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Graphene-supported tunable extraordinary transmission
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Nanotechnology 25 325201 (http://iopscience.iop.org/0957-4484/25/32/325201) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 134.153.184.170 This content was downloaded on 03/08/2014 at 15:45
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Nanotechnology Nanotechnology 25 (2014) 325201 (6pp)
doi:10.1088/0957-4484/25/32/325201
Graphene-supported tunable extraordinary transmission Xiaoyong He1 and Hongxia Lu2 1
Mathematics & Science College, Shanghai Normal University, No. 100 Guilin Rd., Shanghai, 200234, People’s Republic of China 2 School of Material Science and Engineering, Zhengzhou University, No. 100 Science Rd., Zhengzhou, Henan, 450001, People’s Republic of China E-mail: [email protected] Received 2 April 2014, revised 8 June 2014 Accepted for publication 17 June 2014 Published 25 July 2014 Abstract
By depositing a graphene layer on the metallic film with subwavelength hole arrays, the tunable extraordinary transmission property based on the metal-dielectrics-graphene (MDG) structure has been investigated in the terahertz (THz) and near-infrared (NIR) regimes. The influences of operation frequency, composed materials, and the Fermi level of the graphene layer have been taken into account. The results show that by varying the Fermi level of the graphene layer, the transmission of the MDG structure can be tuned in a wide range and the modulation depth of the peak value of the transmission can reach more than 50%. But the tunable mechanisms in the THz and NIR regimes are quite different. In the infrared (THz) regime, the graphene behaves like the dielectric (metallic) layer; its dielectric constant decreases (increases) with the increase of Fermi level, resulting in the transmission increasing (decreasing). Compared with the metallic structure, the transmission of the semiconductor structure can also be modulated by using the doping or varying temperature; its peak position can also be changed in a much broader range. The results are very useful to understand the mechanism of the graphene plasmonic devices and to design novel filters, switchers, modulators, and sensors. Keywords: terahertz, graphene, extraordinary transmission, surface plasmon (Some figures may appear in colour only in the online journal) 1. Introduction
subwavelength scale [8–12]. The MHA structure manifests potential applications in many fields, such as near-field microscopy, resonators, and microlens [13, 14]. For instance, with the help of the semiconductor gain layer, the MHA structure can be used as resonators to fabricate SP lasers and has been realized experimentally [15]. Graphene, a flat monolayer of carbon atoms packed into a dense 2D honeycomb crystal lattice, has the merits of near-zero effective electron mass, high carrier motilities, and strong interaction with light in a broad frequency regime with the help of doping or regular structured patterns [16–19]. The conductivity of graphene can also be modified by means of chemical doping, electric field, or magnetic field [20, 21]. In addition, when the imaginary part of graphene conductivity is negative, graphene can support a transverse electric mode and display prospects for the development of optoelectronic devices [22, 23]. With those
In 1998, Ebbesen et al discovered the enhanced extraordinary optical transmission (EOT) phenomenon, which means that when the optical light passes through subwavelength metallic hole arrays (MHA), the transmission shows an enhancement of several orders of magnitude with respect to the classical aperture theory [1]. Since then, much research work has been devoted to the EOT [2, 3], which has been investigated at different wavelengths [4, 5], hole shapes [6], and different lattice configurations [7]. This phenomenon is largely attributed to the resonant interaction of the incident light, with surface plasmons (SPs) generated by the subwavelength grating on the metal surface. SPs are electromagnetic waves that describe the collective excitations of electrons and propagate along the surface of conducting materials, with the properties of concentrating electromagnetic waves on the 0957-4484/14/325201+06$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
Nanotechnology 25 (2014) 325201
X He and H Lu
excited electronic transport properties, graphene is an alternative to traditional metallic materials [24, 25]. Recently, research based on graphene MHA or similar structures has been conducted [26–28]. For instance, the grapheme-coated metal films can be used as tunable molecular sensors in the near-infrared (NIR) region, and the SPs resonances can be enhanced because of the coupling between carriers in graphene and metal SPs [27]. Nguyen et al experimentally investigated the EOT phenomenon using pyrolytic graphite, which showed that though the conductivity of the graphite is smaller than that of the conventional metals, the graphitebased MHA structure manifests similar resonant transmission properties [28]. The graphene periodic micro- or nanosize antidot arrays have also been investigated to show that the GSPs are excited and exhibit strong absorption resonances [29]. To dynamically control the transmission of the MHA structure is a very interesting and important research topic, which can find many applications, such as in the design of switchers, filters, and phase shifters. Currently, there are some methods to modulate the transmission, but most of them depend on adjusting the structure parameters, using semiconductor-to-metal transition, or coating a dielectric layer on the MHA structure [30]. By depositing a graphene layer on the metal film with subwavelength hole arrays, we suggest the metal-dielectrics-graphene (MDG) structure can realize the modulation of transmission. Because the permittivity of the graphene layer can be changed by applying electric fields or chemical doping, the transmission of the MDG structure can be easily tuned. In addition, semiconductors can manifest ‘metallic’ characters, such as InSb in the THz regime [31, 32] or transparent conducting oxides and transition metal nitrides in the NIR spectral range [33]. Compared with the metals, the dielectric properties of the semiconductor can be modified by chemical doping or by varying the temperature, giving us much more freedom in the design of plasmonic devices. Therefore, the tunable transmission properties of the proposed MDG structure have been explored in the infrared and THz regimes, taking into account the effects of the Fermi level of the graphene layer, operation frequency, and the composed materials.
