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Bi-function Compact graphene lens antenna in terahertz (THz) band has been investigated. The array function is switched between two status, reflectarray and/or transmitarray. The tunability of graphene conductivity introduces the bi-function characteristics of a single array structure in the THz band. The design depends on changing the graphene DC biasing voltage to transform the transmitting antenna to reflecting antenna. The compact structure of the antenna array saves the cost and the allocation area for the terahertz communication applications. A 13 × 13 reflectarray/ transmitarray antenna covering an area of 364 × 364 μm
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is proposed. A dual-beams reflectarray/
transmitarray antenna is achieved by rearranging the cell elements of the array successively. Finally, a single structure is used to work as reflectarray and transmitarray antenna at the same time by rearranging the applied voltages between the different pieces of the graphene sheet using chess board arrangement. The phases of the successive unit-cells are kept the same of their locations in the original full array. The radiation characteristics of the array are investigated using the CST Microwave Studio for the bi-function operation.

Enormous applications have been introduced due to the development of the terahertz science and technology. The terahertz applications are spectroscopy, communication, defense, and biomedical imaging [

Graphene has attracted the attention of the research community due to its novel characteristics [

In this paper, a single structure of perforated dielectric sheet with inserted graphene sheet has been proposed for reflectarray and transmitarray antenna operation using a single DC-bias. The radiation characteristics of this single structure in the reflectarray mode and the transmitarray mode have been investigated. Dual-beam reflectarray and transmitarray antenna can be obtained using successive unit-cell elements arrangement. The radiation characteristics of reflectarray and transmitarray in the same time using the same structure have been investigated. The reflectarray and transmitarray unit cell elements are arranged in a chess board arrangement. The antenna structures are simulated and investigated using the CST Microwave Studio [

Graphene is a 2-D carbon sheet in which the atoms are arranged in a honeycomb lattice structure. Graphene can be modeled as infinitely thin surface of complex conductivity . The complex surface conductivity of a monolayer graphene sheet is represented by [

where

_{e} is the electron charge, _{B} is the Boltzman’s constant,

time, T is the temperature, _{c}. The graphene layer behaves as a constant resistance in series with an inductive reactance that increases with increasing frequency. The graphene material is represented by a surface impedance of 8.52 + j 321.57 Ω. The relationship between the applied electric field and the chemical potential, µ_{c}, can be calculated by [

where

where d is the thickness of the graphene sheet, and _{F} ≈ 10^{6} m/s). The relationship between the complex conductivity and biasing electric field of the graphene sheet is shown in

where p_{1} = 1.0526 × 10^{−5}, p_{2} = 9.6588 × 10^{−7}, p_{3} = −3.97 × 10^{−4}, and p_{4} = −3.6413 × 10^{−5}.

The detailed dimensions of the proposed unit-cell element are shown in _{1} = 28 µm, thickness h = 12.5 µm, and dielectric constant ε_{r} = 12 (HiK500F). The unit-cell element has four identical circular holes with radius r. A single graphene sheet is inserted between the two square dielectric boxes with sheet length L_{2} = L_{1} − 0.002 µm. The required phase and magnitude compensations of each unit-cell element are achieved by varying the holes radii using the waveguide simulator. A waveguide simulator has a perfect electric and perfect magnetic conductor boundary conditions to assume an infinite array [

Two cases for the graphene sheet are considered for the unit cell element. In the first case, the graphene sheet is considered as a conductor with µ_{c} = 1, while in the second case, the graphene sheet is considered as a dielectric with µ_{c} = 0, by altering the DC applied voltage. The variations of the reflection coefficient phase and magnitude versus hole radius at 6 THz for µ_{c} = 1, are shown in _{c} = 0 are shown in _{c} = 1 and µ_{c} = 0. Abrupt change in reflected/transmitted magnitude is due to reflected wave from the perforated dielectric sheet, which acts as a circular waveguide with different radii results in different resonance frequencies. Phase variation for the design of transmitarray and reflectarray in a single structure is shown in

^{2}. The number of array elements is limited by the core (the cash memory) of the CPU- memory of the available computer. Separate pieces from the graphene sheet are considered for the unit cell elements arrangement in two modes of operation using a single DC-biasing. For µ_{c} = 1 the reflectarray mode dominates while for µ_{c} = 0 the transmitarray mode dominates without altering the array design. A circular horn antenna located at a distance F normal to the array aperture is used to feed the array structure. The horn has a circular aperture with radius 44 µm, waveguide outer radius 22 µm, and length = 83.1 µm. The required phase compensation distribution

