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Wide-Band Circularly Polarized ReflectarrayUsing Graphene-Based Pancharatnam-Berry Phase Unit-Cells for Terahertz Communication Li Deng *

ID

, Yuanyuan Zhang, Jianfeng Zhu and Chen Zhang

Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China; [email protected] (Y.Z.); [email protected] (J.Z.); [email protected] (C.Z.) * Correspondence: [email protected]





Received: 2 May 2018; Accepted: 1 June 2018; Published: 5 June 2018

Abstract: A wide-band and high gain circularly polarized (CP) graphene-based reflectarray operating in the THz regime is proposed and theoretically investigated in this paper. The proposed reflectarray consists of a THz CP source and several graphene-based unit-cells. Taking advantages of the Pancharatnam Berry (PB) phase principle, the graphene-based unit-cell is capable of realizing a tunable phase range of 360◦ in a wide-band (1.4–1.7 THz) by unit-cell rotating, overcoming the restriction of intrinsic narrow-band resonance in graphene. Therefore, this graphene-based unit-cell exhibits superior bandwidth and phase tunability to its previous counterparts. To demonstrate this, a wide-band (1.4–1.7 THz) focusing metasurface based on the proposed unit-cell that exhibits excellent focusing effect was designed. Then, according to the reversibility of the optical path, a CP reflectarray was realized by placing a wide-band CP THz source at the focal point of the metasurface. Numerical simulation demonstrates that this reflectarray can achieve a stable high gain up to 15 dBic and an axial ratio around 2.1 dB over the 1.4–1.7 THz band. The good radiation performance of the proposed CP reflectarray, as demonstrated, underlines its suitability for the THz communication applications. Moreover, the design principle of this graphene-based reflectarray with a full 360◦ phase range tunable unit-cells provides a new pathway to design high-performance CP reflectarray in the THz regime. Keywords: circularly polarized; Pancharatnam Berry phase; graphene; metasurface

1. Introduction Terahertz (THz) science and technology that is undergoing an unprecedented rapid development has attracted considerable attention in the scientific community. As a promising technology, it has enormous potential in applications such as communication [1], sensing [2], imaging [3], detection [4] and spectroscopy [5]. In terms of communication applications, the THz communication system is particularly promising as it has a sufficient bandwidth that is capable of handling high data rate up to 100 Gb/s [6]. Consequently, new requirements for THz antennas have been put forward. Generally, high gain THz antennas are indispensable due to the intrinsic high path loss characteristic of THz waves in free space. Besides, considering the performance deterioration of linearly polarized antennas when they are polarization misaligned, circularly polarized (CP) antennas are often required in scenarios where multi-path effect are prominent. Therefore, high gain CP THz antennas are highly desirable. Reflectarrays [7–12], which consist of an array of passive cells, are well suited for high gain THz applications [13,14]. They combine the merits of both conventional reflect and array antennas, namely, low loss, compact profile, low cross polarization, easy manufacturing, and high efficiency.

Materials 2018, 11, 956; doi:10.3390/ma11060956

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By controlling the phase distribution on the array surface, the far-field radiation properties can be easily manipulated without bulky and lossy beamforming networks. In terms of CP reflectarray, several CP reflectarrays with excellent performances have been designed at microwave or millimeter wave frequencies [15–19]. It seems that reflectarrays can be chosen as a competitive candidate for high gain and CP THz applications. Nevertheless, most of these reflectarrays rely on judiciously designed metallic structures, which cannot simply scale to the THz frequencies because of the prominent skin effect of the conventional metal.The ohm loss of the metallic will immensely affect the array gain and radiation efficiency. Toavoid these drawbacks brought by the skin effect of metals at THz frequencies, there is a great demand for new types of THz antenna. Fortunately, graphene has several advantages over convention metals at the THz band. It has a high electron mobility up to 230,000 cm2 /Vs at room temperature [20], and a low electrical resistivity about 10−6 Ω·cm [21,22] in THz band, demonstrating lower loss than conventional metals. In addition, the surface plasmons resonant frequencies of graphene are quite lower than that in metals, which are often in optical frequencies. Meanwhile, graphene surface plasmons exhibit extremely small wavelengths (λ/10–λ/100) and tight field confinement on the graphene sheet [23,24], while maintaining reasonably small losses in the THz band. Furthermore, the imaginary conductivity of graphene is highly tunable via chemical doping or electrical gating [25–31] at THz frequencies, which is impossible or inefficient if metals are used. Based on excellent physical properties of graphene at THz frequencies, several graphene-based THz antennas have been reported in recent years [32–41]. It evaluates the feasibility of a fixed beam reflectarray antenna at THz based on graphene and compares its performance to a similar implementation using gold for the first time [42]. Soon after, diverse graphene-based reflectarrays operating at THz frequencies have been proposed [43–46]. As is well known, tunable unit-cell with a full 360◦ reflected phase coverage is crucial for realizing a high-performance reflectarray. A small reflected phase tunable range of the unit-cell often leads to deteriorative radiation performance, limiting the function of the whole reflectarray. However, phase tunable ranges of unit-cells in previously reported graphene-based reflectarrays or even metasurfaces [47] are essentially realized by tuning physical parameters of the graphene-based structures. Thus, due to the intrinsic resonant properties and finite losses (such asa damped oscillator) of the graphene-based material, only a narrow band phase tunable range of 300◦ has been presented [20,42–44], which restrict their applications in scenarios where high radiation performances are required. Especially, to the best of our knowledge, the CP graphene-based reflectarrays have also been seldom reported in previous literature, although there is a great demand on them at THz communications. One of the reason is that it is hard to achieve an excellent phase tunability by using graphene-based unit-cells. Therefore, designing a unit-cell with a wide-band tunable phase range of 360◦ is a meaningful and challenging work for the graphene-based reflectarray design. In this article, we propose a graphene-based wide-band CP reflectarray operating in the THz regime. The proposed reflectarray consists of a THz CP source and several graphene-based unit-cells. Based on PB phase principle [48], the graphene-based unit-cell is designed to obtain a wide-band (1.4–1.7 THz) tunable phase range of 360◦ , which overcomes the restriction of intrinsic narrow band resonant in graphene. Therefore, the graphene-based unit-cell exhibits superior bandwidth and phase tunability to its previous counterparts. Based on the proposed graphene-based unit-cell, a focusing metasurface operating in 1.4–1.7 THz bands is demonstrated firstly, which exhibits prominent focusing effect. Then, according to the reversibility of the optical path, we realize a CP reflectarray by placing a wide-band CP THz source at the focal point of the metasurface. Numerical simulation demonstrates that this reflectarray can achieve a stable high gain up to 15 dBic and an axial ratio around 2.1 dB over the 1.4–1.7 THz bands. The good radiation performance of the proposed CP reflectarray, as demonstrated, underlines its suitability for the THz communication applications.