Figure 1. (a) The top view of the schematic picture of metallic
subwavelength hole arrays. The lattice period lengths are dx and dy along the x and y directions, and the sizes of the holes are ax and ay along the x and y directions, respectively. Figure 1(b) the side view of the schematic picture of metallic subwavelength hole arrays, which are deposited on the dielectrics layer (SiO2) and the graphene layer. The light is normally incident upon the metal film along the z direction.
radiation frequency ω, temperature T, phenomenological scattering rate Γ, and chemical potential (Fermi level, Ef). The conductivity of the monolayer graphene can be calculated by using the Kubo formula [34]:
(
)
σ ω , μc , τ , T = σinter + σintra
(
)
je2 ω − jτ −1 =
2
πℏ ⎡ 1 ×⎢⎢ −1 ⎣ ω − jτ
(
−
2. Theoretic model and research method Figure 1(a) shows the sketch of the top view of the metallic subwavelength hole arrays. The lattice period lengths are dx and dy along the x and y directions, and the sizes of the holes are ax and ay along the x and y directions, respectively. The subwavelength metal hole arrays are covered first with a graphene monolayer patterned on the dielectric layer (SiO2), as shown in figure 1(b). The thicknesses of the metallic hole arrays, SiO2, and graphene layers are dMHA, dSiO2, and dg, respectively. The incident waves are normally transmitted through the MDG structure along the z direction. Graphene can be considered a 2D material and described by a surface conductivity σg, which is related to the
∫0
)
∞
2
∫0
∞
∂fd (ε) ∂ε
−1 2
∂fd ( − ε) ∂ε
⎤ dε⎥⎥ 2 − 4 (ε ℏ) ⎦
fd ( − ε) − fd (ε)
( ω − jτ )
−
dε
(1)
where fd(ε) is the Fermi–Dirac distribution, j is the imaginary unit, ε is the energy of the incident wave, kB is Boltzmann’s constant, and ℏ is the reduced Planck’s constant. The first part of the equation is the intraband contribution, and the second part contributes to the interband contribution. The dielectric constant of the graphene layer can be expressed as: εg = 1 + j
2
σg ωε0 Δ
,
(2)
Nanotechnology 25 (2014) 325201
X He and H Lu
The permittivity of metal in the THz regime can be written as [35]: ε (ω) = ε∞ −
ω p2 ω ( ω + iωτ )
,
(3)
where ωp and ωτ are the plasma and damping frequencies, respectively. Besides metal, some large band-gap semiconductors (Aldoped ZnO (AZO), Ga-doped ZnO (GZO), indium-tin-oxide (ITO)), and transition metal nitrides (TiN, ZrN) can also be highly doped and exhibit metallic properties in the NIR regime. Furthermore, their losses are very small, and the real parts of the dielectric constant are comparable to that of the common dielectric materials, which are suitable for fabricating metamaterials devices. The frequency-dependent dielectric constants of metals and semiconductors in the visible and NIR spectral ranges can be described by using the DrudeLorentz equation [33]: ε (ω) = ε∞ −
ω p2 ω ( ω + iωτ )
f j ω 2j
m
+
∑ j=1
(ω
2 j
)
− ω2 − iωγj
, (4)
in which m is the number of oscillators, fj is the oscillator strength, ωj is the resonant frequency of the oscillator, and γj is the oscillator damping frequency. Figure 2. (a) The transmission of the MDG structure at different
Fermi levels in the NIR regime. The thickness of the Ag film is 1200 nm. The lattice periodic lengths along the x and y directions (dx and dy) are both 1500 nm, and the hole lengths along the x and y directions (ax and ay) are both 600 nm. The substrate layer is SiO2 with a thickness of 5 nm. Figure 2(b) the dielectric constants of the graphene layer in the infrared regime. The Fermi levels of the graphene layer are 0.1, 0.2, 0.3, 0.4, and 0.5 eV, respectively. The insets in figures 2(a) and (b) show the top and back views of the unit cell of the MHA.
3. Results and discussion Figure 2 shows the transmission of the incident light through MDG structures at different Fermi levels in the NIR spectral range. The simulation results have been acquired by using the CST Microwave Studio, which is based on the finite integration technique. The frequency domain solver and unit cell boundary condition are adopted. The thicknesses of the Ag and SiO2 layers are 1200 nm and 5 nm, respectively. The Fermi levels of the graphene layer are 0.1, 0.2, 0.3, 0.4, and 0.5 eV, respectively. The lattice periodic lengths along the x and y directions (dx and dy) are both 1500 nm, and the hole lengths along the x and y directions (ax and ay) are both 600 nm. The EOT phenomenon, i.e., the resonant transmission efficiency higher than unity when normalized to the area, can be realized in the MDG structure. When a thin SiO2 layer is deposited on the metal film, the transmission decreases, and the peak position shifts to the longer wavelength. Compared with the conventional MHA structure, the transmission of the proposed MDG structure can be tuned in a wide range by adjusting the Fermi level of the graphene layer. Though the thickness of the graphene layer is very thin, only about 0.34 nm, its influence on the transmission is significant. Compared with the structure without the graphene layer (the peak value of the transmission is about 0.45), when the Fermi level of the graphene layer is 0.1 eV, the peak value of the transmission of the MDG structure decreases drastically, only about 0.12. This result from the graphene layer shows a large dielectric constant. As the Fermi level of the graphene layer increases, the transmission of the MDG structure increases
significantly. The possible reasons are as follows. In the NIR regime, when the Fermi level is small, the real part of the dielectric constant of the graphene layer is positive; the graphene behaves much more like a dielectric layer. As the Fermi level increases, the absolute value of the permittivity of the graphene layer (|εm|) decreases, as shown in figure 2(b). When the Fermi level is 0.5 eV, |εm| shows a dip near 1.55 μm (193.5 THz). If the Fermi level of the graphene layer is beyond 0.5 eV, the sign of the real part of the graphene layer changes from positive to negative, and the graphene layer shows metallic properties. Therefore, the peak absolute transmittance can be tuned from 0.12 to 0.36 when the Fermi levels of the graphene layer change in the range of 0.1–0.5 eV. The modulation depth ((TEf0.5eV − TEf0.1eV)/ TEf0.5eV) can reach more than 60%. Heavily doped semiconductors can also manifest ‘metallic’ properties and be considered alternatives to metals to fabricate SPs devices. Figure 3(b) shows the dielectric constants of several kinds of semiconductors and transition metal nitrides. Ag manifests the best metallic properties in the NIR regime. But the imaginary part of the dielectric constant 3
Nanotechnology 25 (2014) 325201
X He and H Lu
Figure 4. (a) The transmission of the MDG structures in the THz
regime. The thickness of the metal film is 240 μm. The lattice period lengths along the x and y directions (dx and dy) are 300 μm, and the hole lengths along the x and y directions (ax and ay) are 120 μm. One-quarter of the hole area is covered with a graphene layer. The insets in figure 4(a) show the top and back views of the unit cell of the MHA. The substrate layer is SiO2 with a thickness of 0.3 μm. Figure 4(b) the dielectric constants of the graphene layer at different Fermi levels. The Fermi levels of the graphene layer are 0.1, 0.2, 0.3, 0.5, and 0.6 eV, respectively.
