Tunable plasmon-induced transparency with graphene-based T-shaped array metasurfaces

Optics Communications 416 (2018) 77–83

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Tunable plasmon-induced transparency with graphene-based T-shaped array metasurfaces Yuying Niu a , Jicheng Wang a,b,c, *, Zhengda Hu a , Feng Zhang b, ** a b c

School of Science, Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, Jiangnan University, Wuxi 214122, China Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, 912, Beijing 100083, China State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China

a r t i c l e

i n f o

Keywords: Metasurfaces Graphene-based Plasmon-induced transparency Carrier mobility

a b s t r a c t The frequency tunable Plasmonic induced transparency (PIT) effect is researched with a periodically patterned T-shaped graphene array in mid-infrared region. We adjust the geometrical parameters to obtain the optimized combination for the realization of the PIT response and use the coupled Lorentz oscillator model to analysis the physical mechanism. Due to the properties of graphene, the PIT effect can be easily and markedly enhanced with the increase of chemical potential and carrier mobility. The frequency of PIT effect is also insensitive with the angle of incident light. In addition, we also propose the 𝜋 shaped structure to realizing the double-peak PIT effect. The results offer a flexible approach for the development of tunable graphene-based photonic devices.

1. Introduction Graphene is a two-dimensional (2D) conductive material which arranged by a planar sheet of carbon atoms [1]. It has attracted tremendous interest due to its unique tunability, special optical characteristics, high degree of electromagnetic confinement and presumably long plasmon lifetime [2–5]. Since it was produced in 2004, the great potential of it in academia and industry lead to a widely investigated. The plasmonic devices of graphene metasurfaces have attracted worldwide interest currently and are mainly researched with the incorporation of tunable and nonlinear [6–14]. Metasurfaces are the one- and twodimensional artificial composite structures with sub-wavelength periodicity and have exotic electromagnetic properties [15–18]. In 2012 years, Arya Fallahi and Julien Perruisseau-Carrier proposed the biperiodic graphene metasurfaces and researched the tunability of graphene theoretically [19]. In 2015 years, Miao et al. researched the widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces [20]. Electromagnetically induced transparency (EIT) is an optical nonlinear phenomenon based on quantum interference effect that can enhance light transmission over a narrow spectral region [21,22]. Plasmonic induced transparency (PIT) is the novel phenomenon analogous to EIT, also is the special case of Fano resonance. In general, there

are two common approaches to realizing PIT response: the direct destructive interference between bright-dark mode coupling [23,24] and the detuning of two bright modes [25,26]. In recent years, PIT in metasurfaces has been proposed in variety of structures, especially the graphene based metasurfaces [27–32]. Shi et al. proposed the 𝜋 shaped graphene nanostructures and reveal the mechanism of EIT-like response in graphene structures use the coupled radiative and dark elements model, demonstrated that the EIT in graphene is closer to EIT in atomic system then which in metal structures [33]. Liu et al. have researched the dynamic modulation of PIT in graphene-based metamolecules with external magnetic field [34]. Compare to these researches, we have a systematic simulation on the proposed structure and analysis it with theory model. In this work, a simple structure with PIT response is presented and followed by a numerical study. In the proposed system, the physical mechanism of PIT phenomenon can be explained with the coupled Lorentz oscillator model. By adjusting the geometrical parameters, the off-to-on response of PIT and the optimized design can be achieved. The PIT response would be also significant tuned by the varying 𝜇𝑐 and 𝜇 of graphene. In addition, the 𝜋 shaped graphene strips structure are proposed to realize the double PIT peaks. This work provides potential ways for realizing the controlling of light in nanophotonic devices.

* Corresponding author at: School of Science, Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, Jiangnan University, Wuxi 214122, China. ** Corresponding author. E-mail addresses: [email protected] (J. Wang), [email protected] (F. Zhang).

https://doi.org/10.1016/j.optcom.2018.02.009 Received 31 October 2017; Received in revised form 23 January 2018; Accepted 4 February 2018 0030-4018/© 2018 Published by Elsevier B.V.