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To CP reflectarray, reflectarray, firstly, To have have aa clear clear physical physical insight insight of of the the proposed proposed CP firstly, we we have have deduced deduced the the principle of PB phase, obtaining the necessary phase requirement of the unit cell. As shown in Figure Figure 1, 1, principle of PB phase, obtaining the necessary phase requirement of the unit cell. As shown in we a PB unit cell.cell. In Figure 1a, a1a, right-handed CP (RHCP) incident wave we apply applyaarectangle rectangletotorepresent represent a PB unit In Figure a right-handed CP (RHCP) incident normally (along the − z direction) illuminates the surface, with an incident electric field expression wave normally (along the −z direction) illuminates the surface, with an incident electric field expression

→

→

→→

Einc = ( x + j y )e j k

Einc = ( x + jy )e

z jkz

(1) (1)

and the electric field of reflected wave will be and the electric field of reflected wave will be →

→→

→

Eref = (r x x e jϕjφxx + jry y e jϕjφy y)e− j−kjkzz

Eref = ( rx xe

+ jry ye

)e

(2) (2)

→

where represent the the reflectivity where kk denotes denotes the thewavenumber wavenumberin infree freespace. space.rxrxand andrryy represent reflectivity of of x-polarized x-polarized and ϕyy are are the and y-polarized y-polarized waves, waves, respectively. respectively. Similarly, Similarly, ϕφxx and and φ the reflected reflected phases phases of of x-polarized x-polarized and and y-polarized waves, respectively. y-polarized waves, respectively.

Figure 1. 1. Illustration Illustration of of PB PB phase phase unit-cell: unit-cell: (a) PB phase phase unit-cell unit-cell in in the the xy xy coordinate; coordinate; (b) (b) PB PB phase phase Figure (a) PB unit-cell in the uv coordinate, which is transformed by an θ anticlockwise rotation of the original xy unit-cell in the uv coordinate, which is transformed by an θ anticlockwise rotation of the original xy coordinate. Both Both coordinates coordinates have have the the same same original original point. point. coordinate.

As shown in Figure 1b, when the unit cell is anticlockwise rotated with an angle of θ, the As shown in Figure 1b, when the unit cell is anticlockwise rotated with an angle of θ, relationship between the uv coordinate and the xy coordinate can be represented by the relationship between the uv coordinate and the xy coordinate can be represented by

(

→x =→ucosθ − v→sinθ x = u cos θ − v sin θ →y =→usinθ + v→cosθ

(3) (3)

y = u sin θ + v cos θ Thus, in the uvz coordinate, we substitute Equation (3) into Equation (1), and the incident Thus, uvz coordinate, we substitute Equation (3) into Equation (1), and the incident waves waves can in be the expressed as can be expressed as → jθ → + jv → j kjkz→ (4) EEinc==((uu + j v ))e e zee jθ (4) inc

reflected waves waves are are and, corresponding reflected →→ jθ E = ( r→ue jφu + jr→ve jφv )e− jkz e

Erefref= (ru uu e jϕu + jrvvv e jϕv )e− j k z e jθ

(5) (5)

From Figure 1, we can easily obtain that the reflectivity ru and reflected phase φu in the uvz From Figure 1, we can easily obtain that the reflectivity r and reflected phase ϕu in the uvz coordinate are equal to the reflectivity rx and reflected phase φxu in the xyz coordinate, respectively. coordinate are equal to the reflectivity rx and reflected phase ϕx in the xyz coordinate, respectively. In a similar way, the reflectivity rv and reflected phase φv in the uvz coordinate are equal to the In a similar way, the reflectivity rv and reflected phase ϕv in the uvz coordinate are equal to the reflectivity ry and reflected phase φy in the xyz coordinate, respectively. Therefore, ru = rx, φu = φx, rv = ry, and φv = φy. Then, Equation (5) can be expressed as

