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Extraordinary transmission through periodic coaxial aperture arrays at terahertz frequencies
Optik 127 (2016) 178–181
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Extraordinary transmission through periodic coaxial aperture arrays at terahertz frequencies Dan Hu a,∗ , Yan Zhang b a b
College of Physics and Electrical Engineering, Anyang Normal University, Anyang 455002, China Department of Physics, Capital Normal University, Beijing Key Laboratory of Metamaterials and Devices, Beijing 100048, China
a r t i c l e
i n f o
Article history: Received 8 October 2014 Accepted 7 September 2015 Keywords: Terahertz Coaxial aperture arrays Extraordinary transmission
a b s t r a c t Utilizing the finite-difference time-domain (FDTD) method simulation, transmission properties of normally incident plane wave through symmetric and asymmetric cruciform metallic coaxial aperture arrays (CAAs) are investigated. It is found that odd-order resonant peaks can be observed in symmetric CAAs, and both odd- and even-order ones are showed in asymmetric structure. Moreover, the positions of the resonant peaks are not sensitive to the symmetry of coaxial aperture and the polarization of incident light, but strongly depend on the average circumference in a periodic cell. This assumption is further confirmed by examining the CAAs with different circumferences, shapes, as well as periodicities. The underlying origin of multiple resonances is discussed by the simulated fields. These investigations will facilitate the design of desired operating frequencies for various potential applications such as filters and sensors. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction The demonstration of extraordinary transmission (ET) through the optically thick metallic film pierced with a periodic array of subwavelength holes has renewed opticists’ enthusiasm about exploring surface plasmon [1]. Afterwards, Baida et al. proposed a kind of new structure: sub-wavelength annular apertures arrays for achieving high transmission [2]. The structure can enhance optical transmission up to 90% in optical regime due to that a coaxial aperture structure can provide larger cut-off wavelength than a circular one [3]. To date, many theoretical [4–6] and experimental [7–11] studies of the ET properties have been reported. It has been found that the enhanced optical transmission peaks in coaxial aperture structures are mainly attributed to several mechanisms: delocalized (global) surface plasmon [6], localized surface plasmon [9], and resonances of TEm,1 guide modes [12]. Recently, Huang et al. have advanced a charge oscillation-induced light emission mechanism and showed a concrete picture of spoof surface plasmons combined with cavity resonance for the ET phenomenon [13]. The manipulation of light with artificial holes arrays on a subwavelength scale can be affected by the shape [14], periodicity [15], and orientation of polarization [16]. The influence of holeshape on propagation and transmission of light through a single
hole or hole arrays in metals have been investigated for many different shapes including cylindrical coaxial [4], rectangular coaxial [17], rectangle-in-cylinder coaxial [18], polygonal coaxial [6], H[19,20], E-shaped [14], double-hole [21,22], and triangular [23]. In this article, we investigate the transmission characteristics of terahertz pulses through symmetric and asymmetric cruciform metallic CAAs by using the three-dimensional finite difference time-domain method. It is found that odd-order resonant peaks can be observed in symmetric CAAs, both odd- and even-order ones are showed in asymmetric structure. Moreover, the positions of the resonant peaks are insensitive to the symmetry of coaxial aperture and the polarization of incident light, but are determined by the average circumference of the coaxial aperture within a periodic cell. This assumption is further confirmed by examining the CAAs with different circumferences, shapes, as well as periodicities. The underlying origin of multiple resonances is explained by the distribution of the oscillating charges on metal surfaces. This paper is arranged as follows: Section 2 presents the structure design and simulation method, Section 3 gives the simulation results and discussions, and Section 4 summary the conclusions obtained in this paper.