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Optics Communications 416 (2018) 77–83

2. Theoretical and model The schematics of the designed graphene-based three-dimension PIT metasurfaces are presented in Fig. 1. The proposed graphene structures can be made by the Hydrogen Etching method for Chemical Vapor Deposited (CVD) monolayer graphene and then transferred to a silicon dioxide wafer [35–40]. As shown in Fig. 1(b), the structure is composed of periodically patterned 𝑇 shaped graphene nanostrips adheres to a substrate which refractive index is considered to be 1.5. Each 𝑇 shaped graphene strip consists of two nanostrips which are shown in Fig. 1(a). The gray one strip in Fig. 1(a) is used to show the moving process of strip 2 from Fig. 1(b). The period of the unit cell is 𝑃 in both 𝑥 and 𝑦 directions. The thickness of substrate is denoted by 𝑎. We found that when the thickness 𝑎 set from 60 nm to 120 nm, there are almost not effects of thickness on the transmission spectra. So that in our simulation, the substrate thickness is fixed at 60 nm. The strip 1 and strip 2 are designed as length 𝐿 with width 𝑊 and length 𝑙 with width 𝑤, respectively. The separation of two strips is denoted as 𝑡, and the lateral migration of strip 2 is denoted as 𝑠 which is considered as the structural asymmetry factor. The system is illuminated by the plane wave from 𝑧 direction with the incident angle 𝜃, and its electric component is parallel to 𝑥 axis means the TE polarization. In this structure, the thickness of graphene is ignored, and the surface conductivity 𝜎 is computed by Kubo formula including interband and intraband transition [41]. In midinfrared region, when 𝜇𝑐 ≫ 𝑘𝐵 𝑇𝑚 , the intraband contribution dominates and the surface conductivity can be simplified as [9]: 𝑒2 𝜇𝑐

𝑖 𝜎(𝜔) = , 𝜋ℏ2 𝜔 + 𝑖∕𝜏

Fig. 1. (a) 3D schematic illustration of the unit cell of the periodically patterned T shaped graphene nanostrips. (b) Schematic of the graphene metasurfaces array.

As shown in Fig. 2, the optimized geometric parameters are chosen as 𝑃 = 250 nm, 𝐿 = 140 nm, 𝑊 = 50 nm, 𝑙 = 120 nm, 𝑤 = 30 nm, 𝑑 = 10 nm and 𝑠 = 40 nm, respectively. Under the normal incident light, with above settings, the bright-dark PIT system can be realized obviously in Fig. 2(a) in the light green line with triangle. By contrast, the transmission spectra with only one strip are calculated separately and shown in Fig. 2(a). The resonance of incident light and strip 1 (act as bright mode) leads to the transmission dip in the spectrum with pale blue line and rectangle symbol, while the strip 2 act as the dark mode so there is none-resonance with incident light, the transmission spectrum almost a flat line in dark green with circle symbol in Fig. 2(a). The electric field distributions at 20.25 THz (the points ‘‘b’’ and ‘‘c’’ in Fig. 2(a)) are gathering around the edge of the graphene strip, which are shown in Fig. 2(b)–(c). It can be found that both two strips have energy coupling, but the resonant modes of strip 1 and strip 2 are in different frequency range. The simulations show the resonance frequency of strip 1 is 20.25 THz, which can be regarded as bright mode. The resonance frequency of strip 2 is greater than 50 THz which is out of the investigate frequency domain, therefore it can be seen as a dark mode. Fig. 2(d)–(f) show the electric field distributions corresponding to the points ‘‘d’’, ‘‘e’’ and ‘‘f’’ that labeled in Fig. 2(a). In Fig. 2(d) and (f), the electric modes in strip 2 are obtained the 𝑦-axis distribution with the effect of the resonance in strip 1. The answer to the question of the origin of the PIT is illustrated in Fig. 2(e). The field energy in strip 1 is weak due to the destructive interference of the coupling between two excitation ways: strip 1 with incident field, and strip 1 with strip 2. The comparison of simulation and theory is shown in Fig. 3. The parameters are chosen as 𝑃 = 250 nm, 𝐿 = 140 nm, 𝑊 = 50 nm, 𝑙 = 120 nm, 𝑤 = 30 nm, 𝑑 = 10 nm and 𝑠 = 40 nm. The coupled Lorentz oscillator model can be fitted well with the simulation result with 𝜔𝑄 = 𝜔𝐷 = 20.25 THz, 𝛾𝑄 = 0.01, 𝛾𝐷 = 0.233, 𝑔 = 0.17 and 𝜅 = 0.835. Here we add a loss factor with value of 0.04 in the theoretical transmittance for the substrate of structure.