Eref =

1 jφ jφ [( rx x − jry y )( e jφx − e y )e j 2θ + ( rx x + jry y )( e jφx − e y )]e − jkz 2

(6)

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reflectivity ry and reflected phase ϕy in the xyz coordinate, respectively. Therefore, ru = rx , ϕu = ϕx , rv = ry , and ϕv = ϕy . Then, Equation (5) can be expressed as Eref =

→→ → → → → 1 [(r x x − jry y )(e jϕx − e jϕy )e j2θ + (r x x + jry y )(e jϕx − e jϕy )]e− j k z 2

(6)

From Equation (6), if rx = ry , it is found that the reflected waves consist of two components, RHCP and left hand CP (LHCP), respectively. Eref(RHCP) =

→→ → 1 → r x ( x − j y )(e jϕx − e jϕy )e j2θ e− j k z 2

(7)

→→ → 1 → r x ( x + j y )(e jϕx + e jϕy )e− j k z 2

(8)

Eref(LHCP) =

and when |ϕx − ϕy | = π, Equations (7) and (8) change to Eref(RHCP) =

→→ → 1 → r x ( x − j y )e jϕx e− j k z e j2θ 2

(9)

Eref(LHCP) = 0

(10)

Obviously, there is only an RHCP component inside the reflected wave, and the phase variation is 2θ, equal to two times of the rotation angle. Contrary to the metallic plate, the reflected waves of the PB unit-cell based metasurface only contain the co-polarized components. It is worth noting that the conditions of |ϕx − ϕy | ≈ π and rx ≈ ry must be fulfilled. 3. Graphene Based PB Unit-Cell Graphene can strongly interact with electromagnetic waves in THz regime through plasmonic resonance [23,24]. However, for practical applications, wave-graphene interactions have to be further improved. In this paper, a graphene-based PB phase unit-cell is proposed, as shown in Figure 2b. The structure of the unit-cell consists of a top layer rectangular graphene patch and a square grounded quartz glass (SiO2 ) substrate. When we extend these unit-cells periodically along both the x and y directions, a 2-D graphene-based metasurface can be obtained, as shown in Figure 2a. Incident terahertz waves can excite the plasmonic resonances of the graphene patches, and can be totally reflected by the bottom metallic ground. The top layer graphene-patches work as a partially reflecting mirror, and the bottom metallic ground operates as a fully reflecting mirror, respectively. Because of the rectangular shape of the graphene patch, the phases of the reflected waves can be independently manipulated by changing w or l, as shown in Figure 2d. The reason is that the Ex component of the incident wave can only excite the plasmonic resonance in the x direction, and Ey component of the incident wave can only excite the plasmonic resonance in the y direction [49]. Based on this characteristic, we can easily design a unit-cell fulfilling the conditions of |ϕx −ϕy | ≈ π and rx ≈ ry . The modeling method of the graphene-based unit-cell is given in the following section. In the terahertz frequencies, the complex surface conductivity of graphene is determined by intraband transition. It can be approximated by a semi-classical Drude model [50] σ(ω ) =

Ef 2e2 i k B T ln[2 cosh( )] 2 2k B T ω + iτ −1 π}

(11)

where e is the elementary charge, kB is the Boltzmann’s constant, } is the reduced Plank’s constant, T is temperature, τ is the relaxation time, ω is the radian frequency, and Ef is the Fermi energy. When Ef is much larger than the thermal energy kB T, the complex conductivity of graphene can be simplified to σ(ω ) =

e2 E f i . π }2 ω +iτ −1

The electron relaxation time τ is the function of the carrier mobility µ, the Fermi

energy Ef , and Fermi velocity vf . It can be expressed as τ =

Ef µ , ev f 2

which implies that increasing

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µ will reduce the loss and enhance the efficiency of the device. The carrier mobility µ often has a variation range from ~1000 cm2 /Vs to ~230,000 cm2 /Vs with varied fabricated technologies [20]. Materials 2018, 11, x FOR PEER REVIEW 5 of 13 In our simulation, according to the experimental results in Ref. [51], it is reasonable to assume that the −2 in Ref. [51]), 13 cm−2Ein energy 0.64[51]), eV (corresponding to electron concentration of n = 3 ×T10=13300 cmK n =Fermi 3 × 10 carrier mobility μ = 10,000 cm2/Vs, temperature and Fermi f =Ref. carriervmobility µ = 10,000 cm2 /Vs, temperature T = 300 K and Fermi velocity vf = 106 m/s. velocity f = 106 m/s.

