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

^{*}

## Abstract

**:**

## 1. Introduction

^{2}/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 [25,26,27,28,29,30,31] 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 [32,33,34,35,36,37,38,39,40,41]. 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 [43,44,45,46]. 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 [20,42,43,44], 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.

## 2. PB Principle

_{x}and r

_{y}represent the reflectivity of x-polarized and y-polarized waves, respectively. Similarly, φ

_{x}and φ

_{y}are the reflected phases of x-polarized and y-polarized waves, respectively.

_{u}and reflected phase φ

_{u}in the uvz coordinate are equal to the reflectivity r

_{x}and reflected phase φ

_{x}in the xyz coordinate, respectively. In a similar way, the reflectivity r

_{v}and reflected phase φ

_{v}in the uvz coordinate are equal to the reflectivity r

_{y}and reflected phase φ

_{y}in the xyz coordinate, respectively. Therefore, r

_{u}= r

_{x}, φ

_{u}= φ

_{x}, r

_{v}= r

_{y}, and φ

_{v}= φ

_{y}. Then, Equation (5) can be expressed as

_{x}= r

_{y}, it is found that the reflected waves consist of two components, RHCP and left hand CP (LHCP), respectively.

_{x}− φ

_{y}| = π, Equations (7) and (8) change to

_{x}− φ

_{y}| ≈ π and r

_{x}≈ r

_{y}must be fulfilled.

## 3. Graphene Based PB Unit-Cell

_{2}) 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 E

_{x}component of the incident wave can only excite the plasmonic resonance in the x direction, and E

_{y}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 |φ

_{x}−φ

_{y}| ≈ π and r

_{x}≈ r

_{y}.

_{B}is the Boltzmann’s constant, $\hslash $ is the reduced Plank’s constant, T is temperature, τ is the relaxation time, ω is the radian frequency, and E

_{f}is the Fermi energy. When E

_{f}is much larger than the thermal energy k

_{B}T, the complex conductivity of graphene can be simplified to $\sigma (\omega )=\frac{{e}^{2}{E}_{f}}{\pi {\hslash}^{2}}\frac{i}{\omega +i{\tau}^{-1}}$. The electron relaxation time τ is the function of the carrier mobility μ, the Fermi energy E

_{f}, and Fermi velocity v

_{f}. It can be expressed as $\tau =\frac{{E}_{f}\mu}{e{v}_{f}{}^{2}}$, which implies that increasing μ will reduce the loss and enhance the efficiency of the device. The carrier mobility μ often has a variation range from ~1000 cm

^{2}/Vs to ~230,000 cm

^{2}/Vs with varied fabricated technologies [20]. In our simulation, according to the experimental results in Ref. [51], it is reasonable to assume that the Fermi energy E

_{f}= 0.64 eV (corresponding to electron concentration of n = 3 × 10

^{13}cm

^{−2}in Ref. [51]), carrier mobility μ = 10,000 cm

^{2}/Vs, temperature T = 300 K and Fermi velocity v

_{f}= 10

^{6}m/s.

_{2}substrate. The SiO

_{2}substrate has a relative permittivity of ε

_{r}= 3.75, and a loss tangent tanδ = 0.0184. The parameter w and l are the width and length of the graphene patch in the x and y directions, respectively, and p = 15 µm denotes unit-cell side-length which also equal to a periodicity to form the 2-D metasurface. Besides, t = 10 nm and d = 26 µm are the thickness of the metallic ground and quartz glass (SiO

_{2}) substrate, respectively. In our simulation, the master and slaver boundary condition was added to the unit-cell to modeling an infinite array. Meanwhile, Floquet port is placed at z = 6d and utilized to interact with the periodic unit-cell structure. In addition, the reflectivity and phases are obtained by the parametric sweep module of HFSS solver. The center frequency is set to 1.52 THz.

_{RR}and r

_{LR}indicate the co-polarized conversion ratio and cross-polarized conversion ratio, respectively.

## 4. Graphene Metasurface for Focusing

_{0}represents wavelength in free space, φ

_{0}represents initial phase at the original point. Following Equation (12), we design a focusing graphene metasurface with 51 × 51 unit-cells at 1.52 THz, and the focal length is set to 190 μm. The phase distribution is illustrated in Figure 4a, and corresponding unit-cell distribution is plotted in Figure 4b. In the numerical simulation, a normally RHCP incident wave is placed along the −z direction, obtaining energy distribution in the xoz plane at 1.4, 1.52, 1.6 and 1.7 THz, respectively, as depicted in Figure 5a–d. From these results, the prominent focusing effect can be observed, verifying our design. Furthermore, as the frequency increases, the focal length increases proportional, in accord with Equation (12). It is worth noting that a full 360° reflected phase range is quite important for generating such focusing metasurface. If narrower phase range is applied, as presented by previous studies [20,42,43], focusing performances will be degraded because of out of phase values in some positions of the metasurface.

## 5. High Gain CP Graphene-Based Reflectarray

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Illustration of PB phase unit-cell: (

**a**) PB phase unit-cell in the xy coordinate; (

**b**) PB phase unit-cell in the uv coordinate, which is transformed by an θ anticlockwise rotation of the original xy coordinate. Both coordinates have the same original point.