(1)

where 𝑒, ℏ and 𝑘𝐵 are the universal constants representing the electron charge, Boltzmann’s constant and reduced Planck’s constant, respectively. 𝜔 is the photon frequency. 𝜇𝑐 , 𝜏 and 𝑇𝑚 are the chemical potential, relaxation time and temperature, respectively. And the relaxation time 𝜏 can be expressed by 𝜏 = (𝜇𝜇𝑐 )∕(𝑒𝑉 2𝑓 ). Here, 𝑉𝑓 = 1 × 106 m∕s is the Fermi velocity and 𝜇 is the electron mobility. In this work, the room temperature is assumed to be 300 K. The chemical potential and electron mobility are set to 0.5 eV and 20,000 cm2 V−1 s−1 initially. Due to the tunability of graphene, the resonance frequency 𝜔𝑟 can be controlled by the chemical potential. Here the wave vector of surface plasmon along the graphene nanostrip can be expressed as 𝑘𝑠𝑝𝑝 = ℏ𝜔2𝑟 ∕(2𝛼0 𝜇𝑐 𝑐) [42], which also satisfies 𝑘𝑠𝑝𝑝 ∝ 1∕𝐿𝐺 . Where 𝛼0 = 𝑒2 ∕(ℏ𝑐) is the fine structure constant, 𝐿𝐺 is the length of graphene nanostrip and 𝑐 is the velocity of light in vacuum. The three-level plasmonic system is adapted to explain the physical mechanism of the wavelength tunable PIT response between two graphene strips in the unit cell. The incident electromagnetic field is ̃0 𝑒𝑖𝜔𝑡 . The bright mode and dark mode in the PIT system denoted as 𝐸 𝑖𝜔𝑡 and |𝑄⟩ = 𝑄(𝜔)𝑒 𝑖𝜔𝑡 . The resonance ̃ ̃ can be expressed as |𝐷⟩ = 𝐷(𝜔)𝑒 frequencies and the damping factors of the bright mode and the dark mode are 𝜔𝐷 , 𝜔𝑄 and 𝛾𝐷 , 𝛾𝑄 , respectively. According to the coupled Lorentz oscillator model [43–45], the field amplitudes are obtained in: ( ) )( ) ( ̃ ̃0 𝜔 − 𝜔𝐷 + 𝑖𝛾𝐷 𝜅 𝐷 𝑔𝐸 = . (2) ̃ 𝜅 𝜔 − 𝜔𝑄 + 𝑖𝛾𝑄 0 𝑄 Here, 𝑔 is the geometrical parameter expressing the coupling strength of the bright mode with the incident field and 𝜅 is the coupling coefficient between bright and dark modes. The complex amplitude of the bright mode can be derived as: ̃= 𝐷

̃0 (𝜔 − 𝜔𝑄 + 𝑖𝛾𝑄 ) −𝑔 𝐸 (𝜔 − 𝜔𝐷 + 𝑖𝛾𝐷 )(𝜔 − 𝜔𝑄 + 𝑖𝛾𝑄 ) − 𝜅 2

.

(3)

3. Results and discussion

Thus, the transmission of the metasurfaces PIT device can be deduced as: |𝐷 |2 | ̃| 𝑇 (𝜔) = 1 − | | . |𝐸 | | ̃0 |

The three-dimension simulations are calculated by COMSOL Multiphysics based on finite element method. In our simulation, the graphene is considered as a planar and modeled by using the surface current boundary condition, the 𝑥 and 𝑦 directions are applied the periodic

(4) 78

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Fig. 2. (a) Transmission spectra of strip 1 only, strip 2 only and both of them, respectively. The system is illuminated normally by 𝑥-polarization plane wave and the geometric parameters are choose as 𝑃 = 250 nm, 𝐿 = 140 nm, 𝑊 = 50 nm, 𝑙 = 120 nm, 𝑤 = 30 nm, 𝑠 = 40 nm, 𝑡 = 10 nm, the chemical potential 𝜇𝑐 is set to 0.5 eV. (b)–(f) are the distributions of electric field for the corresponding points ‘‘b’’, ‘‘c’’, ‘‘d’’, ‘‘e’’ and ‘‘f’’ in Fig. 2(a). The pictures are observed from 𝑥–𝑦 plane. The color bar means the electric field intensity with the unit of V/m.