Figure 2.2.(a) theproposed proposedgraphene-based graphene-based reflectarray, which is composed of a Figure (a)Schematic Schematic of the reflectarray, which is composed of a focusing focusing graphene metasurface and a CP THz (b) source. (b) unit-cell, The PB unit-cell, is composed of a graphene metasurface and a CP THz source. The PB which is which composed of a rectangular graphene graphene patch andpatch a grounded quartz glass (SiO2glass ) substrate. side lengths of the rectangle rectangular and a grounded quartz (SiO 2) The substrate. The side lengths of theare w and l,are in wx and l,y in direction, p represents the side length of length the unit-cell, which can rectangle x and y respectively. direction, respectively. p represents the side of the unit-cell, be extended in both x and y direction, forming a 2-D metasurface. (c) Side view of the which can be extended in both x and y direction, forming a 2-D metasurface. (c) Side viewproposed of the PB unit-cell. Geometric parameters t and d tdenote thickness of the ground plate and substrate, proposed PB unit-cell. Geometric parameters and d the denote the thickness of the ground plate and respectively. (d) Simulated reflectedreflected phases under theunder normal of the x-and y-polarized substrate, respectively. (d) Simulated phases theillumination normal illumination of the x-and plane waves. Fixing l = Fixing 3.2 µm,l =the range of parameter w is from 2wµm to 132µm, at 1.52 THz. y-polarized plane waves. 3.2variation µ m, the variation range of parameter is from µ m to 13 µ m, at 1.52 THz.

The reflectivity and phases of the proposed unit-cell were full-wave simulated using Ansoft HFSS The reflectivity and Pittsburgh, phases of the unit-cell were full-wave simulated Ansoft 2017 software (Ansoft, PA,proposed USA). The unit-cell depicted in Figure 2b,c isusing modeled with HFSS 2017 software (Ansoft, Pittsburgh, PA, USA). The unit-cell depicted in Figure 2b,c is modeled a graphene patch on the top layer, then it was deposited on a square grounded SiO2 substrate. The SiO2 with a graphene onpermittivity the top layer, it was deposited on a square grounded SiO 2 substrate. substrate has a patch relative of εthen r = 3.75, and a loss tangent tanδ = 0.0184. The parameter w and The SiO 2 substrate has a relative permittivity of εr = 3.75, and a loss tangent tanδ = 0.0184. The l are the width and length of the graphene patch in the x and y directions, respectively, and p = 15 µm parameter w and lside-length are the width and length graphenetopatch in the and y directions, denotes unit-cell which also equal of to athe periodicity form the 2-Dxmetasurface. Besides, respectively, and p = 15 µ m denotes unit-cell side-length which also equal to a periodicity to form t = 10 nm and d = 26 µm are the thickness of the metallic ground and quartz glass (SiO2 ) substrate, therespectively. 2-D metasurface. Besides, t = 10 nm and d = 26 µ m are the thickness of the metallic ground and to In our simulation, the master and slaver boundary condition was added to the unit-cell quartz glass (SiO 2) substrate, respectively. In our simulation, the master and slaver boundary modeling an infinite array. Meanwhile, Floquet port is placed at z = 6d and utilized to interact with condition was unit-cell added to the unit-cell to modeling an infinite array. Meanwhile, port is the periodic structure. In addition, the reflectivity and phases are obtained Floquet by the parametric placed at z = 6d and utilized to interact with the periodic unit-cell structure. In addition, the sweep module of HFSS solver. The center frequency is set to 1.52 THz. reflectivity are obtained byas the module HFSS solver. The center Suchand a PBphases unit cell can be looked anparametric anisotropicsweep scatterer, whichofhas a polarization dependent frequency is set to 1.52 THz. response. In normally incident case, we optimize the geometric parameters of the unit-cell, and choose a PBparameters unit cell can be looked as l an has a polarization theSuch geometric w = 13.39 µm, and = 3.2anisotropic µm. Figurescatterer, 3a displayswhich the reflectivity and reflected dependent response. In normally incident case, we optimize the geometric parameters of theare phases of the x- and y-polarized waves, respectively. The reflectivity of x- and y-polarized waves unit-cell, and choose the geometric parameters w = 13.39 μm, and l = 3.2 μm. Figure 3a displays the ◦ almost equal, with values near 1, indicating high efficiency. A nearly constant 180 reflected phase reflectivity and reflected phases of the x- and y-polarized waves, respectively. The reflectivity of xand y-polarized waves are almost equal, with values near 1, indicating high efficiency. A nearly constant 180° reflected phase difference between the x- and y-polarized incident waves can be achieved in a wide frequency band (1.4–1.7 THz), realizing exactly 180° at 1.52 THz, as shown in Figure 3b.

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Materials 2018, 11, x FOR PEER REVIEW 6 of 13 difference between the x- and y-polarized incident waves can be achieved in a wide frequency band ◦ (1.4–1.7 THz), realizing exactly 180 at 1.52 THz, as shown in Figure 3b. According to the principle of PB phase, the proposed graphene-based unit-cell can realize According to the principle of PB phase, the proposed graphene-based unit-cell can realize co-polarized conversion, which can convert the illuminated CP wave into a co-polarized CP wave co-polarized conversion, which can convert the illuminated CP wave into a co-polarized CP wave efficiently. Figure 3c gives the co-polarized and cross-polarized conversion ratios when there is a efficiently. Figure 3c gives the co-polarized and cross-polarized conversion ratios when there is normally RHCP incident wave, verifying the co-polarized conversion. In 1.4–1.7 THz bands, a normally RHCP incident wave, verifying the co-polarized conversion. In 1.4–1.7 THz bands, high-efficiency co-polarized transformation has been achieved. Parameters rRR and rLR indicate the high-efficiency co-polarized transformation has been achieved. Parameters rRR and rLR indicate co-polarized conversion ratio and cross-polarized conversion ratio, respectively. the co-polarized conversion ratio and cross-polarized conversion ratio, respectively.