**Figure 2.**(

**a**) Schematic of the proposed graphene-based reflectarray, which is composed of a focusing graphene metasurface and a CP THz source. (

**b**) The PB unit-cell, which is composed of a rectangular graphene patch and a grounded quartz glass (SiO

_{2}) substrate. The side lengths of the rectangle are w and l, in x and y direction, respectively. p represents the side length of the unit-cell, which can be extended in both x and y direction, forming a 2-D metasurface. (

**c**) Side view of the proposed PB unit-cell. Geometric parameters t and d denote the thickness of the ground plate and substrate, respectively. (

**d**) Simulated reflected phases under the normal illumination of the x-and y-polarized plane waves. Fixing l = 3.2 µm, the variation range of parameter w is from 2 µm to 13 µm, at 1.52 THz.

**Figure 3.**(

**a**) Simulated reflection performance of the PB unit-cell under the normal illumination of x-and y-polarized plane waves. The red and blue curves represent the amplitude and phase of the reflected wave, respectively. Optimizing geometric parameters w = 13.39 µm and l = 3.2 µm are chosen in the simulation. (

**b**) Simulated phase differences of the x-and y-polarized reflected waves. Yellow area in the figure demonstrates the frequency range of a nearly 180° phase difference. (

**c**) Simulated co-polarized and cross-polarized conversion ratios under the normal RHCP incident plane wave. The blue and red curves represent the co-polarized conversion ratio and cross-polarized conversion ratio, respectively.

**Figure 4.**(

**a**) The reflected phase distribution of the proposed focusing graphene metasurface with an area 714 µm × 714 µm. (

**b**) The unit-cells distribution of the proposed focusing graphene metasurface 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 point is less than 190 µm. (

**b**) Normalized energy distribution in xoz plane at 1.52 THz, the center z position of the focal point is almost 190 µm. (

**c**) Normalized energy distribution in xoz plane at 1.6 THz, the center z position of the focal point is a little larger than 190 µm. (

**d**) Normalized energy distribution in xoz plane at 1.7 THz, the center z position of the focal point is quite larger than 190 µm.

**Figure 6.**(

**a**) Simulated 2-D radiation pattern of the feeding horn antenna at 1.4 THz. (

**b**) The simulated 2-D radiation pattern of the feeding horn antenna at 1.52 THz. (

**c**) The simulated 2-D radiation pattern of the feeding horn antenna at 1.6 THz. (

**d**) The simulated 2-D radiation pattern of the feeding horn antenna at 1.7 THz. In all panels the gain of RHCP and LHCP components in φ = 0° plane and φ = 90° plane are demonstrated, respectively.

**Figure 7.**(

**a**) Simulated axial ratio of the feeding horn antenna at 1.4 THz. (

**b**) Simulated axial ratio of the feeding horn antenna at 1.52 THz. (

**c**) Simulated axial ratio of the feeding horn antenna at 1.6 THz. (

**d**) Simulated axial ratio of the feeding horn antenna at 1.7 THz. In all panels the axial ratios in φ = 0° plane and φ = 90° plane are demonstrated, respectively.

**Figure 8.**(

**a**) 3-D radiation pattern of the proposed reflectarray at 1.4 THz. (

**b**) 2-D radiation pattern of the proposed reflectarray at 1.4 THz in ϕ = 0° plane. (

**c**) 2-D radiation pattern of the proposed reflectarray at 1.4 THz in ϕ = 90° plane. (

**d**) 3-D radiation pattern of the proposed reflectarray at 1.52 THz. (

**e**) 2-D radiation pattern of the proposed reflectarray at 1.52 THz in ϕ = 0° plane. (

**f**) 2-D radiation pattern of the proposed reflectarray at 1.52 THz in ϕ = 90° plane. (

**g**) 3-D radiation pattern of the proposed reflectarray at 1.6 THz. (

**h**) 2-D radiation pattern of the proposed reflectarray at 1.6 THz in ϕ = 0° plane. (

**i**) 2-D radiation pattern of the proposed reflectarray at 1.6 THz in ϕ = 90° plane. (

**j**) 3-D radiation pattern of the proposed reflectarray at 1.7 THz. (

**k**) 2-D radiation pattern of the proposed reflectarray at 1.7 THz in ϕ = 0° plane. (

**l**) 2-D radiation pattern of the proposed reflectarray at 1.7 THz in ϕ = 90° plane.

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

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**MDPI and ACS Style**

Deng, L.; Zhang, Y.; Zhu, J.; Zhang, C.
Wide-Band Circularly Polarized ReflectarrayUsing Graphene-Based Pancharatnam-Berry Phase Unit-Cells for Terahertz Communication. *Materials* **2018**, *11*, 956.
https://doi.org/10.3390/ma11060956

**AMA Style**

Deng L, Zhang Y, Zhu J, Zhang C.
Wide-Band Circularly Polarized ReflectarrayUsing Graphene-Based Pancharatnam-Berry Phase Unit-Cells for Terahertz Communication. *Materials*. 2018; 11(6):956.
https://doi.org/10.3390/ma11060956

**Chicago/Turabian Style**

Deng, Li, Yuanyuan Zhang, Jianfeng Zhu, and Chen Zhang.
2018. "Wide-Band Circularly Polarized ReflectarrayUsing Graphene-Based Pancharatnam-Berry Phase Unit-Cells for Terahertz Communication" *Materials* 11, no. 6: 956.
https://doi.org/10.3390/ma11060956