component of the incident electric field with the presented system at the frequency of PIT window. Fig. 4(g)–(i) show the distributions of the field 𝐻𝑧 for points of ‘‘a’’, ‘‘b’’ and ‘‘c’’ in Fig. 4(a), which reveal the transformation of the modes in strip 2. As descripted in Ref. [46], the SPP waves are excited by a dipole point source, which the direction of electric field is perpendicular to the plane of graphene and the wave vector is in the propagation direction 𝑥. The SPPs are propagating along the 𝑥-direction with the edge modes distributions of the field 𝐻𝑧 . While in our structure, the modes are excited by the normal incident 𝑥-polarized planar wave, which are different with the references. To make an analogy with the references, the distributions of the field 𝐻𝑧 are concentrated in the aims of the nanostrips in 𝑥–𝑦 cross section shown in Fig. 4(g)–(i). Those field modes could be treated as the edge modes. Here, the maximums and minimums of the energies in each figure are selected for different, which can make the field distributions more clarity. In this section, we will present several typical variation trends of the transmission with some parameters which are shown in Table 1. In Fig. 5(a), the asymmetry factor 𝑠 of the system is chosen impact on the transmission spectra. When 𝑠 is set to 0 nm, there is none-PIT response because of the symmetrical of the structure, with the increase of the lateral migration 𝑠 of the strip 2, the PIT windows arising from the transmission dip and increasingly apparent until reaching the maximum at 𝑠 = 40 nm. Then we discussed the influence of the periods of each unit cell ranging from 200 nm to 400 nm. As shown in Fig. 5(b), the PIT spectra tend to be stable when 𝑃 greater than 250 nm, the transmission dips are raised with the increase 𝑃 . Hence, 𝑃 = 250 nm is the best value. Next, we continued to study the influence of the length 𝐿 of graphene strip 1 on transmission spectra. The length 𝐿 is adjusted from 120 nm to 160 nm with other parameters remained the same. As shown in Fig. 5(c), the length 𝐿 can dramatically affect the spectra of PIT response, especially on the frequency of the PIT spectra and the quality of the PIT effects. When 𝐿 changes from 120 nm to 160 nm, the left dip value is increasing and the right dip is shifting down. It is

Fig. 3. The comparison of simulation and coupled Lorentz oscillator model theory.

boundary conditions. We discretize the domain by using the inhomogeneous mesh with the maximal element size being less than 10% of graphene surface plasmons wavelength. For the further studying of PIT response, the distributions of electric and magnetic field under the normal incident light are shown in Fig. 4. At the frequency of PIT window (marked by ‘‘b’’ in Fig. 4(a)), the normal magnetic field and 𝑥 components of magnetic field are mainly coupled to strip 2, which shown in Fig. 4(b)–(c). As shown in the inset context images of Fig. 4(c), the out of phase modes can be observed from 𝑦–𝑧 cross section. In Fig. 4(d)–(f), the electric energies are almost completely distributed in strip 2 due to the destructive interference in strip 1. The 𝑥, 𝑦 and 𝑧 components of electric field are located in different positions around the graphene strip 2, it is made clear that the coupling between each 79

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Fig. 4. (a) The transmission spectrum of the PIT response with 𝑃 = 250 nm, 𝐿 = 140 nm, 𝑊 = 50 nm, 𝑙 = 120 nm, 𝑤 = 30 nm, 𝑠 = 40 nm, 𝑡 = 10 nm and 𝜇𝑐 = 0.5 eV, same as the setting in Fig. 2(a). (b)–(i) The distributions of the components of electric or magnetic field that marked in the bottom right corner of each figure. The color bar in Fig. (d)–(f) means the electric field intensity with the unit of V/m. The color bar in Fig. (b)–(c) and Fig. (g)–(i) means the magnetic field intensity with the unit of A/m.