Figure3.3.(a) (a)Simulated Simulatedreflection reflectionperformance performanceofofthe thePB PBunit-cell unit-cellunder underthe thenormal normalillumination illuminationofof Figure x-andy-polarized y-polarizedplane planewaves. waves.The Thered redand andblue bluecurves curvesrepresent representthe theamplitude amplitudeand andphase phaseofofthe the x-and reflected wave, respectively. Optimizing geometric parameters w = 13.39 µ m and l = 3.2 µ m are reflected wave, respectively. Optimizing geometric parameters w = 13.39 µm and l = 3.2 µm are chosen chosen in the simulation. (b) Simulated phase differences of the x-and y-polarized reflected waves. in the simulation. (b) Simulated phase differences of the x-and y-polarized reflected waves. Yellow Yellow area in the figure demonstrates the frequency range of 180° phase(c) difference. (c) area in the figure demonstrates the frequency range of a nearly 180a◦ nearly phase difference. Simulated Simulated co-polarized and cross-polarized conversion underRHCP the normal RHCP co-polarized and cross-polarized conversion ratios under ratios the normal incident planeincident wave. plane wave. The blue and red curves represent the co-polarized conversion ratio and cross-polarized The blue and red curves represent the co-polarized conversion ratio and cross-polarized conversion conversion ratio, respectively. ratio, respectively.

GrapheneMetasurface Metasurfacefor forFocusing Focusing 4.4.Graphene Afterverifying verifying wide-band efficiency co-polarized converting of the After thethe wide-band high high efficiency co-polarized converting capabilitycapability of the proposed proposed we can compensate arbitrary phaseofin0a◦ –360 range of element 0°–360° by element rotating. ◦ by PB unit-cell,PB weunit-cell, can compensate arbitrary phase in a range rotating. 2π φ( x, y )2π = q( x 2 + y 2 + f 2 − f ) + φ0 (12) λ(0 x2 + y2 + f 2 − f ) + ϕ0 ϕ( x, y) = (12) λ0 To focus the reflected CP wave of a normally incident plane wave, a phase distribution must To focus the reflected CP wave of a normally incident plane wave, a phase distribution must be be fulfilled, where f represents focal length, λ0 represents wavelength in free space, φ0 represents fulfilled, where f represents focal length, λ0 represents wavelength in free space, ϕ0 represents initial initial phase at the original point. Following Equation (12), we design a focusing graphene phase at the original point. Following Equation (12), we design a focusing graphene metasurface metasurface with 51 × 51 unit-cells at 1.52 THz, and the focal length is set to 190 μm. The phase with 51 × 51 unit-cells at 1.52 THz, and the focal length is set to 190 µm. The phase distribution distribution is illustrated in Figure 4a, and corresponding unit-cell distribution is plotted in Figure is illustrated in Figure 4a, and corresponding unit-cell distribution is plotted in Figure 4b. In the 4b. In the numerical simulation, a normally RHCP incident wave is placed along the −z direction, numerical simulation, a normally RHCP incident wave is placed along the −z direction, obtaining obtaining energy distribution in the xoz plane at 1.4, 1.52, 1.6 and 1.7 THz, respectively, as depicted energy distribution in the xoz plane at 1.4, 1.52, 1.6 and 1.7 THz, respectively, as depicted in Figure 5a–d. in Figure 5a–d. From these results, the prominent focusing effect can be observed, verifying our From these results, the prominent focusing effect can be observed, verifying our design. Furthermore, design. Furthermore, as the frequency increases, the focal length increases proportional, in accord as the frequency increases, the focal length increases proportional, in accord with Equation (12). It is with Equation (12). It is worth noting that a full 360° reflected phase range is quite important for worth noting that a full 360◦ reflected phase range is quite important for generating such focusing generating such focusing metasurface. If narrower phase range is applied, as presented by previous metasurface. If narrower phase range is applied, as presented by previous studies [20,42,43], focusing studies [20,42,43], focusing performances will be degraded because of out of phase values in some performances will be degraded because of out of phase values in some positions of the metasurface. positions of the metasurface.

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Figure 4. 4. (a) (a) The reflected phase distribution ofofthe proposed focusing graphene metasurface with an Figure Thereflected reflectedphase phasedistribution distributionof the proposed focusing graphene metasurface with Figure 4. (a) The the proposed focusing graphene metasurface with an area 714 µ m × 714 µ m. (b) The unit-cells distribution of the proposed focusing graphene metasurface an area × 714 unit-cells distribution theproposed proposedfocusing focusinggraphene graphenemetasurface metasurface area 714714 µ mµm × 714 µ m.µm. (b)(b) TheThe unit-cells distribution ofof the with51 51× × 51 unit-cells. Each unit-cell rotates aa corresponding phase angle angle θθ == ϕ/2. φ/2. with 51 unit-cells. Each unit-cell rotates corresponding phase with 51 × 51 unit-cells. Each unit-cell rotates a corresponding phase angle θ = φ/2.

