be used to understand why the amplitude of the 840 nm peak corresponding to y-axis directional asymmetry is smaller, as
B. Ni et al. / Optics Communications 298–299 (2013) 237–241
239
Fig. 3. The electric field distributions of 9Ez9 of the 840 nm peak corresponding to (a) the symmetrical cross-shaped hole, (b) asymmetrical cross-shaped hole in x-direction (Dx¼ 30 nm) and (c) in y direction (Dy¼30 nm). The electric field are distributed among the rectangle and cross-shaped hole edges and the two type holes have an interaction with each other. The interaction intensity in (a) is almost the same as that in (b), however, it is a little weaker in (c).
shown in Fig. 1. Hence, it is clear that the 840 nm peak is resulted from the collective effect of the compound cell no matter whether the symmetry of cross-shaped hole changes. The electric field distributions of 9Ez9 of the 1168 nm peak corresponding to symmetrical cross-shaped hole and asymmetrical cross-shaped hole in x-direction (Dx ¼30 nm) is shown in Fig. 4(a) and (b), respectively. It is found that surface charges are only distributed at the edges of the cross-shaped hole, and the cross-shaped hole possesses the axial symmetry along the incident light polarization in the two cases. Moreover, there is not a great deal of difference of the electric field distributions between Fig. 4(a) and (b). On the other hand, Fig. 4(c) and (d) presents the electric field distributions of 1038 nm and 1220 nm peaks, respectively. The peak at 1038 nm mainly benefits from the resonance of LSP modes on the lower part edges of the asymmetric cross-shaped hole, while the other peak at 1220 nm mainly results from the resonance of the LSP modes on the upper part edges. Because the upper section of asymmetric cross-shaped hole is longer than the lower section, the amplitude of the 1220 nm peak is higher than that of the 1038 nm peak. Thus, we can see that the transmission spectra are not influenced by the asymmetry of the cross-shaped hole at x-axis direction, but strongly depend on the asymmetry at y-axis direction. We also have studied the transmission spectra as a function of the asymmetry (Dx and Dy), as shown in Fig. 5(a) and (b). It is seen that the transmission peaks almost do not move with the increase
of Dx. Although the 1168 nm peak exhibits little redshift after Dx4110 nm, it exhibits only 51 nm redshift even the asymmetric cross-shaped hole becomes a horizontal T-shaped hole (Dx¼155 nm). On the other hand, for Dy40, the 1168 nm peak has split into two peaks. The two peaks are located at shorter and longer wavelengths than that of 1168 nm peak, respectively. With the increase of Dy, the ‘‘shorter peak’’ and ‘‘longer peak’’ positions exhibit blueshift and redshift, respectively. When Dy4120 nm, the ‘‘shorter peak’’ does not exist anymore. It is because the peak is resulted from the resonance of LSP modes on the lower part edges of asymmetric cross-shaped hole, and the lower part edges is nearly zero in this case. When the asymmetric cross-shaped hole becomes an inverted T-shaped hole (Dy¼155 nm), the 1168 nm peak exhibits large redshift of 344 nm. In all cases, the 840 nm peak does not move. It can be clearly seen that the transmission spectra are more sensitive to the asymmetry of y-axis direction.
4. Conclusions We have calculated the transmissions of light through a compound metal periodic hole arrays comprised of rectangle and cross-shaped holes. It is found that a new transmission peak originates from the collective effect of the compound periodic hole arrays. In addition, the calculated results show that the transmission spectra are more sensitive to the asymmetry of the
240
B. Ni et al. / Optics Communications 298–299 (2013) 237–241
Fig. 4. The electric field distributions of 9Ez9 of the 1168 nm peak corresponding to (a) the symmetrical and (b) asymmetrical cross-shaped hole in x-direction (Dx ¼ 30 nm), respectively. The electric fields are only distributed at the edges of cross-shaped hole and possess the axial symmetry along the incident light polarization in these two cases. (c) and (d) are the electric field distributions of the 1038 nm peak and 1220 nm peak, respectively. The two peaks correspond to y-axis directional asymmetrical cross-shaped hole (Dy ¼30 nm). The electric field of the 1038 nm peak is only distributed at the lower part edges of the asymmetric cross-shaped hole, while the electric field of the 1220 nm peak is only distributed at the upper part edges.
Fig. 5. The transmission spectra as a function of the asymmetry (Dx and Dy). (a) While Dx increasing, the 840 nm peak almost does not move and the 1168 nm peak exhibits little redshift after Dx4110 nm. (b) While Dy increasing, the 840 nm peak also almost does not move and the 1168 nm peak splits into two peaks which are located at shorter and longer wavelengths than that of 1168 nm peak, respectively. The ‘‘shorter peak’’ exhibits blueshift and disappears after Dy4120 nm. The ‘‘longer peak’’ exhibits redshift. When Dy¼ 155 nm, the 1168 nm peak exhibits large redshift of 344 nm.