Figure 3. (a) The transmission of the ZrNDG structures at different Fermi levels in the NIR regime. The thickness of the semiconductor ZrN film is 800 nm. The lattice period lengths along the x and y directions are both 1500 nm, and the hole lengths along the x and y directions are both 600 nm. The Fermi levels of the graphene layer are 0.1, 0.2, 0.3, 0.4, and 0.5 eV, respectively. The insets in figure 3(a) show the top and back views of the unit cell of the MHA. Figure 3(b) the dielectric constants of several kinds of semiconductor layer in the NIR regime.
is small and shows a dip near 1.55 μm, leading to an increase in transmission. For the Fermi level of the graphene layer in the range of 0.1–0.5 eV, the peak value of the transmission of the ZrDG structure can be tuned in the range of 0.15–0.30, and the modulation depth ((TEf0.5eV − TEf0.1eV)/TEf0.5eV) can reach more than 50%. In addition, compared with the results seen with the AgDG structure, the transmission line width of the ZrDG structure becomes broader, which can be attributed to variation in the larger imaginary part of the dielectric constant and losses of the ZrN layer, as shown in figure 3(b). Figure 4(a) shows the transmission of the MDG structures in the THz regime. Cu is adopted as the metal layer, with a thickness of 240 μm. The lattice period lengths along the x and y directions (dx and dy) are both 300 μm, and the hole lengths along the x and y directions (ax and ay) are both 120 μm. The substrate layer is SiO2 with a thickness of 0.3 μm. In the mid-IR and terahertz regimes, because the dielectric constant of metal is large, the transmission of light passing through the metal film is very small [36]. To enhance the transmission of the MDG structures, only part of the hole area is covered with the graphene layer. The insets in figure 4(a) show the top and back views of the unit cell of the MHA. In the THz regime, when the graphene is ‘doped,’ the graphene shows ‘metallic’ properties, with a negative real part of the dielectric constant and a positive imaginary part of the dielectric constant. Therefore, if a graphene layer is covered
of the doped semiconductor, such as AZO, is smaller than that of Ag, and its real part is also smaller. The transition metal nitride shows much better ‘metallic’ properties, but regretfully, the losses are also larger than that with Ag. The transmission of the incident light through ZrN-SiO2-graphene (ZrDG) structures at different Fermi levels is shown in figure 3(a). The ZrN layer is adopted as the ‘metallic’ film. The Fermi levels of the graphene layer are 0.1, 0.2, 0.3, 0.4, and 0.5 eV, respectively. The lattice periodic lengths along the x and y directions (dx and dy) are both 1500 nm, and the hole lengths along the x and y directions (ax and ay) are both 600 nm. The thicknesses of the ZrN and SiO2 layers are 800 nm and 5 nm. The EOT phenomenon is closely related to the dielectric constant of metal, and the large value of the ratio of the real to imaginary dielectric constants is beneficial to the SPs propagation. By adjusting the Fermi level of the graphene layer, the transmission of the ZrNDG structure can be modulated, as shown in figure 3(a). The transmission increases as the Fermi level of the graphene layer increases, which is similar to the results seen with the AgDG structure. When the Fermi level of the graphene layer is 0.5 eV, the absolute value of the dielectric constant of the graphene layer 4
Nanotechnology 25 (2014) 325201
X He and H Lu
Figure 6. The transmission of the InSbDG structures in the THz
regime. The thickness of the InSb film is 120 μm. The lattice periodic lengths along the x and y directions (dx and dy) are both 300 μm, and the hole lengths along the x and y directions (ax and ay) are both 120 μm. Half of the hole area is covered with a graphene layer. The insets in figure 5(a) show the top and back views of the unit cell of the MHA. The substrate layer is SiO2 with a thickness of 0.3 μm.
regime. The thickness of the InSb film is 120 μm. The lattice periodic lengths along the x and y directions (dx and dy) are both 300 μm, and the hole lengths along the x and y directions (ax and ay) are both 120 μm. Half of the hole area is covered with the graphene layer. The Fermi level of the graphene layer is 0.2 eV. The insets in figure 6 show the top and back views of the unit cell of the MHA. The substrate layer is SiO2 with a thickness of 0.3 μm. The temperatures of the InSb layer are 280, 300, 350, 400, 500, and 600 K, respectively.