2. Structure design and simulation method ∗ Corresponding author. Tel.: +86 18738222975. E-mail address: [email protected] (D. Hu). http://dx.doi.org/10.1016/j.ijleo.2015.09.047 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
Fig. 1 shows pictures of the two cruciform CAAs. The first type is a perfect symmetric cruciform CAAs structure in which all arms have
D. Hu, Y. Zhang / Optik 127 (2016) 178–181
179
Fig. 1. Schematic of a symmetric CAAs (a) and an asymmetric cruciform CAAs (b).
the same lengths (see Fig. 1(a)). In the second type, we gently break the symmetry between the right and left arms (w1 = / w2 ); .i.e. the asymmetric cruciform CAAs considered here are symmetric to the x axis and asymmetric to the y axis (see Fig. 1(b)). These structures parameters are: l1 = 40 m, l2 = 200 m, l3 = 30 m, w1 = 110 m, w2 = 50 m, and period = 300 m. The thickness of the metal film is fixed as 50 m. The gray and white parts denote aluminum (Al) and air, respectively. We employ numerical simulations based on the finite-difference time-domain method to investigate the transmission properties of the proposed structures [24]. The calculated constant space step is 1.25 m × 1.25 m × 1.25 m. Since the metallic structure is periodic in the x and y directions, the periodic boundary conditions are imposed in these directions, while in the propagation direction the perfectly matched absorbing boundary conditions are applied at the two ends of the computational space. The polarized plane wave is used as the light source. The metal Al is described by the perfect electric conductivity to fit its realistic characteristic, because the conductivity of the metal is extreme high at terahertz frequencies.
Fig. 2. Transmission spectra for the proposed symmetric cruciform CAAs (a) and asymmetric cruciform CAAs (b).
3. Results and discussion The zero-order transmission spectrum of the metallic film perforated with an array of symmetric cruciform CAAs is shown in Fig. 2(a). Three distinct peaks are located at 0.40 THz, 1.19 THz, and 1.97 THz, respectively. Additionally, according to the momentum matching conduction, the calculated fundamental [1,0] and [2,0] order surface plasmon modes due to periodicity are located at 1.00 THz and 2.00 THz, which agree well with the simulated results. Different responses are observed in the transmission spectra of the asymmetric cruciform CAAs, as shown in Fig. 2(b). Apart from the three resonant peaks mentioned above, two new resonant peaks appear in the transmission spectra of the proposed asymmetric structure. They are located at 0.79 THz and 1.59 THz, respectively. The fundamental order surface plasmon modes in the transmission spectra is also visible at 1.00 THz. From Fig. 2(b), it is also found that these resonant peaks always appear and their positions are not changed, regardless of the incidence electric field parallel to the x-axis or y-axis. Moreover, breaking the symmetry of the cruciform CAAs has little effect on the positions of these resonant peaks. Here some questions rise: Why do the two new resonant peaks cannot appear in the transmission spectra of the symmetric cruciform CAAs, but appear in that of the asymmetric
Fig. 3. Simulated Ez and Hz distributions on the surface of symmetric cruciform CAAs. The snapshot moment is when the field amplitude reached its maximum. Only one periodicity on the x–y plane is shown. The polarization of the illuminating electric field E is chosen to be polarized parallel to the y axis. The field quantity is normalized with respect to the incident field E0 .
one? What parameters mainly determine the positions of these resonant peaks? For answering the above questions and further insight into the origins of the resonant peaks in these structures, the electric and magnetic fields distributions at z = 5 m above/below the structures for symmetric and asymmetric cruciform CAAs are shown in Figs. 3 and 4, respectively. The characters of the resonant peaks can be explained using the distributions of Ez component. The positive and negative charges alternately accumulate on entrance/exit edges at each side of the coaxial aperture (Fig. 3(a), (d), (g) and (b), (e), (h)), and form some dipoles. Since these dipoles oscillate with
180
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Fig. 5. Multiple resonant frequencies from simulation (black squares) and theoretical calculation (red dots) are plotted vs. the resonant modes. The first three CAAs are simulated with same period = 300 m and different average circumferences including (a) L = 920 m, (b) L = 940 m, and (c) L = 1020 m. The last one is simulated with period = 500 m and L = 1160 m. The blue double arrows stand for the polarized direction of the incidence terahertz wave. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Simulated Ez and Hz distributions on the surface of asymmetric cruciform CAAs. The snapshot moment is when the field amplitude reached its maximum. Only one unit cell on the x–y plane is shown. The polarization of the illuminating electric field E is parallel to the y axis. The field quantity is normalized with respect to the incident field E0 .
