Terahertz wavefront manipulating by double-layer graphene ribbons metasurface

Optics Communications 402 (2017) 523–526

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Terahertz wavefront manipulating by double-layer graphene ribbons metasurface Hongliang Zhao a,b , Zhihong Chen a,b, *, Fei Su a,b, *, Guangjun Ren a,b, *, Fei Liu a,b , Jianquan Yao c,d a b c d

School of Electrical and Electronic Engineering, Tianjin University of Technology, Tianjin 300384, PR China Tianjin Key Lab of Film Electronic & Communication Devices, Tianjin University of Technology, Tianjin 300384, PR China College of Precision Instrument and Opto-electronics Engineering, Institute of Laser and Opto-electronics, Tianjin University, Tianjin 300072, PR China Key Laboratory of Optoelectric Information Science and Technology, Ministry of Education, Tianjin University, Tianjin 300072, PR China

a r t i c l e

i n f o

a b s t r a c t

Keywords: Terahertz wavefront Graphene Metasurface Phase shift

It was recently presented that the phase gradient metasurface can focus the reflection in terahertz range. However, narrow bandwidth and complex tuning method are still challenges. For instance, the size is difficult to be changed once the device is built. We propose a tunable double-layer graphene ribbons array (DLGRA) metasurface which has great potentials for applications in terahertz wavefront control. By changing the Fermi level of each graphene ribbon independently, the DLGRA separated by a bonding agent and a thin dielectric spacer can achieve nearly 2𝜋 phase shift with high reflection efficiency. A reflector which can focus terahertz waves over a broad frequency range is demonstrated numerically by the DLGRA. Intriguingly, through a lateral shift between the nearby graphene ribbons, the variation of coupling induces a shift of focusing frequency. Hence, this approach increases the frequency range to a higher degree than the fixed state. The proposed metasurface provides an effective way for manipulating terahertz waves in a broad frequency range. © 2017 Elsevier B.V. All rights reserved.

1. Introduction

studied in this paper. Some popular applications have been proposed such as source [10,11] and SERS [12–14], etc. As a monolayer metamaterial, graphene has attracted numerous interest because of its novel optical and electrical properties. The properties provide a emerging field for graphene applications, such as optical modulators [15], optical detectors [16], bending waveguides [17] and self-focusing lens [18]. Earlier research has demonstrated that the graphene conductivity can be controlled by bias voltage and chemical doping [19]. Recently, different kinds of graphene-based metasurfaces have been studied such as ribbons [20], multilayer transmit-array [21], cut-wires [22] and concentric rings [23] experimentally and numerically. However, the response frequency range is still narrow. To further increase the range, we design a double-layer graphene ribbons array (DLGRA) interleaving structure. Besides, we also discuss the effects of lateral shift on the tunability of the DLGRA. In this paper, in order to get a simplified approach to achieve the S-parameters and phase, circuit model is exploited to overcome the difficulties of the calculation brought by the mutilayer graphene periodic arrays, the fundamental mode is only considered throughout the rest of the paper.

For purpose of wavefront shaping, metasurface [1], a technique to create a phase gradient surface, has introduced inconceivable superiority to modify the phase of light. Unlike the conventional Snell’s law, gradient metasurface can exhibit anomalous reflection and transmission. Due to the precise phase setting at each position of the metasurface, uncharacteristically, this approach has superiority in spherical aberration elimination, ultrahigh resolution imaging and integrated devices. Several designs have been put forward to realize wavefront control, examples of metasurfaces include slotted metallic resonator arrays [2], V-shaped antennas [3] and metal ribbons antennas [4]. The metal metasurface can provide a good response in terahertz range and a easy fabrication [5,6]. However, the metasurface of metal structure has limitations, in general, the poor tuning flexibility such as a specific structure corresponds to a specific frequency. As a consequence, several alternative materials are mentioned up to now such as graphene [7], semiconductor [8], liquid crystal [9] and composite structure. Among them, graphene as the particularly promising material has already been widely investigated. Besides, as the promising field, terahertz has been * Corresponding authors.

E-mail addresses: [email protected] (Z. Chen), [email protected] (F. Su), [email protected] (G. Ren). http://dx.doi.org/10.1016/j.optcom.2017.06.044 Received 6 April 2017; Received in revised form 23 May 2017; Accepted 12 June 2017 0030-4018/© 2017 Elsevier B.V. All rights reserved.

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Optics Communications 402 (2017) 523–526

Fig. 3. The desired phase distribution at 5.5 THz (solid line), 6 THz (dashed line) and 6.5 THz (dot-dashed line).