B. Ni et al. / Optics Communications 298–299 (2013) 237–241
cross-shaped hole in the direction vertical to the light polarization than in the direction that parallel to the light polarization. The 1168 nm peak is split into two peaks when the cross-shaped hole symmetry in y-axis direction is broken. However, it is found that there is no obvious change of transmissions with changing the asymmetry in x-axis direction. The results may be utilized to tune the electromagnetic wave in subwavelength optics.
Acknowledgment This work was supported in part by the State Key Program for Basic Research of China Grants (2011CB922004, 2013CB632705), the National Natural Science Foundation of China Grants (10990104, 60976092 and 61290301); the Fund of Shanghai Science and Technology Foundation Grant (10JC1416100). References [1] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Nature 391 (1998) 667. [2] A. Degiron, H.J. Lezec, W.L. Barnes, T.W. Ebbesen, Applied Physics Letters 81 (2002) 4327. [3] A. Degiron, T.W. Ebbesen, Journal of Optics A: Pure and Applied Optics 7 (2005) S90. [4] S.M. Williams, A.D. Stafford, T.M. Rogers, S.R. Bishop, J.V. Coe, Applied Physics Letters 85 (2004) 1472. [5] K.L. van der Molen, K.J. Klein Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, L. Kuipers, Physical Review B 72 (2005) 045421. [6] F. Przybilla, A. Degiron, J.Y. Laluet, C. Genet, T.W. Ebbesen, Journal of Optics A: Pure and Applied Optics 8 (2006) 458. [7] M.W. Tsai, T.H. Chuang, H.Y. Chang, S.C. Lee, Applied Physics Letters 88 (2006) 213112. [8] C.Y. Chen, M.W. Tsai, T.H. Chuang, Y.T. Chang, S.C. Lee, Applied Physics Letters 91 (2007) 063108. [9] J.Y. Li, Y.L. Hua, J.X. Fu, Z.Y. Li, Journal of Applied Physics 107 (2010) 073101.
241
[10] M. Najiminaini, F. Vasefi, B. Kaminska, J.L. Carson, Optics Express 18 (2010) 22255. [11] E. Popov, M. Nevie0 re, S. Enoch, R. Reinisch, Physical Review B 62 (16) (2000) 100. [12] L. Salomon, F. Grillot, A.V. Zayats, F. de Fornel, Physical Review Letters 86 (2001) 1110. [13] L. Martı´n-Moreno, F.J. Garcı´a-Vidal, H.J. Lezec, K.M. Pellerin, T. Thio, J.B. Pendry, T.W. Ebbesen, Physical Review Letters 86 (2001) 1114. [14] S. Enoch, E. Popov, M. Neviere, R. Reinisch, Journal of Optics A: Pure and Applied Optics 4 (2002) S83. [15] P. Lalanne, C. Sauvan, J.P. Hugonin, J.C. Rodier, P. Chavel, Physical Review B 68 (2003) 125404. [16] K.L. van der Molen, K.J. Klein Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, L. Kuipers, Physical Review B 72 (2005) 045421. [17] R. Gordon, A.G. Brolo, Optics Express 13 (2005) 1933. [18] K.J. Webb, J. Li, Physical Review B 73 (2006) 033401. [19] A. Mary, G. Rodrigo, L. Martı´n-Moreno, F.J. Garcı´a-Vidal1, Physical Review B 76 (2007) 195414. [20] M. Zhang, C.P. Huang, G.D. Wang, Y.Y. Zhu, Journal of Optics—IOP Science 12 (2010) 015004. [21] M.D. He, J.Q. Liu, Z.Q. Gong, Y.F. Luo, X.S. Chen, Solid State Communications 150 (2010) 104. [22] Y.M. Strelniker, Physical Review B 76 (2007) 085409. [23] X.Y. He, X.N. Fu, Y.W. Luo, Journal of Modern Optics 56 (15) (2009) 1698. [24] X.Y. He, Optics Express 17 (17) (2009) 15359. [25] X.Y. He, Q.J. Wang, S.F. Yu, IEEE Journal of Quantum Electronics 48 (12) (2012) 1554. [26] M. Bayindir, K. Aydin, E. Ozbay, P. Markoˇs, C.M. Soukoulis, Applied Physics Letters 81 (2002) 120. [27] Y. Yuan, C. Bingham, T. Tyler, S. Palit, T.H. Hand, W.J. Padilla, D.R. Smith, N.M. Jokerst, S.A. Cummer, Optics Express 16 (2008) 9746. [28] M. Li, Z.C. Wen, J.X. Fu, X. Fang, Y.M. Dai, R.J. Liu, X.F. Han, X.G. Qiu, Journal of Physics D: Applied Physics 42 (2009) 115420. [29] K.J. Wang, L. Ding, J.S. Liu, J. Zhang, X.M. Yang, J.Y. Chin, T.J. Cui, Optics Express 19 (2011) 11375. [30] Y.G. Chen, Y.H. Wang, Y. Zhang, S.T. Liu, Optics Communications 274 (2007) 236. [31] EastFDTD v2.0, DONGJUN Science and Technology Co. China. [32] X.R. Huang, R.W. Peng, Z. Wang, F. Gao, S.S. Jiang, Physical Review A 76 (2007) 035802.