the incident electric field, they can form standing waves in the aperture and act as light sources emitting photons on the exit end. The interference between the photons radiated from each unit leads to the ET [13]. For the symmetric structure, it can be concluded from the Ez -component distribution that the opposite directions of electric polarizations P appear in pairs on the exit end of the horizontal slits opening in each unit cell. They are antiphase so that the electric polarizations P cancel each other out in the far field and do not contribute to the ET. However, on the exit end of the vertical slits opening, there are same phase (Fig. 3(b) and (h)) or both the same and opposite phase (Fig. 3(e)). Consequently, their interactions can lead to the ET. For simplicity, we only discuss the two new resonant peaks with the resonant frequencies of 0.79 THz and 1.59 THz for the asymmetric structure. Positive and negative charges also alternately accumulate on entrance/exit edges at each side of the CAAs (Fig. 4(e) and (k)), and form dipoles. The opposite directions of electric polarizations P of the dipoles in pairs appear on the exit end of the horizontal and vertical slits opening in each unit cell. Because the electric polarizations P of the dipoles appearing on the exit end of the asymmetric structures are not total equal, so the interaction between them cannot totally offset each other in the far field. For symmetric structure, interactions between the opposite directions of electric polarizations P of the dipoles absolutely cancel each other out and cannot lead to transmission enhancement in the far field. From the Hz -component of the fields, one can also easily see that positive and negative magnetic fields do not symmetrically distribute around the coaxial aperture (Fig. 4(f) and (l)). Therefore, the total magnetic fields cannot offset each other in the far field. That is why the two new resonant peaks cannot emerge for the symmetric structure, but can appear for asymmetric one.
For the proposed cruciform CAAs with narrow gap, the localized surface plasmon can be excited under terahertz wave illumination. The opposite surface charges distribute on the entrance/exit surface and form standing waves, which are assembled at the edges of the apertures. Therefore, the resonant frequencies should satisfy the follow condition: m·c fm = (1) L where fm is the resonant frequency, m is the order of resonant mode, c is the speed of light in vacuum, and L is the average of the outer and inner edge circumferences of the coaxial aperture. For the proposed cruciform CAAs, both the average circumferences (L) are 780 m. According to the Eq. (1), the calculated first five plamonic modes are, respectively, 0.38 THz, 0.77 THz, 1.15 THz, 1.54 THz, and 1.92 THz, which are in good agreement with the simulated results. In order to confirm our prediction, we investigate the influence of CAAs’ structural parameters on the resonant transmission peak response for horizontal polarized terahertz wave. In this case, the metal film thickness and the gap of CAAs are fixed as 50 m and 5 m, respectively. We simulate CAAs with different shapes, such as C-shaped, E-shaped, cruciform, and square CAAs. The average circumferences of the first three CAAs are, respectively, L = 920 m, 940 m, and 1020 m, and their periods are all 300 m. The fourth CAAs has the average circumference of 1160 m and period of 500 m. Fig. 5 presents the simulation results and the corresponding shapes are shown in the inserts. The corresponding resonant frequencies for different CAAs agree well with the theoretical calculation results. From Fig. 5, one can find that these resonant frequencies are insensitive to the geometric shape and period, but strongly depend on the average circumference of the CAAs. In short, the model of the plasmonic resonances, indeed, unambiguously provides the universal expression for the multiple resonances in CAAs with narrow gap, and allows additionally us to accurately estimate the modes, frequencies, and responses of those plasmonic resonances. 4. Conclusion In summary, we numerically investigate the ET characteristics of the CAAs with narrow gap. The calculated results reveal that the multiple resonant frequencies are insensitive to the