According to the Ref. [26], the shunt admittance 𝑌𝑢𝑝𝑝𝑒𝑟 and 𝑌𝑙𝑜𝑤𝑒𝑟 can be simply calculated by: )−1 2 ( 𝑆1 𝑞1 𝑌 = 𝜎𝑔−1 + (2) 2𝑗𝜔𝜀𝑒𝑓 𝑓 𝑃

Fig. 1. (a) The schematic of the structure. The missing part is cut to more clearly show the lower graphene array. (b) The circuit model of the structure.

here, different filling factor 𝑑1,2 ∕𝑃 corresponding to different 𝑞1 (see table II in Ref. [26]). 𝑆12 ≈ 0.89𝑑1,2 , the average permittivity of ( ) 2 the( medium ) surrounding graphene ribbons 𝜀𝑒𝑓 𝑓 = 𝜀0 1 + 𝑛𝑠 ∕2 and

The schematic of the metasurface is shown as Fig. 1(a), which is a sandwich structure composed by two layers of periodic array and a bonding agent. The period length of DLGRA unit cell is 𝑃 = 5 μm. The width of upper and lower graphene ribbons is 𝑑1 = 2.2 μm and 𝑑2 = 1.7 μm, respectively. We use SiO2 as the substrate, the refractive index and the thickness are 𝑛𝑠 = 1.45 and 𝑡𝑠 = 3 μm, respectively. The two layers of graphene arrays are bonded by Epikote828 [24] with the refractive index 𝑛𝑔 = 1.6 and thickness 𝑡𝑔 = 2.5 μm. It should be noted that the 2𝜋 phase coverage is achieved through different widths 𝑑1 and 𝑑2 of the upper and lower graphene ribbons.

𝜀0 𝑛2𝑔 + 𝑛2𝑠 ∕2 for upper and lower graphene ribbons. The reflection coefficient 𝛤 can be achieved after a series of equivalent process [27]: 𝛤 =

(3)

where 𝑌𝑒 is the equivalent admittance and 𝑌0 is the free space admittance. The average reflection can reach 56.6% with the frequency from 5 to 7 THz by calculation. Besides, higher average reflection can be achieved by choosing the Fermi levels for practice. The variation of Fermi levels exhibit a flexible way to tune the reflection.

2. Theoretical analysis

3. Simulation of focusing lens

The incident light travels along 𝑧 axis with the polarization along 𝑥 axis. Due to the dominance of the intraband transition in the lowfrequency terahertz, Drude model is used to achieve the conductivity 𝜎𝑔 of graphene, and the expression is [25]:

Fig. 2 show the variation of phase at 5.5 THz, 6 THz and 6.5 THz when the Fermi level 𝐸𝑓 of upper and lower graphene ribbons change, separately. By changing the Fermi level, 2𝜋 coverage of the phase shift is realized obviously. Besides, the high Fermi level can be realized by an ion-gel electrolyte, making the structure practically possible [28,29]. Typical example of modulating the wavefront of reflection by DLGRA, for instance, a focusing lens, has been simulated explicitly by designing a desired phase transverse distribution 𝜙 (𝑥). As the expression [30]: ( ) 2𝜋 √ 2 𝑥 + 𝑓2 − 𝑓 (4) 𝜙 (𝑥) = 𝜆0

𝑞 2 𝐸𝑓

𝑖 . (1) 𝜋ℏ2 𝜔 + 𝑖𝜏 −1 In which 𝑞 is the quantity of electric charge, ℏ is the reduced Planck constant, 𝐸𝑓 is the graphene Fermi level and 𝜏 is the relaxation time. For the multilayer metamaterials, the transmission line theory [26,27] has been widely adopted. The equivalent circuit is shown in Fig. 1(b), where 𝑛0 , 𝑛𝑠 and 𝑛𝑔 are wave impedance in vacuum, SiO2 and bonding agent, respectively. Besides, 𝑌𝑢𝑝𝑝𝑒𝑟 , 𝑌𝑙𝑜𝑤𝑒𝑟 , 𝑌𝑠 , 𝑌𝑔 and 𝑌𝑃 𝐸𝐶 represent the admittance of upper graphene array, lower graphene array, silicon dioxide layer, glue layer and metallic base, respectively. For the sake of simplicity, the metallic base admittance is assumed to be infinity.

𝜎𝑔 =

𝑌0 − 𝑌𝑒 𝑌0 + 𝑌𝑒

where 𝜆0 is the working wavelength and 𝑥 is the corresponding transverse position. 𝑓 is the desired focal length, in this simulation, we set it as 150 μm.