Figure 5. (a) Normalized energy distribution in xoz plane at 1.4 THz, the center z position of the focal Figure 5. (a) Normalized energy distribution in xoz plane at 1.4 THz, the center z position of the focal Figure (a) Normalized energy distributionenergy in xoz distribution plane at 1.4 THz, center z position of the focalz point is5.less than 190 µ m. (b) Normalized in xozthe plane at 1.52 THz, the center point is less than 190 µ m. (b) Normalized energy distribution in xoz plane at 1.52 THz, the center zz point is less than 190point µm. is(b) Normalized distribution in xoz plane at in 1.52 position of the focal almost 190 µ m.energy (c) Normalized energy distribution xozTHz, planethe at center 1.6 THz, position of the focal point is almost 190 µ m. (c) Normalized energy distribution in xoz plane at 1.6 THz, position of the focal point almost µm. (c) energy in xoz plane at 1.6 THz, the center z position ofisthe focal190 point is aNormalized little larger than distribution 190 µ m. (d) Normalized energy the centerz zposition position of the focal point is alarger little than larger than 190Normalized µ m. (d) Normalized energy the center of the focal point is a little 190 µm. (d) energy distribution distribution in xoz plane at 1.7 THz, the center z position of the focal point is quite larger than 190 µ m. distribution planethe at 1.7 THz,z the centerofzthe position of the is focal point is quite than 190 µ m. in xoz plane in at xoz 1.7 THz, center position focal point quite larger than larger 190 µm.

5. High Gain CP Graphene-Based Reflectarray 5. High Gain CP Graphene-Based Reflectarray 5. High Gain CP Graphene-Based Reflectarray Previously, we have proposed a graphene metasurface which has prominent focusing Previously, we have proposed a graphene metasurface which has prominent focusing Previously, have proposed a graphene which to hasthe prominent focusing capability capability in a we wide-band of 1.4–1.7 THz. metasurface Then, according principle of optical path capability in a wide-band of 1.4–1.7 THz. Then, according to the principle of optical path in a wide-band of 1.4–1.7 THz. Then, according to the principle of optical path reversibility [52], we can reversibility [52], we can place a wide-band CP THz source at the focal point of the metasurface. reversibility [52], we can place a wide-band CP THz source at the focal point of the metasurface. place wide-band THz source the focal pointsource of the can metasurface. Thus, incident spherical Thus,athe incidentCP spherical waveatfrom the THz be converted tothe reflected plane wave Thus, the incident spherical wave from the THz source can be converted to reflected plane wave wave from the THz source can be converted to reflected plane wave with enhanced gain. In our with enhanced gain. In our simulation, we choose a THz CP horn antenna as the feeding sourceand with enhanced gain. In our simulation, we choose a THz CP horn antenna as the feeding sourceand simulation, we choose a THz CP horn antenna as the feeding sourceand optimize its radiation pattern optimize its radiation pattern (−10 dB beam width) for effective illumination. Simulated radiation optimize its radiation pattern (−10 dB beam width) for effective illumination. Simulated radiation (patterns −10 dB beam for effective Simulated radiation and and axial1.7 ratios of the and width) axial ratios of the illumination. proposed feeding source at 1.4,patterns 1.52, 1.6, THz are patterns and axial ratios of the proposed feeding source at 1.4, 1.52, 1.6, and 1.7 THz are proposed feeding source at 1.4, 1.52, 1.6, and 1.7 THz are demonstrated in Figures 6 and 7, respectively. demonstrated in Figures 6 and 7, respectively. Obviously, a stable −10 dB RHCP beam-width demonstrated in Figures 6 and 7, respectively. Obviously, stable −10 dB RHCP beam-width ◦ cana be Obviously, a stable 10 dB RHCP beam-width achieved, as shown in the figures. around 120° can be−achieved, as shown in thearound figures.120 According to the calculated radiation angle, around 120° can be achieved, as shown in the figures. According to the calculated radiation angle, According to thedistance calculated radiation center feeding distance µmlength is chosen, keeping center feeding 190 μm is angle, chosen, in keeping with the190 focal f = in 190 μm ofwith the center feeding distance 190 μm is chosen, in keeping with the focal length f = 190 μm of the the focal length f = 190 µm of the proposed metasurface. proposed metasurface. proposed metasurface.

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Figure Simulated pattern horn atat(b) 1.4 THz. (b) Figure 6.6.(a) Simulated 2-D2-D radiation pattern of theoffeeding horn antenna at 1.4 THz. simulated Figure 6.(a) (a) Simulated 2-Dradiation radiation pattern ofthe thefeeding feeding hornantenna antenna 1.4The THz. (b)The The simulated 2-D radiation pattern of the feeding horn antenna at 1.52 THz. (c) The simulated 2-D 2-D radiation pattern of the feeding horn antenna at 1.52 THz. (c) The simulated 2-D radiation pattern simulated 2-D radiation pattern of the feeding horn antenna at 1.52 THz. (c) The simulated 2-D radiation pattern ofof the horn antenna 1.6 2-D radiation pattern ofof of the feeding horn antenna at 1.6 THz. (d) Theatat simulated 2-D radiation pattern the feeding horn radiation pattern thefeeding feeding horn antenna 1.6THz. THz.(d) (d)The Thesimulated simulated 2-Dof radiation pattern ◦ plane andin ◦ the feeding horn antenna at 1.7 THz. In all panels the gain of RHCP and LHCP components φ = 0° antenna at 1.7 THz. In all panels the gain of RHCP and LHCP components in ϕ = 0 ϕ = 90 the feeding horn antenna at 1.7 THz. In all panels the gain of RHCP and LHCP components in φ = 0° plane and φφ= =90° are plane are demonstrated, plane and 90°plane planerespectively. aredemonstrated, demonstrated,respectively. respectively.