D. Hu, Y. Zhang / Optik 127 (2016) 178–181
structural shape, periodicity, and polarization of the incident light, but strongly depend on the average circumference of the coaxial aperture. The resonant frequencies for different CAAs are in line with theoretical calculation. Both odd- and even-order resonant peaks are showed in asymmetric CAAs, and odd-order ones can be observed in symmetric structure. The simulated fields distributions explain all the results well. The model of the plasmonic resonances establishes a design guidance of the CAAs structures for practical electromagnetic applications. Acknowledgements This work was partly supported by the 973 Program of China (No. 2013CBA01702), the National Natural Science Foundation of China (Nos. 11204188, 61205097, 91233202, 11174211 and 11504006), the National High Technology Research and Development Program of China (No. 2012AA101608-6), the Beijing Natural Science Foundation (No. KZ201110028035), the Program for New Century Excellent Talents in University, the Key Scientific Research Project of Higher Education of Henan Province (No. 15A140002) and the Science and Technology Planning Project of Henan Province (No. 142300410366). References [1] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Extraordinary optical transmission through sub-wavelength hole arrays, Nature 391 (1998) 667–669. [2] F.I. Baida, D.V. Labeke, Light transmission by subwavelength annular aperture arrays in metallic films, Opt. Commun. 209 (2002) 17–22. [3] Y. Poujet, J. Salvi, F.I. Baida, 90% extraordinary optical transmission in the visible range through annular aperture metallic arrays, Opt. Lett. 32 (2007) 2942–2944. [4] M.I. Haftel, C. Schlockermann, G. Blumberg, Role of cylindrical surface plasmons in enhanced transmission, Appl. Phys. Lett. 88 (2006) 193104–193106. [5] S.M. Orbons, A. Roberts, Resonance and extraordinary transmission in annular aperture arrays, Opt. Express 14 (2006) 12623–12628. [6] J. Wang, W. Zhou, P. Li, Enhancing the light transmission of plasmonic metamaterials through polygonal aperture arrays, Opt. Express 17 (2009) 20349–20354. [7] W.J. Fan, S. Zhang, B. Minhas, K.J. Malloy, S.R.J. Brueck, Enhanced infrared transmission through subwavelength coaxial metallic arrays, Phys. Rev. Lett. 94 (2005) 033902.
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[8] Y. Poujet, M. Roussey, J. Salvi, F.I. Baida, D. Van, V. Labeke, A. Perentes, C. Santschi, P. Hoffmann, Super-transmission of light through subwavelength annular aperture arrays in metallic films: spectral analysis and near-field optical images in the visible range, Photon. Nanostruct. 4 (2006) 47–53. [9] C.K. Chang, D.Z. Lin, C.S. Yeh, C.K. Lee, Y.C. Chang, M.W. Lin, J.T. Yeh, J.M. Liu, Experimental analysis of surface plasmon behavior in metallic circular slits, Appl. Phys. Lett. 90 (2007) 061113–061115. [10] S.M. Orbons, M.I. Haftel, C. Schlockermann, D. Freeman, M. Milicevic, T.J. Davis, B. Luther, D.N. Davies, A. Jamieson, Roberts, Dual resonance mechanisms facilitating enhanced optical transmission in coaxial waveguide arrays, Opt. Lett. 33 (2008) 821–823. [11] M.J. Kofke, D.H. Waldeck, Z. Fakhraai, S. Lp, G.C. Walker, The effect of periodicity on the extraordinary optical transmission of annular aperture arrays, Appl. Phys. Lett. 94 (2009) 023104–023106. [12] F.I. Baida, D. Vanlabe, G. Granet, A. Moreau, A. Belkhir, Origin of the superenhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands, Appl. Phys. B 79 (2004) 1–8. [13] X.R. Huang, R.W. Peng, Z. Wang, F. Gao, S.S. Jiang, Charge-oscillation-induced light transmission through