on the MDG structure, the transmission of the MDG structure decreases. Furthermore, the transmission of the MDG structure decreases with as the Fermi level of the graphene layer increases, which is rather different from the results in the NIR. The possible reasons are as follows. As the Fermi level increases, the negative real part of the dielectric constant of the graphene layer decreases and the positive imaginary part of the dielectric constant of the graphene layer increases, which means that at a larger Fermi level, the graphene layer shows a much better metallic property and larger losses. For instance, at the frequency of 1 THz, when the Fermi levels are 0.1, 0.2, and 0.5 eV, the dielectric constants of the graphene layer are −3.56 × 105 + 2.20 × 105i, −7.14 × 105 + 4.39 × 105i, and −1.78 × 106 + 1.10 × 106i, respectively. Therefore, the transmission of the MDG structure decreases as the Fermi level increases. Figure 4(a) shows that by varying the Fermi level in the range of 0.1–0.6 eV, the peak value of the transmission of the CuDG structure can be tuned in the range of 0.22–0.48, and the modulation depth ((TEf0.1eV − TEf0.5eV)/ TEf0.1eV) can reach about 50%. Some semiconductors, e.g., InSb, also show metallic properties in the THz regime. Figure 5 shows the transmission of the InSbDG structures in the THz regime. InSb is adopted as the metal layer, with a thickness of 120 μm. The lattice period lengths along the x and y directions (dx and dy) are both 300 μm, and the hole lengths along the x and y directions (ax and ay) are both 120 μm. The dielectric layer is SiO2 with a thickness of 0.3 μm. The insets in figure 5 show the top and back views of the unit cell of the MHA; half of the hole area is covered with a graphene layer. As stated earlier, as the Fermi level of the graphene layer increases, the dielectric constant of the graphene layer increases, leading to a decrease
in transmission of the InSbDG structure. Figure 5 shows that by varying the Fermi level of the graphene layer in the range of 0.1–0.6 eV, the peak value of the transmission of the InSbDG structure can be tuned in the range of 0.32–0.37, and the modulation depth can reach about 14%. It should be noted that the modulation depth of the InSbDG structure is not larger than that of the CuDG structure. Furthermore, the line width of the transmission of the InSbDG structure is much broader than that of the CuDG structure, which may result from the fact that the dielectric constant of the InSb is much smaller than that of the Cu. For example, at the frequency of 1 THz, the dielectric constants of Cu and InSb are −5.50 × 105 + 1.20 × 106i and −2.21 × 102 + 9.79 × 102i, respectively. For the InSbDG structure, the temperature of the InSb layer also affects the transmission property. Figure 6 shows the transmission of the InSbDG structures at different temperatures. The thickness of the InSb layer is 120 μm. The insets in figure 6 show the top and back views of the unit cell of the MHA, and half of the hole area is covered with a graphene layer. The Fermi level of the graphene layer is 0.2 eV. The temperatures of the InSb layer are 280, 300, 350, 400, 500, and 600 K, respectively. As the temperature increases, the transmission of the InSbDG increases and the line width of the transmission decreases. The possible reasons are as follows. As the temperature increases, the carrier concentration of the InSb layer increases, showing much better ‘metallic’ properties. The larger negative real dielectric constant means smaller field penetration into the metal, and a smaller imaginary dielectric constant results in smaller losses. There is a tradeoff between the confinement and losses. The figure of merits (FOM) can be defined by Re(εm)2/Im(εm)
Figure 5. The transmission of the InSbDG structures in the THz
5
Nanotechnology 25 (2014) 325201
X He and H Lu
[33]. As the temperature increases, the carrier concentration and plasma frequency of the InSb layer increases, resulting in the large negative real permittivity, which affects the FOM much stronger than the imaginary part of the dielectric constant. For instance, at the frequency of 1 THz, when the temperatures are 300, 400, and 500 K, the dielectric constants of the InSb layer are −41.95 + 126.77i, −172.30 + 407.93i, and −281.32 + 609.41i, respectively, and the values of the FOM are 13.88, 72.78, and 129.86, respectively. As a result, the transmission of InSb increases as the temperature increases. Figure 6 shows with the change in temperature, the peak value of the transmission of the InSbDG structure can be tuned in the range of 0.16–0.40 THz, and the modulation depth Tmod ((T600K − T280K)/T600K) can reach about 60%. The temperature also has a large influence on the peak position of transmission, which can be tuned in the range of 1.0–1.08 THz by changing the temperature. This probably results from the fact that the dielectric constant of InSb changes drastically as the temperature increases. This is very useful to fabricate plasmonic spectrometers, tunable filters, and beam steering devices.
[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
4. Conclusions On the basis of the MDG structure, the tunable transmission properties have been given and discussed in the NIR and THz regimes, including the effects of the Fermi levels of the graphene layer, composed materials, and operation frequency. The results show that the transmission properties of the MDG structure can be widely modulated by adjusting the Fermi level of the graphene layer. The modulation depth of transmission can reach more than 50%, but the situations in the NIR and THz regimes are rather different. In the NIR spectral range, the graphene behaves like a dielectric layer, and the graphene permittivity decreases as the Fermi level increases, leading to the transmission increasing; while in the THz regime, the graphene layer shows metallic properties, and its permittivity increases in response to the chemical potential, resulting in the value of the transmission decreasing. In addition, some highly doped semiconductors can shows metallic properties. Compared with the metal structure, the transmission and modulation depth of the semiconductor structure are smaller. But the transmission of the semiconductor structure can also be modulated by varying the carrier concentration or temperature, and the peak position can also be changed in a wider range. These results are very useful to gain a better understanding of the mechanisms of the graphene plasmonic devices, which can find applications in the fields of polarization control, filtering, and switching.
[19] [20] [21]
[22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]
References [1] Barnes W L, Dereux A and Ebbesen T W 2003 Nature 424 824
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Genet C and Ebbesen T W 2007 Nature 445 39 Liu H and Lalanne P 2008 Nature 452 728 He X Y, Fu X N and Luo Y W 2009 J. Mod. Opt. 56 1698 Wu S, Zhang Z, Zhang Y, Zhang K, Zhou L, Zhang X and Zhu Y 2013 Phys. Rev. Lett. 110 207401 Gordon R, Brolo A G, Sinton D and Kavanagh K L 2009 Laser & Photon. Rev. 4 311 Matsui T, Agrawal A, Nahata A and Vardeny Z V 2007 Nature 320 517 Raether H 1988 Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Berlin: Springer) Li H, Cao J C, Lü J T and Han Y J 2008 Appl. Phys. Lett. 92 221105 Cao J C 2003 Phys. Rev. Lett. 91 237401 He X Y 2009 J. Opt. Soc. Am. B 26 A23 He X Y, Wang Q J and Yu S F 2012 IEEE J. Quantum Electron. 48 1554 Gao H, Hyun J K, Lee M H, Yang J, Lauhon L J and Odom T W 2010 Nano Lett. 10 4111 Mousavi S H, Khanikaev A B, Neuner B, Avitzour Y, Korobkin D, Ferro G and Shvets G 2010 Phys. Rev. Lett. 105 176803 van Beijnum F, van Veldhoven P J, Geluk E J, de Dood M J A, Hooft G W and van Exter M P 2013 Phys. Rev. Lett. 110 206802 Jablan M, Buljan H and Soljacic M 2009 Phys. Rev. B 80 245435 Wright A R and Zhang C 2010 Phys. Rev. B 81 165413 Wright A R, Cao J C and Zhang C 2009 Phys. Rev. Lett. 103 207401 Yan H, Low T, Zhu W, Wu Y, Freitag M, Li X, Guinea F, Avouris P and Xia F 2013 Nat. Photonics 7 394 He X Y, Tao J and Meng B 2013 Nanotechnology 24 345203 Li Z Q, Henriksen E A, Jiang Z, Hao Z, Martin M C, Kim P, Stromer H L and Basov D N 2008 Nat. Phys. 4 532 Craciun M F, Khrapach I, Barnes M D and Russo S 2013 J. Phys.: Condens. Matter 25 423201 Craciun M F, Russo S, Yamamoto M and Tarucha S 2011 Nano Today 6 42–60 Mikhailov S A and Ziegler K 2007 Phys. Rev. Lett. 99 016803 He X Y and Li R 2014 IEEE J. Sel. Top. Quantum Electron. 