Fig. 5. Transmission spectra in relation to different (a) lateral migration of strip 2, (b) periods of the unit cell, (c) length of graphene strip 1, (d) incident angle, (e) chemical potential.

obvious that the best result is when 𝐿 set to 140 nm, the PIT spectrum has good symmetry. What is interesting is that the PIT spectra with the length of 120 nm or 130 nm and 160 nm or 150 nm are almost symmetric with the PIT window of the length of 140 nm. Moreover, the influence of the angle of incident light and chemical potential of graphene is investigated. In Fig. 5(d), the angle of incident light is tuned from 0◦ to 60◦ . The whole transmission spectrum is moving down

increasingly apparent with the frequency of PIT windows remained the same, this phenomenon illustrates the proposed structure is angleinsensitive for 𝑥-polarization incident field in the mid-infrared region. The chemical potential 𝜇𝑐 has great influence to the surface conductivity of graphene, can be controlled by electrostatic and chemical doping. Fig. 5(e) plots the transmission spectra for various values of 𝜇𝑐 at normal incident light with the remained optimized geometric parameters. With 80

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Fig. 8. The spectra of transmission, reflection and absorption in normal incident light with 𝑃 = 250 nm, 𝐿 = 140 nm, 𝑊 = 50 nm, 𝑙 = 120 nm, 𝑤 = 30 nm, 𝑠 = 40 nm, 𝑡 = 10 nm and 𝜇𝑐 = 0.9 eV.

Fig. 6. The relationship of central resonance frequency and chemical potential.

the increase of 𝜇𝑐 , there is a notable frequency-shifting and dramatic resonance enhancement of the PIT spectra. Fig. 6 shows the relationship of central resonance frequency and chemical potential. For expressing the advantage of our device, we provide Table 2 to contrast the transmittance of two dips and the difference of transmittance between two dips. Besides, our spectra have narrower dip width and broader PIT peak width. There are obvious that our device has better performance. We further propose the 𝜋 shaped graphene nanostrips structure that can generate the double PIT windows. Another nanostrip is introduced

into the T-shaped configuration shown in Fig. 7(a). Same with strip 2, the structure parameters of strip 3 is set to 120 nm and 30 nm. We introduce the new asymmetry factor by changing the chemical potential of strip 3 for realizing the double PIT response, As the difference of 𝜇𝑐 and lateral migration (structural asymmetry factor 𝑠 and 𝑡) between two strips, the double PIT windows can be achieved when 𝑠 = 40 nm, 𝑡 = 20 nm and the chemical potential of strip 1, strip 2 and strip 3 are 0.5 eV, 0.5 eV, and 0.55 eV, respectively. The transmission spectrum is

Fig. 7. (a) Schematic of the structure with 𝜋 shaped graphene nanostrips. (b) Double PIT response with the 𝜋 shaped system. (c)–(g) are the distributions of electric field for the corresponding points ‘‘1’’, ‘‘2’’, ‘‘3’’, ‘‘4’’ and ‘‘5’’ in Fig. 5(b). The field distributions are observed from 𝑥–𝑦 plane. The color bar means the normalized electric field intensity from 0 to 1. 81

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Fig. 9. (a) Transmission spectra in relation to different 𝜇. (b) Transmission of two dips (𝑓1 = 19.425 THz and 𝑓2 = 21.1 THz) of the PIT spectra which displayed in Fig. (a) with tuned carrier mobility. 𝜇0 = 10,000 cm2 V−1 s−1 . Table 1 The range and step size of the parameters simulated in this work and their effects to the transmission spectra. Parameters

Range

Step size

Regulation effects

𝒔 (Shifting of strip 2) 𝑷 (period of unit cell) 𝑳 (length of strip 1) 𝜽 (Incident angle) 𝝁𝑐 (Chemical potential)

0∼40 (nm) 200∼400 (nm) 120∼160 (nm) 0∼60 (◦ ) 0.3∼0.9 (eV)

5 (nm) 50 (nm) 10 (nm) 15 (◦ ) 0.2 (eV)

Off-to-on of PIT response Transmittance of resonance dips Blue shift and symmetry of spectra The whole transmittance of spectra Blue shift and the transmittance of dips

Table 2 Contrast of our work and former works in transmittance of dips and the difference of transmission between two dips. Contents (𝜇𝑐 = 0.5 eV) Transmittance of dips

Low frequency High frequency

Transmission difference of two dips

[42]

[44]