subwavelength slits and holes, Phys. Rev. A 76 (2007) 035802. [14] N. Zhang, P.H. Zhou, J.L. Xie, L.J. Deng, Comparisons of two subwavelength aperture arrays with different lattice structure for light transmission, Optik 124 (2013) 2401–2405. [15] R.J. Singh, C. Rockstuhl, W.L. Zhang, Strong influence of packing density in terahertz metamaterials, Appl. Phys. Lett. 97 (2010) 241108–241110. [16] H. Luo, X.L. Wang, M. Wen, Z.Y. Chen, W. Guo, W.H. Zhu, Effects of incident light polarization on optical transmittance through subwavelength metal holes arrays, Optik 124 (2013) 2020–2022. [17] X.C. Lu, J.G. Han, W.L. Zhang, Transmission field enhancement of terahertz pulses in plasmonic, rectangular coaxial geometries, Opt. Lett. 35 (2010) 904–906. [18] S. Wu, Q.J. Wang, X.G. Yin, J.Q. Li, D. Zhu, S.Q. Liu, Y.Y. Zhu, Enhanced optical transmission: role of the localized surface plasmon, Appl. Phys. Lett. 93 (2008) 101113–101115. [19] M. Sun, R.J. Liu, Z.Y. Li, B.Y. Cheng, D.Z. Zhang, H.F. Yang, A.Z. Jin, Enhanced near-infrared transmission through periodic H-shaped arrays, Phys. Lett. A 365 (2007) 510–513. [20] R.J. Liu, J.X. Fu, Z.Y. Li, Near-field analysis of the transmission properties of subwavelength periodic H-shaped arrays in thin metal film, J. Opt. 12 (2010) 065002. [21] L.K.S. Kumar, A. Lesuffleur, M.C. Hughes, R. Gordon, Double nanohole apexenhanced transmission in metal films, Appl. Phys. B 84 (2006) 25–28. [22] S. Iyer, S. Popov, A.T. Friberg, Impact of apexes on the resonance shift in double hole nanocavities, Opt. Express 18 (2010) 193–203. [23] J.H. Kim, P.J. Moyer, Transmission characteristics of metallic equilateral triangular nanohole arrays, Appl. Phys. Lett. 89 (2006) 121106–121108. [24] Simulations were performed using the software package CONCERTO 7.5, developed by Vector Fields Limited, England, 2012.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Extraordinary transmission through periodic coaxial aperture arrays at terahertz frequencies Dan Hu a,∗ , Yan Zhang b a b
College of Physics and Electrical Engineering, Anyang Normal University, Anyang 455002, China Department of Physics, Capital Normal University, Beijing Key Laboratory of Metamaterials and Devices, Beijing 100048, China
a r t i c l e
i n f o
Article history: Received 8 October 2014 Accepted 7 September 2015 Keywords: Terahertz Coaxial aperture arrays Extraordinary transmission
a b s t r a c t Utilizing the finite-difference time-domain (FDTD) method simulation, transmission properties of normally incident plane wave through symmetric and asymmetric cruciform metallic coaxial aperture arrays (CAAs) are investigated. It is found that odd-order resonant peaks can be observed in symmetric CAAs, and both odd- and even-order ones are showed in asymmetric structure. Moreover, the positions of the resonant peaks are not sensitive to the symmetry of coaxial aperture and the polarization of incident light, but strongly depend on the average circumference in a periodic cell. This assumption is further confirmed by examining the CAAs with different circumferences, shapes, as well as periodicities. The underlying origin of multiple resonances is discussed by the simulated fields. These investigations will facilitate the design of desired operating frequencies for various potential applications such as filters and sensors. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction The demonstration of extraordinary transmission (ET) through the optically thick metallic film pierced with a periodic array of subwavelength holes has renewed opticists’ enthusiasm about exploring surface plasmon [1]. Afterwards, Baida et al. proposed a kind of new structure: sub-wavelength annular apertures arrays for achieving high transmission [2]. The structure can enhance optical transmission up to 90% in optical regime due to that a coaxial aperture structure can provide larger cut-off wavelength than a circular one [3]. To