20 4600106 Vakil A and Engheta N 2011 Science 332 1291 He X Y and Kim S 2013 J. Opt. Soc. Am. B 30 2461 Liu J, Xu G, Rochford C, Lu R, Wu J, Edwards C M, Berrie C L, Chen Z and Maroni V A 2011 Appl. Phys. Lett. 99 023111 Reckinger N, Vlad A, Melinte S, Colomer J and Sarrazin M 2013 Appl. Phys. Lett. 102 211108 Nguyen T D, Liu S, Kumar G, Nahata A and Vardeny Z V 2013 Appl. Phys. Lett. 102 171107 Nikitin A Y, Guinea F and Martin-Moreno L 2012 Appl. Phys. Lett. 101 151119 Han J, Lu X and Zhang W 2008 J. Appl. Phys. 103 033108 He X Y, Wang Q J and Yu S F 2012 Plasmonics 7 571 He X Y 2009 Opt. Express 17 15359 Naik G V, Shalaev V M and Boltasseva A 2013 Adv. Mater. 25 3264 Gusynin V P and Sharapov S G 2007 J. Phys. Condes. Matter 19 026222 Ordal M A, Bell R J, Alexander R W, Long L L and Querry M R 1985 Appl. Opt. 24 4493 Hooper I R and Sambles J R 2008 Opt. Express 16 17258
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Graphene-supported tunable extraordinary transmission
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Nanotechnology 25 325201 (http://iopscience.iop.org/0957-4484/25/32/325201) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 134.153.184.170 This content was downloaded on 03/08/2014 at 15:45
Please note that terms and conditions apply.
Nanotechnology Nanotechnology 25 (2014) 325201 (6pp)
doi:10.1088/0957-4484/25/32/325201
Graphene-supported tunable extraordinary transmission Xiaoyong He1 and Hongxia Lu2 1
Mathematics & Science College, Shanghai Normal University, No. 100 Guilin Rd., Shanghai, 200234, People’s Republic of China 2 School of Material Science and Engineering, Zhengzhou University, No. 100 Science Rd., Zhengzhou, Henan, 450001, People’s Republic of China E-mail: [email protected] Received 2 April 2014, revised 8 June 2014 Accepted for publication 17 June 2014 Published 25 July 2014 Abstract
By depositing a graphene layer on the metallic film with subwavelength hole arrays, the tunable extraordinary transmission property based on the metal-dielectrics-graphene (MDG) structure has been investigated in the terahertz (THz) and near-infrared (NIR) regimes. The influences of operation frequency, composed materials, and the Fermi level of the graphene layer have been taken into account. The results show that by varying the Fermi level of the graphene layer, the transmission of the MDG structure can be tuned in a wide range and the modulation depth of the peak value of the transmission can reach more than 50%. But the tunable mechanisms in the THz and NIR regimes are quite different. In the infrared (THz) regime, the graphene behaves like the dielectric (metallic) layer; its dielectric constant decreases (increases) with the increase of Fermi level, resulting in the transmission increasing (decreasing). Compared with the metallic structure, the transmission of the semiconductor structure can also be modulated by using the doping or varying temperature; its peak position can also be changed in a much broader range. The results are very useful to understand the mechanism of the graphene plasmonic devices and to design novel filters, switchers, modulators, and sensors. Keywords: terahertz, graphene, extraordinary transmission, surface plasmon (Some figures may appear in colour only in the online journal) 1. Introduction
subwavelength scale [8–12]. The MHA structure manifests potential applications in many fields, such as near-field microscopy, resonators, and microlens [13, 14]. For instance, with the help of the semiconductor gain layer, the MHA structure can be used as resonators to fabricate SP lasers and has been realized experimentally [15]. Graphene, a flat monolayer of carbon atoms packed into a dense 2D honeycomb crystal lattice, has the merits of near-zero effective electron mass, high carrier motilities, and strong interaction with light in a broad frequency regime with the help of doping or regular structured patterns [16–19]. The conductivity of graphene can also be modified by means of chemical doping, electric field, or magnetic field [20, 21]. In addition, when the imaginary part of graphene conductivity is negative, graphene can support a transverse electric mode and display prospects for the development of optoelectronic devices [22, 23]. With those
In 1998, Ebbesen et al discovered the enhanced extraordinary optical transmission (EOT) phenomenon, which means that when the optical light passes through subwavelength metallic hole arrays (MHA), the transmission shows an enhancement of several orders of magnitude with respect to the classical aperture theory [1]. Since then, much research work has been devoted to the EOT [2, 3], which has been investigated at different wavelengths [4, 5], hole shapes [6], and different lattice configurations [7]. This phenomenon is largely attributed to the resonant interaction of the incident light, with surface plasmons (SPs) generated by the subwavelength grating on the metal surface. SPs are electromagnetic waves that describe the collective excitations of electrons and propagate along the surface of conducting materials, with the properties of concentrating electromagnetic waves on the 0957-4484/14/325201+06$33.00
1
© 2014 IOP Publishing Ltd Printed in the UK
Nanotechnology 25 (2014) 325201
X He and H Lu
excited electronic transport properties, graphene is an alternative to traditional metallic materials [24, 25]. Recently, research based on graphene MHA or similar structures has been conducted [26–28]. For instance, the grapheme-coated metal films can be used as tunable molecular sensors in the near-infrared (NIR) region, and the SPs resonances can be enhanced because of the coupling between carriers in graphene and metal SPs [27]. Nguyen et al experimentally investigated the EOT phenomenon using pyrolytic graphite, which showed that though the conductivity of the graphite is smaller than that of the conventional metals, the graphitebased MHA structure manifests similar resonant transmission properties [28]. The graphene periodic micro- or nanosize antidot arrays have also been investigated to show that the GSPs are excited and exhibit strong absorption resonances [29]. To dynamically control the transmission of the MHA structure is a very interesting and important research topic, which can find many applications, such as in the design of switchers, filters, and phase shifters. Currently, there are some methods to modulate the transmission, but most of them depend on adjusting the structure parameters, using semiconductor-to-metal transition, or coating a dielectric layer on the MHA structure [30]. By depositing a graphene layer on the metal film with subwavelength hole arrays, we suggest the metal-dielectrics-graphene (MDG) structure can realize the modulation of transmission. Because the permittivity of the graphene layer can be changed by applying electric fields or chemical doping, the transmission of the MDG structure can be easily tuned. In addition, semiconductors can manifest ‘metallic’ characters, such as InSb in the THz regime [31, 32] or transparent conducting oxides and transition metal nitrides in the NIR spectral range [33]. Compared with the metals, the dielectric properties of the semiconductor can be modified by chemical doping or by varying the temperature, giving us much more freedom in the design of plasmonic devices. Therefore, the tunable transmission properties of the proposed MDG structure have been explored in the infrared and THz regimes, taking into account the effects of the Fermi level of the graphene layer, operation frequency, and the composed materials.