Our work

0.72 0.75

0.68 0.73

0.467 0.469

0.03

0.05

0.002

a conspicuous resonance enhancement of the PIT spectra. When the incident angle changed from 0◦ to 60◦ , the frequency is insensitive to the incident angle and the spectra were moving down. We have also considered the 𝜋 shaped structure and realize the double PIT effects. In applications, the T shaped structure also can be used for two-channel filters, reflectors and absorbers. This research will provide the foundation for potential applications with tunable graphene-based photonic devices. Acknowledgments

shown in Fig. 7(b). Fig. 7(c)–(g) show the electric field distributions corresponding to the points ‘‘1’’, ‘‘2’’, ‘‘3’’, ‘‘4’’ and ‘‘5’’ that labeled in Fig. 7(b). We can see that at each dip, the fields gathering around different nanostrips. In application, Fig. 8 shows the transmission, reflection and absorption of the T shaped structure. The geometric parameters are setting same with that in Fig. 4(a), and with 𝜇𝑐 = 0.9 eV. Those results provide the potential applications in two-channel filters [47], reflectors and absorbers [6,48]. In consideration of the losses of graphene, the structure in Fig. 4(a) is regarded as an example. Due to the carrier mobility has effect on the image part of effective refractive index of graphene. As shown in Fig. 9, we set 𝜇0 = 10,000 cm2 V−1 s−1 and calculated the PIT system with different 𝜇 range from 0.1𝜇0 to 100𝜇0 . The depths of the PIT transmission dips demonstrate an evident variation with the carrier mobility and the affect is weakly when the carrier mobility exceeding 20𝜇0 . In fabrication, the carrier mobility can be controlled by chemical doping or by compensating for gained media. According to the present manufacturing level, the carrier mobility of 2𝜇0 can be achieved and if the technology progress, our proposed structure can achieve better effect.

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11504139, 11504140), the Natural Science Foundation of Jiangsu Province (Grant Nos. BK20140167, BK20140128), Fundamental Research Funds for the Central Universities (Grant No. JUSRP115A15), the China Postdoctoral Science Foundation (2017M611693), the Key Laboratory Open Fund of Institute of Semiconductors of CAS (Grant No. KLSMS-1604), and the Open Fund of State Key Laboratory of Millimeter Waves (Grant No. K201802). References [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature 438 (2005) 197–200. [2] B. Sensale-Rodriguez, R. Yan, M.M. Kelly, T. Fang, K. Tahy, W.S. Hwang, D. Jena, L. Liu, H.G. Xing, Broadband graphene terahertz modulators enabled by intraband transitions, Nature Commun. 3 (2012) 780. [3] F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, Y.R. Shen, Gate-variable optical transitions in graphene, Science 320 (2008) 206–209. [4] Z. Fei, A.S. Rodin, G.O. Andreev, W. Bao, A.S. McLeod, M. Wagner, L.M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M.M. Fogler, A.H. Castro Neto, C.N. Lau, F. Keilmann, D.N. Basov, Gate-tuning of graphene plasmons revealed by infrared nano-imaging, Nature 487 (2012) 82–85. [5] F.H.L. Koppens, D.E. Chang, F.J. Garcia de Abajo, Graphene plasmonics: a platform for strong light–matter interactions, Nano Lett. 11 (2011) 3370–3377. [6] S. Ke, B. Wang, H. Huang, H. Long, K. Wang, P. Lu, Plasmonic absorption enhancement in periodic cross-shaped graphene arrays, Opt. Express 23 (2015) 8888–8900. [7] L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H.A. Bechtel, X. Liang, A. Zettl, Y.R. Shen, F. Wang, Graphene plasmonics for tunable terahertz metamaterials, Nat. Nanotechnol. 6 (2011) 630–634. [8] S.H. Mousavi, I. Kholmanov, K.B. Alici, D. Purtseladze, N. Arju, K. Tatar, D.Y. Fozdar, J.W. Suk, Y. Hao, A.B. Khanikaev, R.S. Ruoff, G. Shvets, Inductive tuning of Fanoresonant metasurfaces using plasmonic response of graphene in the mid-infrared, Nano Lett. 13 (2013) 1111–1117.