Fig. 2. The phase variation at (a) 5.5 THz, (b) 6 THz and (c) 6.5 THz when 𝐸𝑓 of upper and lower graphene ribbons change from 0.2 to 0.8 eV. The required phase can be picked out from the region of the black frame. 524

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due to the melting of the bonding agent in 90 ◦ C, an idea of postprocessing approach has been brought. The approach makes it possible to get a fine-tuning device. In the previous study [31], the resonance curve will generate a shift when the upper and lower graphene ribbons have a lateral shift and vertical distance. The shift can be exploited to fine tune the focal length. The electric field intensity is depicted in Fig. 4(b), (d) and (f) when upper and lower graphene ribbons are staggered for half a period (𝑃 ∕2 = 2.5 μm, as shown in the left of Fig. 4). After a lateral shift, the focal plane move to 168 μm, 160 μm and 150 μm for 5.5 THz, 6 THz and 6.5 THz, respectively. The focal planes have moved about 10 μm displacement, which is owing to the phase variation by lateral staggering [31]. The tiny shift can be realized without changing the complex phase gradient of graphene ribbons, which is helpful to the applications of the ultrasensitive sensor, ultrahigh resolution imaging and holography. 4. Conclusion In a word, thanks to the low loss and flexible tunability of graphene, a metasurface composed of the double-layer periodic graphene ribbons has been presented. Compared to previous study [22], only smaller tuning range can be provided, the metasurface provides a large tuning range (∼1 Thz) and a post approach of errors reduction or fine tuning. The relation between the Fermi level and the phase variation is analyzed and evaluated by means of equivalent circuit, in which the results show that the near 2𝜋 phase coverage can be realized. On the other side, as an example of wavefront control, an efficient tunable focusing lens is proposed in this paper. The simulation results indicate that the same focal length can be obtained by this lens from 5.5 to 6.5 THz. In addition, the focal length can achieve about 10 μm fine-tuning by alter the lateral distance between upper and lower graphene ribbons. The metasurface paves the way for optical devices such as sensors, flat lenses and holography. Acknowledgment The authors would like to acknowledge the Tianjin Applied Foundation and Advanced Technology Research Program (Youth Program), Number 14JCQNJC00900 and the Youth Science Foundation Project of National Natural Science Foundation of China, Number 61505144. References [1] A. Epstein, G.V. Eleftheriades, Passive lossless huygens metasurfaces for conversion of arbitrary source field to directive radiation, IEEE Trans. Antennas and Propagation 62 (62) (2014) 1–16. [2] Quanlong Yang, et al., Efficient flat metasurface lens for terahertz imaging, Opt. Express 22 (21) (2014) 25931–25939. [3] N. Yu, et al., Light propagation with phase discontinuities: generalized laws of reflection and refraction, Science 334 (6054) (2011) 333. [4] Shulin Sun, et al., High-efficiency broadband anomalous reflection by gradient metasurfaces, Nano Lett. 12 (12) (2012) 6223–6229. [5] S. Ma, et al., Ultra-wide band reflective metamaterial wave plates for terahertz waves, Europhys. Lett. 117 (2017) 37007. [6] Yuping Zhang, et al., Independently tunable dual-band perfect absorber based on graphene at mid-infrared frequencies, Sci. Rep. 5 (2015) 18463. [7] Zubin Li, et al., Graphene plasmonic metasurfaces to steer infrared light, Sci. Rep. 5 (2015) 12423. [8] Jianwen Zhong, et al., Broadband and tunable-focus flat lens with dielectric metasurface, Plasmonics 11 (2) (2016) 537–541. [9] Huan Peng Xin, et al., A liquid crystals modulated optical tunable filter based on Fano resonance of Au nanorod trimer, Opt. Commun. 389 (2017) 92–96. [10] Hong Liang Zhao, et al., Tunable terahertz source via liquid crystal grating coated with electron beam excited graphene: A theoretical analysis, Opt. Commun. 390 (2017) 137–139. [11] Tian Bo Tan, et al., Terahertz generation from surface plasmon polaritons in graphene induced by a moving electron beam, Opt. Commun. 346 (2015) 149–153. [12] Yong Ming Zhang, G.J. Ren, J.Q. Yao, Surface-enhanced Raman scattering effects of gold and InSb nanoparticles at THz frequencies, Opt. Commun. 341 (2015) 173–177.

Fig. 4. Electric field intensity at (a) 5.5 THz, (b) Lateral 5.5 THz, (c) 6 THz, (d) Lateral 6 THz, (e) 6.5 THz and (f) Lateral 6.5 THz.

In total, 40 phase points have been extracted from Fig. 3 in regular intervals, correspond to the different Fermi level as shown in Fig. 2. In order to clearly demonstrate the focusing effect of DLGRA, the simulation results of electric field intensity have been presented in Fig. 4. The focusing effect can be well identified at 150 μm for 6 THz. However, the focal planes for 5.5 THz and 6.5 THz are observed at 154 and 140 μm, the mesh-accuracy can explain why the focal plane shift. Interestingly, 525

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