Figure 1. (a) The top view of the schematic picture of metallic
subwavelength hole arrays. The lattice period lengths are dx and dy along the x and y directions, and the sizes of the holes are ax and ay along the x and y directions, respectively. Figure 1(b) the side view of the schematic picture of metallic subwavelength hole arrays, which are deposited on the dielectrics layer (SiO2) and the graphene layer. The light is normally incident upon the metal film along the z direction.
radiation frequency ω, temperature T, phenomenological scattering rate Γ, and chemical potential (Fermi level, Ef). The conductivity of the monolayer graphene can be calculated by using the Kubo formula [34]:
(
)
σ ω , μc , τ , T = σinter + σintra
(
)
je2 ω − jτ −1 =
2
πℏ ⎡ 1 ×⎢⎢ −1 ⎣ ω − jτ
(
−
2. Theoretic model and research method Figure 1(a) shows the sketch of the top view of the metallic subwavelength hole arrays. The lattice period lengths are dx and dy along the x and y directions, and the sizes of the holes are ax and ay along the x and y directions, respectively. The subwavelength metal hole arrays are covered first with a graphene monolayer patterned on the dielectric layer (SiO2), as shown in figure 1(b). The thicknesses of the metallic hole arrays, SiO2, and graphene layers are dMHA, dSiO2, and dg, respectively. The incident waves are normally transmitted through the MDG structure along the z direction. Graphene can be considered a 2D material and described by a surface conductivity σg, which is related to the
∫0
)
∞
2
∫0
∞
∂fd (ε) ∂ε
−1 2
∂fd ( − ε) ∂ε
⎤ dε⎥⎥ 2 − 4 (ε ℏ) ⎦
fd ( − ε) − fd (ε)
( ω − jτ )
−
dε
(1)
where fd(ε) is the Fermi–Dirac distribution, j is the imaginary unit, ε is the energy of the incident wave, kB is Boltzmann’s constant, and ℏ is the reduced Planck’s constant. The first part of the equation is the intraband contribution, and the second part contributes to the interband contribution. The dielectric constant of the graphene layer can be expressed as: εg = 1 + j
2
σg ωε0 Δ
,
(2)
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The permittivity of metal in the THz regime can be written as [35]: ε (ω) = ε∞ −
ω p2 ω ( ω + iωτ )
,
(3)
where ωp and ωτ are the plasma and damping frequencies, respectively. Besides metal, some large band-gap semiconductors (Aldoped ZnO (AZO), Ga-doped ZnO (GZO), indium-tin-oxide (ITO)), and transition metal nitrides (TiN, ZrN) can also be highly doped and exhibit metallic properties in the NIR regime. Furthermore, their losses are very small, and the real parts of the dielectric constant are comparable to that of the common dielectric materials, which are suitable for fabricating metamaterials devices. The frequency-dependent dielectric constants of metals and semiconductors in the visible and NIR spectral ranges can be described by using the DrudeLorentz equation [33]: ε (ω) = ε∞ −
ω p2 ω ( ω + iωτ )
f j ω 2j
m
+
∑ j=1
(ω
2 j
)
− ω2 − iωγj
, (4)
in which m is the number of oscillators, fj is the oscillator strength, ωj is the resonant frequency of the oscillator, and γj is the oscillator damping frequency. Figure 2. (a) The transmission of the MDG structure at different
Fermi levels in the NIR regime. The thickness of the Ag film is 1200 nm. The lattice periodic lengths along the x and y directions (dx and dy) are both 1500 nm, and the hole lengths along the x and y directions (ax and ay) are both 600 nm. The substrate layer is SiO2 with a thickness of 5 nm. Figure 2(b) the dielectric constants of the graphene layer in the infrared regime. The Fermi levels of the graphene layer are 0.1, 0.2, 0.3, 0.4, and 0.5 eV, respectively. The insets in figures 2(a) and (b) show the top and back views of the unit cell of the MHA.