4. Conclusion In conclusion, we have investigated the tunable PIT response in T shaped graphene-based nanostrips array metasurfaces. By the simulation and theory analysis, under the normal incident of 𝑥-polarization plane wave, the off-to-on of PIT response can be realized by the increase of structural asymmetry of structure (shifting 𝑠) until reaching the optimal value. Others parameters such as the period of unit cell and the length of strip 1 can control the PIT response. In particular, as the chemical potential and the carrier mobility increases, there was 82

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Optics Communications 416 (2018) 77–83 [29] X. Zhao, C. Yuan, L. Zhu, J. Yao, Graphene-based tunable terahertz plasmon-induced transparency metamaterial, Nanoscale 8 (2016) 15273–15280. [30] H. Yan, T. Low, F. Guinea, F. Xia, P. Avouris, Tunable phonon-induced transparency in bilayer graphene nanoribbons, Nano Lett. 14 (2014) 4581–4586. [31] Z. Dong, C. Sun, J. Si, X. Deng, Tunable polarization-independent plasmonically induced transparency based on metal-graphene metasurface, Opt. Express 25 (2017) 12251–12259. [32] C. Sun, Z. Dong, J. Si, X. Deng, Independently tunable dual-band plasmonically induced transparency based on hybrid metal-graphene metamaterials at mid-infrared frequencies, Opt. Express 25 (2017) 1242–1250. [33] X. Shi, D. Han, Y. Dai, Z. Yu, Y. Sun, H. Chen, X. Liu, J. Zi, Plasmonic analog of electromagnetically induced transparency in nanostructure graphene, Opt. Express 21 (2013) 28438–28443. [34] J.Q. Liu, Y.X. Zhou, L. Li, P. Wang, A.V. Zayats, Controlling plasmon-induced transparency of graphene metamolecules with external magnetic field, Opt. Express 23 (2015) 12524–12532. [35] S. Park, R.S. Ruoff, Chemical methods for the production of graphenes, Nat. Nanotech. 4 (2009) 217–224. [36] Y. Zhang, Z. Li, P. Kim, L. Zhang, C. Zhou, Anisotropic hydrogen etching of chemical vapor deposited graphene, Acs Nano 6 (2011) 126–132. [37] J.W. Suk, A. Kitt, C.W. Magnuson, Y. Hao, S. Ahmed, J. An, A.K. Swan, B.B. Goldberg, R.S. Ruoff, Transfer of CVD-grown monolayer graphene onto arbitrary substrates, ACS Nano 5 (2011) 6916–6924. [38] X. Wang, Y. Ouyang, X. Li, H. Wang, J. Guo, H. Dai, Room-temperature allsemiconducting sub-10-nm graphene nanoribbon field-effect transistors, Phys. Rev. Lett. 100 (2008) 206803. [39] A. Fairbrother, J.R. Sanchez-Valencia, B. Lauber, I. Shorubalko, P. Ruffieux, T. Hintermann, R. Fasel, High vacuum synthesis and ambient stability of bottom-up graphene nanoribbons, Nanoscale 9 (2017) 2785–2792. [40] J. Cai, P. Ruffieux, R. Jaafar, et al., Atomically precise bottom-up fabrication of graphene nanoribbons, Nature 466 (2010) 470–473. [41] L.A. Falkovsky, S.S. Pershoguba, Optical far-infrared properties of a graphene monolayer and multilayer, Phys. Rev. B 76 (2007) 153410. [42] F.H. Koppens, D.E. Chang, F.J. García de Abajo, Graphene plasmonics: a platform for strong light–matter interactions, Nano Lett. 11 (2011) 3370–3377. [43] H. Cheng, S. Chen, P. Yu, X. Duan, B. Xie, J. Tian, Dynamically tunable plasmonically induced transparency in periodically patterned graphene nanostrips, Appl. Phys. Lett. 103 (2013) 203112. [44] A. Artar, A.A. Yanik, H. Altug, Multispectral plasmon induced transparency in coupled meta-atoms, Nano Lett. 11 (2011) 1685–1689. [45] X.J. Shang, X. Zhai, X.F. Li, L.L. Wang, B.X. Wang, G.D. Liu, Realization of graphene-based tunable plasmon-induced transparency by the dipole–dipole coupling, Plasmonics 11 (2016) 419–423. [46] H.J. Li, L.L. Wang, B. Sun, Z.R. Huang, X. Zhai, Gate-tunable mid-infrared plasmonic planar band-stop filters based on a monolayer graphene, Plasmonics 11 (2016) 87– 93. [47] X.S. Lin, X.G. Huang, Tooth-shaped plasmonic waveguide filters with nanometeric sizes, Opt. Lett. 33 (2008) 2874–2876. [48] Y. Yao, R. Shankar, M.A. Kats, Y. Song, J. Kong, M. Loncar, F. Capasso, Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators, Nano Lett. 14 (2014) 6526–6532.