date, many theoretical [4–6] and experimental [7–11] studies of the ET properties have been reported. It has been found that the enhanced optical transmission peaks in coaxial aperture structures are mainly attributed to several mechanisms: delocalized (global) surface plasmon [6], localized surface plasmon [9], and resonances of TEm,1 guide modes [12]. Recently, Huang et al. have advanced a charge oscillation-induced light emission mechanism and showed a concrete picture of spoof surface plasmons combined with cavity resonance for the ET phenomenon [13]. The manipulation of light with artificial holes arrays on a subwavelength scale can be affected by the shape [14], periodicity [15], and orientation of polarization [16]. The influence of holeshape on propagation and transmission of light through a single
hole or hole arrays in metals have been investigated for many different shapes including cylindrical coaxial [4], rectangular coaxial [17], rectangle-in-cylinder coaxial [18], polygonal coaxial [6], H[19,20], E-shaped [14], double-hole [21,22], and triangular [23]. In this article, we investigate the transmission characteristics of terahertz pulses through symmetric and asymmetric cruciform metallic CAAs by using the three-dimensional finite difference time-domain method. It is found that odd-order resonant peaks can be observed in symmetric CAAs, both odd- and even-order ones are showed in asymmetric structure. Moreover, the positions of the resonant peaks are insensitive to the symmetry of coaxial aperture and the polarization of incident light, but are determined by the average circumference of the coaxial aperture within a periodic cell. This assumption is further confirmed by examining the CAAs with different circumferences, shapes, as well as periodicities. The underlying origin of multiple resonances is explained by the distribution of the oscillating charges on metal surfaces. This paper is arranged as follows: Section 2 presents the structure design and simulation method, Section 3 gives the simulation results and discussions, and Section 4 summary the conclusions obtained in this paper.
2. Structure design and simulation method ∗ Corresponding author. Tel.: +86 18738222975. E-mail address: [email protected] (D. Hu). http://dx.doi.org/10.1016/j.ijleo.2015.09.047 0030-4026/© 2015 Elsevier GmbH. All rights reserved.
Fig. 1 shows pictures of the two cruciform CAAs. The first type is a perfect symmetric cruciform CAAs structure in which all arms have
D. Hu, Y. Zhang / Optik 127 (2016) 178–181
179
Fig. 1. Schematic of a symmetric CAAs (a) and an asymmetric cruciform CAAs (b).
the same lengths (see Fig. 1(a)). In the second type, we gently break the symmetry between the right and left arms (w1 = / w2 ); .i.e. the asymmetric cruciform CAAs considered here are symmetric to the x axis and asymmetric to the y axis (see Fig. 1(b)). These structures parameters are: l1 = 40 m, l2 = 200 m, l3 = 30 m, w1 = 110 m, w2 = 50 m, and period = 300 m. The thickness of the metal film is fixed as 50 m. The gray and white parts denote aluminum (Al) and air, respectively. We employ numerical simulations based on the finite-difference time-domain method to investigate the transmission properties of the proposed structures [24]. The calculated constant space step is 1.25 m × 1.25 m × 1.25 m. Since the metallic structure is periodic in the x and y directions, the periodic boundary conditions are imposed in these directions, while in the propagation direction the perfectly matched absorbing boundary conditions are applied at the two ends of the computational space. The polarized plane wave is used as the light source. The metal Al is described by the perfect electric conductivity to fit its realistic characteristic, because the conductivity of the metal is extreme high at terahertz frequencies.
Fig. 2. Transmission spectra for the proposed symmetric cruciform CAAs (a) and asymmetric cruciform CAAs (b).