Figure (a) Simulated axial ratio ofof the feeding horn antenna atat 1.4 THz. (b) Simulated axial ratio ofof Figure 7.7.7. (a) Simulated axial ratio of the feeding horn antenna at 1.4 THz. Simulated axial ratio of Figure (a) Simulated axial ratio the feeding horn antenna 1.4 THz.(b) (b) Simulated axial ratio the feeding horn antenna at 1.52 THz. (c) Simulated axial ratio of the feeding horn antenna at 1.6 the feeding horn antenna at 1.52 THz. (c) Simulated axial ratio of the feeding horn antenna at 1.6 THz. the feeding horn antenna at 1.52 THz. (c) Simulated axial ratio of the feeding horn antenna at 1.6 ◦ THz. (d) axial ofofthe horn atat1.7 InInall the axial (d) Simulated axial ratio ofratio the feeding horn antenna at 1.7 THz. InTHz. all panels the axial ratios inratios ϕ = 0in THz. (d)Simulated Simulated axial ratio thefeeding feeding hornantenna antenna 1.7 THz. allpanels panels the axial ratios in ◦ φφ= =0°0° plane and φ = 90° plane are demonstrated, respectively. plane and ϕ = 90 plane are demonstrated, respectively. plane and φ = 90° plane are demonstrated, respectively.

Figure 8a–l presents the radiation pattern ofofthe the reflectarray atat1.4, 1.4, 1.52, 1.6 and 1.7 THz, Figure8a–l 8a–lpresents presentsthe theradiation radiationpattern patternof thereflectarray reflectarrayat 1.4,1.52, 1.52,1.6 1.6and and1.7 1.7THz, THz, Figure respectively. It is shown that the enhanced gains produced by the proposed reflectarray are 14.32, respectively. It shown is shown enhanced produced the proposed reflectarray are15.34, 14.32, respectively. It is thatthat the the enhanced gainsgains produced by thebyproposed reflectarray are 14.32, 15.34, 14.95 and 14.70 atat1.4, 1.6 and Besides, the 15.34, 14.95 and 14.70 dBic, 1.4,1.52, 1.52,1.7 1.6THz, and1.7 1.7THz, THz,respectively. respectively. Besides, thecross-polarization cross-polarization 14.95 and 14.70 dBic, at dBic, 1.4, 1.52, 1.6 and respectively. Besides, the cross-polarization levels are levels are at least 15 dB lower than the co-polarization levels all across the 1.4–1.7 THz aredBatlower least than 15 dB than the co-polarization all across 1.4–1.7 THzbands, bands, atlevels least 15 thelower co-polarization levels all acrosslevels the 1.4–1.7 THz the bands, demonstrating demonstrating good CP properties. It is worth noting that the co-polarization radiation patterns demonstrating good CP properties. It is worth noting that the co-polarization radiation patterns good CP properties. It is worth noting that the co-polarization radiation patterns have little asymmetric have havelittle littleasymmetric asymmetricfeature. feature.Due Duetotothe thecenter-feeding center-feedingregime regime[53,54] [53,54]ofofthe theproposed proposedreflectarray, reflectarray, the CP feeding horn will inevitably interact with the reflected waves, causing the CP feeding horn will inevitably interact with the reflected waves, causingdistortion distortionofofthe the

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feature. Due to the center-feeding regime [53,54] of the proposed reflectarray, the CP feeding horn will Materials 2018, 11, x FOR PEER REVIEW 9 of 13 inevitably interact with the reflected waves, causing distortion of the radiation pattern. Thus, we have toradiation optimize the design parameters to maximally the blockage effect to of the feeding structure. pattern. Thus, we have to optimizereduce the design parameters maximally reduce the Besides, we can alleviate such interaction by off-axial feeding regime. Furthermore, wide-band blockage effect of the feeding structure. Besides, we can alleviate such interaction by off-axial feeding gain and axial ratio results are displayed Figure 9, stable around 15indBic and9,axial ratio regime. Furthermore, wide-band gain andinaxial ratio results gain are displayed Figure stable gain around 2.1 dB can be achieved in the whole 1.4–1.7 THz bands, exhibiting both high gain and CP around 15 dBic and axial ratio around 2.1 dB can be achieved in the whole 1.4–1.7 THz bands, capability, simultaneously. exhibiting both high gain and CP capability, simultaneously.