[9] Z. Liu, B. Bai, Ultra-thin and high-efficiency graphene metasurface for tunable terahertz wave manipulation, Opt. Express 25 (2017) 8584–8592. [10] E. Hendry, P.J. Hale, J. Moger, A.K. Savchenko, S.A. Mikhailov, Coherent nonlinear optical response of graphene, Phys. Rev. Lett. 105 (2010) 097401. [11] D.A. Smirnova, A.E. Miroshnichenko, Y., S. Kivshar, A.B. Khanikaev, Tunable nonlinear graphene metasurfaces, Phys. Rev. B 92 (2015) 161406. [12] H. Cheng, S. Chen, P. Yu, J. Li, B. Xie, Z. Li, J. Tian, Dynamically tunable broadband mid-infrared cross polarization converter based on graphene metamaterial, Appl. Phys. Lett. 103 (2013) 223102. [13] H. Cheng, S. Chen, P. Yu, J. Li, L. Deng, J. Tian, Mid-infrared tunable optical polarization converter composed of asymmetric graphene nanocrosses, Opt. Lett. 38 (2013) 1567–1569. [14] J. Li, P. Yu, H. Cheng, W. Liu, Z. Li, B. Xie, S. Chen, J. Tian, Optical polarization encoding using graphene-loaded plasmonic metasurfaces, Adv. Opt. Mater. 4 (2016) 91–98. [15] D.R. Smith, J.B. Pendry, M.C.K. Wiltshire, Metamaterials and negative refractive index, Science 305 (2004) 788–792. [16] J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D.A. Genov, G. Bartal, X. Zhang, Three-dimensional optical metamaterial with a negative refractive index, Nature 455 (2008) 376–379. [17] D. Schurig, J.J. Mock, B.J. Justice, S.A. Cummer, J.B. Pendry, A.F. Starr, D.R. Smith, Metamaterial electromagnetic cloak at microwave frequencies, Science 314 (2006) 977–980. [18] T. Ergin, N. Stenger, P. Brenner, J.B. Pendry, M. Wegener, Three-dimensional invisibility cloak at optical wavelengths, Science 328 (2010) 337–339. [19] A. Fallahi, J. Perruisseau-Carrier, Design of tunable biperiodic graphene metasurfaces, Phys. Rev. B 86 (2012) 195408. [20] Z. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. An, Y. Zhang, L. Zhou, Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces, Phys. Rev. X 5 (2015) 041027. [21] K.J. Boller, A. Imamoğlu, S.E. Harris, Observation of electromagnetically induced transparency, Phys. Rev. Lett. 66 (1991) 2593. [22] M. Fleischhauer, A. Imamoglu, J.P. Marangos, Electromagnetically induced transparency: Optics in coherent media, Rev. Modern Phys. 77 (2005) 633. [23] S. Zhang, D.A. Genov, Y. Wang, M. Liu, X. Zhang, Plasmon-induced transparency in metamaterials, Phys. Rev. Lett. 101 (2008) 047401. [24] N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, H. Giessen, Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit, Nat. Mater. 8 (2009) 758–762. [25] N. Papasimakis, V.A. Fedotov, N.I. Zheludev, S.L. Prosvirnin, Metamaterial analog of electromagnetically induced transparency, Phys. Rev. Lett. 101 (2008) 253903. [26] Y. Zhu, X. Hu, H. Yang, Q. Gong, On-chip plasmon-induced transparency based on plasmonic coupled nanocavities, Sci. Rep. 4 (2014). [27] C. Sun, J. Si, Z. Dong, X. Deng, Tunable multispectral plasmon induced transparency based on graphene metamaterials, Opt. Express 24 (2016) 11466–11474. [28] Z.H. Chen, J. Tao, J.H. Gu, J. Li, D. Hu, Q.L. Tan, F. Zhang, X.G. Huang, Tunable metamaterial-induced transparency with gate-controlled on-chip graphene metasurface, Opt. Express 24 (2016) 29216–29225.

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