3. Results and discussion The zero-order transmission spectrum of the metallic film perforated with an array of symmetric cruciform CAAs is shown in Fig. 2(a). Three distinct peaks are located at 0.40 THz, 1.19 THz, and 1.97 THz, respectively. Additionally, according to the momentum matching conduction, the calculated fundamental [1,0] and [2,0] order surface plasmon modes due to periodicity are located at 1.00 THz and 2.00 THz, which agree well with the simulated results. Different responses are observed in the transmission spectra of the asymmetric cruciform CAAs, as shown in Fig. 2(b). Apart from the three resonant peaks mentioned above, two new resonant peaks appear in the transmission spectra of the proposed asymmetric structure. They are located at 0.79 THz and 1.59 THz, respectively. The fundamental order surface plasmon modes in the transmission spectra is also visible at 1.00 THz. From Fig. 2(b), it is also found that these resonant peaks always appear and their positions are not changed, regardless of the incidence electric field parallel to the x-axis or y-axis. Moreover, breaking the symmetry of the cruciform CAAs has little effect on the positions of these resonant peaks. Here some questions rise: Why do the two new resonant peaks cannot appear in the transmission spectra of the symmetric cruciform CAAs, but appear in that of the asymmetric
Fig. 3. Simulated Ez and Hz distributions on the surface of symmetric cruciform CAAs. The snapshot moment is when the field amplitude reached its maximum. Only one periodicity on the x–y plane is shown. The polarization of the illuminating electric field E is chosen to be polarized parallel to the y axis. The field quantity is normalized with respect to the incident field E0 .
one? What parameters mainly determine the positions of these resonant peaks? For answering the above questions and further insight into the origins of the resonant peaks in these structures, the electric and magnetic fields distributions at z = 5 m above/below the structures for symmetric and asymmetric cruciform CAAs are shown in Figs. 3 and 4, respectively. The characters of the resonant peaks can be explained using the distributions of Ez component. The positive and negative charges alternately accumulate on entrance/exit edges at each side of the coaxial aperture (Fig. 3(a), (d), (g) and (b), (e), (h)), and form some dipoles. Since these dipoles oscillate with
180
D. Hu, Y. Zhang / Optik 127 (2016) 178–181
Fig. 5. Multiple resonant frequencies from simulation (black squares) and theoretical calculation (red dots) are plotted vs. the resonant modes. The first three CAAs are simulated with same period = 300 m and different average circumferences including (a) L = 920 m, (b) L = 940 m, and (c) L = 1020 m. The last one is simulated with period = 500 m and L = 1160 m. The blue double arrows stand for the polarized direction of the incidence terahertz wave. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Simulated Ez and Hz distributions on the surface of asymmetric cruciform CAAs. The snapshot moment is when the field amplitude reached its maximum. Only one unit cell on the x–y plane is shown. The polarization of the illuminating electric field E is parallel to the y axis. The field quantity is normalized with respect to the incident field E0 .
the incident electric field, they can form standing waves in the aperture and act as light sources emitting photons on the exit end. The interference between the photons radiated from each unit leads to the ET [13]. For the symmetric structure, it can be concluded from the Ez -component distribution that the opposite directions of electric polarizations P appear in pairs on the exit end of the horizontal slits opening in each unit cell. They are antiphase so that the electric polarizations P cancel each other out in the far field and do not contribute to the ET. However, on the exit end of the vertical slits opening, there are same phase (Fig. 3(b) and (h)) or both the same and opposite phase (Fig. 3(e)). Consequently, their interactions can lead to the ET. For simplicity, we only discuss the two new resonant peaks with the resonant frequencies of 0.79 THz and 1.59 THz for the asymmetric structure. Positive and negative charges also alternately accumulate on entrance/exit edges at each side of the CAAs (Fig. 4(e) and (k)), and form dipoles. The opposite directions of electric polarizations P of the dipoles in pairs appear on the exit end of the horizontal and vertical slits opening in each unit cell. Because the electric polarizations P of the dipoles appearing on the exit end of the asymmetric structures are not total equal, so the interaction between them cannot totally offset each other in the far field. For symmetric structure, interactions between the opposite directions of electric polarizations P of the dipoles absolutely cancel each other out and cannot lead to transmission enhancement in the far field. From the Hz -component of the fields, one can also easily see that positive and negative magnetic fields do not symmetrically distribute around the coaxial aperture (Fig. 4(f) and (l)). Therefore, the total magnetic fields cannot offset each other in the far field. That is why the two new resonant peaks cannot emerge for the symmetric structure, but can appear for asymmetric one.