3. Results and discussion Figure 2 shows the transmission of the incident light through MDG structures at different Fermi levels in the NIR spectral range. The simulation results have been acquired by using the CST Microwave Studio, which is based on the finite integration technique. The frequency domain solver and unit cell boundary condition are adopted. The thicknesses of the Ag and SiO2 layers are 1200 nm and 5 nm, respectively. The Fermi levels of the graphene layer are 0.1, 0.2, 0.3, 0.4, and 0.5 eV, respectively. The lattice periodic lengths along the x and y directions (dx and dy) are both 1500 nm, and the hole lengths along the x and y directions (ax and ay) are both 600 nm. The EOT phenomenon, i.e., the resonant transmission efficiency higher than unity when normalized to the area, can be realized in the MDG structure. When a thin SiO2 layer is deposited on the metal film, the transmission decreases, and the peak position shifts to the longer wavelength. Compared with the conventional MHA structure, the transmission of the proposed MDG structure can be tuned in a wide range by adjusting the Fermi level of the graphene layer. Though the thickness of the graphene layer is very thin, only about 0.34 nm, its influence on the transmission is significant. Compared with the structure without the graphene layer (the peak value of the transmission is about 0.45), when the Fermi level of the graphene layer is 0.1 eV, the peak value of the transmission of the MDG structure decreases drastically, only about 0.12. This result from the graphene layer shows a large dielectric constant. As the Fermi level of the graphene layer increases, the transmission of the MDG structure increases
significantly. The possible reasons are as follows. In the NIR regime, when the Fermi level is small, the real part of the dielectric constant of the graphene layer is positive; the graphene behaves much more like a dielectric layer. As the Fermi level increases, the absolute value of the permittivity of the graphene layer (|εm|) decreases, as shown in figure 2(b). When the Fermi level is 0.5 eV, |εm| shows a dip near 1.55 μm (193.5 THz). If the Fermi level of the graphene layer is beyond 0.5 eV, the sign of the real part of the graphene layer changes from positive to negative, and the graphene layer shows metallic properties. Therefore, the peak absolute transmittance can be tuned from 0.12 to 0.36 when the Fermi levels of the graphene layer change in the range of 0.1–0.5 eV. The modulation depth ((TEf0.5eV − TEf0.1eV)/ TEf0.5eV) can reach more than 60%. Heavily doped semiconductors can also manifest ‘metallic’ properties and be considered alternatives to metals to fabricate SPs devices. Figure 3(b) shows the dielectric constants of several kinds of semiconductors and transition metal nitrides. Ag manifests the best metallic properties in the NIR regime. But the imaginary part of the dielectric constant 3
Nanotechnology 25 (2014) 325201
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Figure 4. (a) The transmission of the MDG structures in the THz
regime. The thickness of the metal film is 240 μm. The lattice period lengths along the x and y directions (dx and dy) are 300 μm, and the hole lengths along the x and y directions (ax and ay) are 120 μm. One-quarter of the hole area is covered with a graphene layer. The insets in figure 4(a) show the top and back views of the unit cell of the MHA. The substrate layer is SiO2 with a thickness of 0.3 μm. Figure 4(b) the dielectric constants of the graphene layer at different Fermi levels. The Fermi levels of the graphene layer are 0.1, 0.2, 0.3, 0.5, and 0.6 eV, respectively.
Figure 3. (a) The transmission of the ZrNDG structures at different Fermi levels in the NIR regime. The thickness of the semiconductor ZrN film is 800 nm. The lattice period lengths along the x and y directions are both 1500 nm, and the hole lengths along the x and y directions are both 600 nm. The Fermi levels of the graphene layer are 0.1, 0.2, 0.3, 0.4, and 0.5 eV, respectively. The insets in figure 3(a) show the top and back views of the unit cell of the MHA. Figure 3(b) the dielectric constants of several kinds of semiconductor layer in the NIR regime.
is small and shows a dip near 1.55 μm, leading to an increase in transmission. For the Fermi level of the graphene layer in the range of 0.1–0.5 eV, the peak value of the transmission of the ZrDG structure can be tuned in the range of 0.15–0.30, and the modulation depth ((TEf0.5eV − TEf0.1eV)/TEf0.5eV) can reach more than 50%. In addition, compared with the results seen with the AgDG structure, the transmission line width of the ZrDG structure becomes broader, which can be attributed to variation in the larger imaginary part of the dielectric constant and losses of the ZrN layer, as shown in figure 3(b). Figure 4(a) shows the transmission of the MDG structures in the THz regime. Cu is adopted as the metal layer, with a thickness of 240 μm. The lattice period lengths along the x and y directions (dx and dy) are both 300 μm, and the hole lengths along the x and y directions (ax and ay) are both 120 μm. The substrate layer is SiO2 with a thickness of 0.3 μm. In the mid-IR and terahertz regimes, because the dielectric constant of metal is large, the transmission of light passing through the metal film is very small [36]. To enhance the transmission of the MDG structures, only part of the hole area is covered with the graphene layer. The insets in figure 4(a) show the top and back views of the unit cell of the MHA. In the THz regime, when the graphene is ‘doped,’ the graphene shows ‘metallic’ properties, with a negative real part of the dielectric constant and a positive imaginary part of the dielectric constant. Therefore, if a graphene layer is covered
of the doped semiconductor, such as AZO, is smaller than that of Ag, and its real part is also smaller. The transition metal nitride shows much better ‘metallic’ properties, but regretfully, the losses are also larger than that with Ag. The transmission of the incident light through ZrN-SiO2-graphene (ZrDG) structures at different Fermi levels is shown in figure 3(a). The ZrN layer is adopted as the ‘metallic’ film. The Fermi levels of the graphene layer are 0.1, 0.2, 0.3, 0.4, and 0.5 eV, respectively. The lattice periodic lengths along the x and y directions (dx and dy) are both 1500 nm, and the hole lengths along the x and y directions (ax and ay) are both 600 nm. The thicknesses of the ZrN and SiO2 layers are 800 nm and 5 nm. The EOT phenomenon is closely related to the dielectric constant of metal, and the large value of the ratio of the real to imaginary dielectric constants is beneficial to the SPs propagation. By adjusting the Fermi level of the graphene layer, the transmission of the ZrNDG structure can be modulated, as shown in figure 3(a). The transmission increases as the Fermi level of the graphene layer increases, which is similar to the results seen with the AgDG structure. When the Fermi level of the graphene layer is 0.5 eV, the absolute value of the dielectric constant of the graphene layer 4
Nanotechnology 25 (2014) 325201
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Figure 6. The transmission of the InSbDG structures in the THz
regime. The thickness of the InSb film is 120 μm. The lattice periodic lengths along the x and y directions (dx and dy) are both 300 μm, and the hole lengths along the x and y directions (ax and ay) are both 120 μm. Half of the hole area is covered with a graphene layer. The insets in figure 5(a) show the top and back views of the unit cell of the MHA. The substrate layer is SiO2 with a thickness of 0.3 μm.