Figure 3-D radiationpattern patternofofthe theproposed proposedreflectarray reflectarrayatat1.4 1.4THz. THz. (b) (b) 2-D 2-D radiation radiation pattern Figure 8. 8. (a)(a) 3-D radiation pattern of ◦ the proposed reflectarray at 1.4 THz in ϕ = 0° plane. (c) 2-D radiation pattern of the proposed of the proposed reflectarray at 1.4 THz in φ = 0 plane. (c) 2-D radiation pattern of the proposed ◦ reflectarray THzininφϕ==90 90°plane. plane. (d) reflectarray at at 1.52 reflectarray at at 1.41.4THz (d) 3-D 3-Dradiation radiationpattern patternofofthe theproposed proposed reflectarray THz. (e)(e) 2-D 1.52 THz THz in inφϕ= =0◦0° plane.(f)(f) 2-D 1.52 THz. 2-Dradiation radiationpattern patternofofthe the proposed proposed reflectarray reflectarray at at 1.52 plane. 2-D ◦ radiation pattern of the proposed reflectarray at 1.52 THz in ϕ = 90° plane. (g) 3-D radiation pattern radiation pattern of the proposed reflectarray at 1.52 THz in φ = 90 plane. (g) 3-D radiation pattern of the proposed reflectarray 1.6 (h) THz. (h)radiation 2-D radiation of the proposed reflectarray at 1.6 theofproposed reflectarray at 1.6 at THz. 2-D patternpattern of the proposed reflectarray at 1.6 THz ◦ ◦ ϕ = 0°(i) plane. (i) 2-D radiation pattern of the proposed reflectarray ϕ = 90° in THz φ = 0inplane. 2-D radiation pattern of the proposed reflectarray at 1.6 THzatin1.6 φ THz = 90 inplane. (j) plane. 3-D (j) 3-D pattern radiation of the reflectarray proposed reflectarray THz. (k) 2-D radiation pattern of the radiation ofpattern the proposed at 1.7 THz.at(k)1.7 2-D radiation pattern of the proposed proposed at reflectarray in ϕ(l)= 2-D 0° plane. (l) 2-D radiation of the proposedatreflectarray reflectarray 1.7 THz inat φ 1.7 = 0◦THz plane. radiation pattern of thepattern proposed reflectarray 1.7 THz ◦ at 1.7 THz in ϕ = 90° plane. in φ = 90 plane.

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9. Simulated RHCP gain and axial ratio of the proposed reflectarray. reflectarray. The red and the blue Figure 9. represent the the RHCP RHCP gain gain and and axial axial ratio, ratio, respectively. respectively. curves represent

6. Conclusions Conclusions 6. We have havesystematically systematically investigated the spectral responses of graphene-based phase We investigated the spectral responses of graphene-based PB phasePBunit-cell unit-cell and demonstrated practical implementation of high wide-band gain CPbased reflectarray and demonstrated a practicalaimplementation of wide-band gain CPhigh reflectarray on this based on this configuration in the THz regime. Based on PB phase principle, an arbitrary reflected configuration in the THz regime. Based on PB phase principle, an arbitrary reflected phase controlling phase can be realized, extremely extending the phase abilitygraphene-based of conventional can becontrolling realized, extremely extending the phase modulated abilitymodulated of conventional graphene-based unit-cells only have a phase range of 300°. Finally, a focusing unit-cells that only have athat phase controlling rangecontrolling of 300◦ . Finally, a focusing graphene-based graphene-based metasurface and a reflectarray were designed, simulated and optimized. metasurface and a reflectarray were designed, simulated and optimized. Simulation results exhibit Simulation results exhibit excellent expectations. performances The as theoretical expectations. proposed excellent performances as theoretical proposed reflectarray hasThe a stable gain reflectarray has a stable gain of 15 dBic and axial ratio of 2 dB over the 1.4–1.7 THz bands, of 15 dBic and axial ratio of 2 dB over the 1.4–1.7 THz bands, demonstrating high gain and CP demonstrating simultaneously. high gain and CP simultaneously. This application reflectarrayinmay have characteristics, Thischaracteristics, reflectarray may have a promising future THza promising application in futurefor THz communications. forthe practical fabrication,unit-cell we can communications. Meanwhile, practical fabrication, Meanwhile, we can design graphene-based design the graphene-based unit-cell which is consist of five layers, such as graphene layer, alumina which is consist of five layers, such as graphene layer, alumina layer, polysilicon layer, quartz glass layer, and polysilicon quartz glass layer, and asground. The polysilicon can be isapplied as the an layer, ground. layer, The polysilicon can be applied an electrode. The Fermi energy related to electrode. The energy related to the conductivity of graphene, can be dynamically conductivity of Fermi graphene, andiscan be dynamically tuned by varying the DCand voltage (VDC) between tuned by varying the DC voltage (VDC) between the graphene and the polysilicon. Detailed the graphene and the polysilicon. Detailed techniques to fabricate these kinds of graphene reflectarray techniques to infabricate these of graphene reflectarray be found in Reference [55], can be found Reference [55],kinds supporting the feasibility of ourcan design. In addition, it is worth supporting the feasibility of our design. In addition, it is worth noting that the general technical noting that the general technical procedure formulated herein facilitates further production of such procedure formulated facilitates further production of such graphene-based devices for graphene-based devicesherein for various applications. various applications. Author Contributions: L.D. proposed the idea and designed the structure; Y.Z. and J.Z. analyzed the data; and L.D.Contributions: and C.Z. wroteL.D. the paper. Author proposed the idea and designed the structure; Y.Z. and J.Z. analyzed the data; and L.D. and C.Z. thewas paper. Funding: Thiswrote research funded by National Natural Science Foundation of China (No. 61601040). Conflicts Interest: The authors declare no conflict of interest. Funding: of This research was funded by National Natural Science Foundation of China (No. 61601040).

Conflicts of Interest: The authors declare no conflict of interest.

References

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