For the proposed cruciform CAAs with narrow gap, the localized surface plasmon can be excited under terahertz wave illumination. The opposite surface charges distribute on the entrance/exit surface and form standing waves, which are assembled at the edges of the apertures. Therefore, the resonant frequencies should satisfy the follow condition: m·c fm = (1) L where fm is the resonant frequency, m is the order of resonant mode, c is the speed of light in vacuum, and L is the average of the outer and inner edge circumferences of the coaxial aperture. For the proposed cruciform CAAs, both the average circumferences (L) are 780 m. According to the Eq. (1), the calculated first five plamonic modes are, respectively, 0.38 THz, 0.77 THz, 1.15 THz, 1.54 THz, and 1.92 THz, which are in good agreement with the simulated results. In order to confirm our prediction, we investigate the influence of CAAs’ structural parameters on the resonant transmission peak response for horizontal polarized terahertz wave. In this case, the metal film thickness and the gap of CAAs are fixed as 50 m and 5 m, respectively. We simulate CAAs with different shapes, such as C-shaped, E-shaped, cruciform, and square CAAs. The average circumferences of the first three CAAs are, respectively, L = 920 m, 940 m, and 1020 m, and their periods are all 300 m. The fourth CAAs has the average circumference of 1160 m and period of 500 m. Fig. 5 presents the simulation results and the corresponding shapes are shown in the inserts. The corresponding resonant frequencies for different CAAs agree well with the theoretical calculation results. From Fig. 5, one can find that these resonant frequencies are insensitive to the geometric shape and period, but strongly depend on the average circumference of the CAAs. In short, the model of the plasmonic resonances, indeed, unambiguously provides the universal expression for the multiple resonances in CAAs with narrow gap, and allows additionally us to accurately estimate the modes, frequencies, and responses of those plasmonic resonances. 4. Conclusion In summary, we numerically investigate the ET characteristics of the CAAs with narrow gap. The calculated results reveal that the multiple resonant frequencies are insensitive to the
D. Hu, Y. Zhang / Optik 127 (2016) 178–181
structural shape, periodicity, and polarization of the incident light, but strongly depend on the average circumference of the coaxial aperture. The resonant frequencies for different CAAs are in line with theoretical calculation. Both odd- and even-order resonant peaks are showed in asymmetric CAAs, and odd-order ones can be observed in symmetric structure. The simulated fields distributions explain all the results well. The model of the plasmonic resonances establishes a design guidance of the CAAs structures for practical electromagnetic applications. Acknowledgements This work was partly supported by the 973 Program of China (No. 2013CBA01702), the National Natural Science Foundation of China (Nos. 11204188, 61205097, 91233202, 11174211 and 11504006), the National High Technology Research and Development Program of China (No. 2012AA101608-6), the Beijing Natural Science Foundation (No. KZ201110028035), the Program for New Century Excellent Talents in University, the Key Scientific Research Project of Higher Education of Henan Province (No. 15A140002) and the Science and Technology Planning Project of Henan Province (No. 142300410366). References [1] T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Extraordinary optical transmission through sub-wavelength hole arrays, Nature 391 (1998) 667–669. [2] F.I. Baida, D.V. Labeke, Light transmission by subwavelength annular aperture arrays in metallic films, Opt. Commun. 209 (2002) 17–22. [3] Y. Poujet, J. Salvi, F.I. Baida, 90% extraordinary optical transmission in the visible range through annular aperture metallic arrays, Opt. Lett. 32 (2007) 2942–2944. [4] M.I. Haftel, C. Schlockermann, G. Blumberg, Role of cylindrical surface plasmons in enhanced transmission, Appl. Phys. Lett. 88 (2006) 193104–193106. [5] S.M. Orbons, A. Roberts, Resonance and extraordinary transmission in annular aperture arrays, Opt. Express 14 (2006) 12623–12628. [6] J. Wang, W. Zhou, P. Li, Enhancing the light transmission of plasmonic metamaterials through polygonal aperture arrays, Opt. Express 17 (2009) 20349–20354. [7] W.J. Fan, S. Zhang, B. Minhas, K.J. Malloy, S.R.J. Brueck, Enhanced infrared transmission through subwavelength coaxial metallic arrays, Phys. Rev. Lett. 94 (2005) 033902.
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