regime. The thickness of the InSb film is 120 μm. The lattice periodic lengths along the x and y directions (dx and dy) are both 300 μm, and the hole lengths along the x and y directions (ax and ay) are both 120 μm. Half of the hole area is covered with the graphene layer. The Fermi level of the graphene layer is 0.2 eV. The insets in figure 6 show the top and back views of the unit cell of the MHA. The substrate layer is SiO2 with a thickness of 0.3 μm. The temperatures of the InSb layer are 280, 300, 350, 400, 500, and 600 K, respectively.
on the MDG structure, the transmission of the MDG structure decreases. Furthermore, the transmission of the MDG structure decreases with as the Fermi level of the graphene layer increases, which is rather different from the results in the NIR. The possible reasons are as follows. As the Fermi level increases, the negative real part of the dielectric constant of the graphene layer decreases and the positive imaginary part of the dielectric constant of the graphene layer increases, which means that at a larger Fermi level, the graphene layer shows a much better metallic property and larger losses. For instance, at the frequency of 1 THz, when the Fermi levels are 0.1, 0.2, and 0.5 eV, the dielectric constants of the graphene layer are −3.56 × 105 + 2.20 × 105i, −7.14 × 105 + 4.39 × 105i, and −1.78 × 106 + 1.10 × 106i, respectively. Therefore, the transmission of the MDG structure decreases as the Fermi level increases. Figure 4(a) shows that by varying the Fermi level in the range of 0.1–0.6 eV, the peak value of the transmission of the CuDG structure can be tuned in the range of 0.22–0.48, and the modulation depth ((TEf0.1eV − TEf0.5eV)/ TEf0.1eV) can reach about 50%. Some semiconductors, e.g., InSb, also show metallic properties in the THz regime. Figure 5 shows the transmission of the InSbDG structures in the THz regime. InSb is adopted as the metal layer, with a thickness of 120 μm. The lattice period lengths along the x and y directions (dx and dy) are both 300 μm, and the hole lengths along the x and y directions (ax and ay) are both 120 μm. The dielectric layer is SiO2 with a thickness of 0.3 μm. The insets in figure 5 show the top and back views of the unit cell of the MHA; half of the hole area is covered with a graphene layer. As stated earlier, as the Fermi level of the graphene layer increases, the dielectric constant of the graphene layer increases, leading to a decrease
in transmission of the InSbDG structure. Figure 5 shows that by varying the Fermi level of the graphene layer in the range of 0.1–0.6 eV, the peak value of the transmission of the InSbDG structure can be tuned in the range of 0.32–0.37, and the modulation depth can reach about 14%. It should be noted that the modulation depth of the InSbDG structure is not larger than that of the CuDG structure. Furthermore, the line width of the transmission of the InSbDG structure is much broader than that of the CuDG structure, which may result from the fact that the dielectric constant of the InSb is much smaller than that of the Cu. For example, at the frequency of 1 THz, the dielectric constants of Cu and InSb are −5.50 × 105 + 1.20 × 106i and −2.21 × 102 + 9.79 × 102i, respectively. For the InSbDG structure, the temperature of the InSb layer also affects the transmission property. Figure 6 shows the transmission of the InSbDG structures at different temperatures. The thickness of the InSb layer is 120 μm. The insets in figure 6 show the top and back views of the unit cell of the MHA, and half of the hole area is covered with a graphene layer. The Fermi level of the graphene layer is 0.2 eV. The temperatures of the InSb layer are 280, 300, 350, 400, 500, and 600 K, respectively. As the temperature increases, the transmission of the InSbDG increases and the line width of the transmission decreases. The possible reasons are as follows. As the temperature increases, the carrier concentration of the InSb layer increases, showing much better ‘metallic’ properties. The larger negative real dielectric constant means smaller field penetration into the metal, and a smaller imaginary dielectric constant results in smaller losses. There is a tradeoff between the confinement and losses. The figure of merits (FOM) can be defined by Re(εm)2/Im(εm)
Figure 5. The transmission of the InSbDG structures in the THz
5
Nanotechnology 25 (2014) 325201
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[33]. As the temperature increases, the carrier concentration and plasma frequency of the InSb layer increases, resulting in the large negative real permittivity, which affects the FOM much stronger than the imaginary part of the dielectric constant. For instance, at the frequency of 1 THz, when the temperatures are 300, 400, and 500 K, the dielectric constants of the InSb layer are −41.95 + 126.77i, −172.30 + 407.93i, and −281.32 + 609.41i, respectively, and the values of the FOM are 13.88, 72.78, and 129.86, respectively. As a result, the transmission of InSb increases as the temperature increases. Figure 6 shows with the change in temperature, the peak value of the transmission of the InSbDG structure can be tuned in the range of 0.16–0.40 THz, and the modulation depth Tmod ((T600K − T280K)/T600K) can reach about 60%. The temperature also has a large influence on the peak position of transmission, which can be tuned in the range of 1.0–1.08 THz by changing the temperature. This probably results from the fact that the dielectric constant of InSb changes drastically as the temperature increases. This is very useful to fabricate plasmonic spectrometers, tunable filters, and beam steering devices.
[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
4. Conclusions On the basis of the MDG structure, the tunable transmission properties have been given and discussed in the NIR and THz regimes, including the effects of the Fermi levels of the graphene layer, composed materials, and operation frequency. The results show that the transmission properties of the MDG structure can be widely modulated by adjusting the Fermi level of the graphene layer. The modulation depth of transmission can reach more than 50%, but the situations in the NIR and THz regimes are rather different. In the NIR spectral range, the graphene behaves like a dielectric layer, and the graphene permittivity decreases as the Fermi level increases, leading to the transmission increasing; while in the THz regime, the graphene layer shows metallic properties, and its permittivity increases in response to the chemical potential, resulting in the value of the transmission decreasing. In addition, some highly doped semiconductors can shows metallic properties. Compared with the metal structure, the transmission and modulation depth of the semiconductor structure are smaller. But the transmission of the semiconductor structure can also be modulated by varying the carrier concentration or temperature, and the peak position can also be changed in a wider range. These results are very useful to gain a better understanding of the mechanisms of the graphene plasmonic devices, which can find applications in the fields of polarization control, filtering, and switching.
[19] [20] [21]
[22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]
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