_{ij} is the distance from the feed point (x_{f}, y_{f}, z_{f}) to the ij^{th} element in the array located at (x_{ij}, y_{ij}). _{c} = 1) and the transmitarray mode (µ_{c} = 0) and horn antenna at frequency 6 THz are shown in

A dual-beam reflectarray mode (µ_{c} = 1) is designed to achieved using the same array structure with single DC-bias. In this case, two separate arrays are designed one to give maximum beam at ζ = −20˚ and the other is designed to give maximum beam at ζ = 0˚. The single structure is achieved by using the chess board arrangement. The chess board arrangement is constructed by rearranging its elements from the previous two arrays. The gain for ζ = 0˚ is 19.9 dB and for ζ = −20˚ is 17.7 dB. The 3D power pattern of the dual beam reflectarray in the same structure is shown in

transmitarray mode (µ_{c} = 0) is designed for two beams at θ = 0˚ and θ = 20˚ directions by using the chess board arrangement. The 3D power patterns of the transmitarray with two beams at θ = 0˚ and θ = 20˚ are shown in

100.8˚ 4.27 µm | 108.5˚ 4.36 µm | 131.6˚ 4.62 µm | 169.7˚ 4.99 µm | 222.1˚^{ } 5.51 µm | 287.9˚ 6.24 µm | 6.472˚ 2.78 µm |
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108.5˚ 4.36 µm | 116.3˚ 4.46 µm | 139.3˚ 4.70 µm | 177.2˚ 5.07 µm | 229.5˚ 5.56 µm | 295.2˚ 6.39 µm | 13.51˚ 3.01 µm |

131.6˚ 4.62 µm | 139.3˚ 4.70 µm | 162.1˚^{ } 4.92 µm | 199.7˚ 5.29 µm | 251.5˚^{ } 5.74 µm | 316.8˚ 6.81 µm | 34.49˚ 3.40 µm |

169.7˚ 4.99 µm | 177.2˚ 5.07 µm | 199.7˚ 5.29 µm | 236.8˚ 5.62 µm | 287.9˚ 6.24 µm | 352.4˚ 6.89 µm | 69.15˚ 3.88 µm |

222.1˚ 5.51 µm | 229.5˚ 5.56 µm | 251.5˚ 5.74 µm | 287.9˚ 6.24 µm | 338.2˚ 6.89 µm | 41.46˚ 3.50 µm | 116.9˚ 4.46 µm |

287.9˚ 6.24 µm | 295.2˚ 6.39 µm | 316.8˚ 6.81 µm | 352.4˚ 6.89 µm | 41.46˚ 3.50 µm | 103.4˚ 4.30 µm | 177.4˚ 5.07 µm |

6.472˚ 2.78 µm | 13.51˚ 3.01 µm | 34.49˚ 3.40 µm | 69.15˚ 3.88 µm | 116.9˚ 4.46 µm | 177.4˚ 5.07 µm | 249.7˚ 5.72 µm |

The chess board unit cells arrangement is used for reflectarray and transmitarray mode of operation in the same time using two DC-voltage biasing. In the chess board structure, the graphene sheet behaves as conductor and dielectric successively by rearranging the applied biased DC-voltages between the different pieces of the graphene sheet (µ_{c} = 0 or µ_{c} = 1). The 3D power pattern of the reflectarray and transmitarray in the same structure is shown in

The design of 13 × 13 unit cell elements transmitarray/reflectarray from perforated dielectric sheet with inserted graphene sheet is proposed for bi-function antenna in THz communication band. The proposed structure is used to reflect or transmit the incident plane wave from the feeder using a single DC bias. The graphene sheet is con- sidered as a conductor with µ_{c} = 1, while in the second case, the graphene sheet is considered as a dielectric with µ_{c} = 0, by altering the DC applied voltage. The reflectarray/transmitarray introduces maximum gain of 24.4

dB/22 dB with the side lobe level of −16.5 dB/−12 dB in the E-plane and −19.5 dB/−15 dB in the H-plane. The 1-dB gain bandwidth is 1.07 THz/1 THz with maximum gain occurs at 6 THz. Dual-beam reflectarray/trans- mitarray antenna is designed by rearranging the unit-cell elements in the array successively. The dual beam transmitarray introduces gain for ζ = 0˚ is 19.9 dB and for ζ = −20˚ is 17.7 dB. The chess board unit-cell element arrangement is used to construct reflectarray and transmitarray operation in the same time using a single structure. The array introduces two maximum beams at θ = 20˚ (transmitarray mode) and at θ = 160˚ (reflectarray mode). The maximum gain for the transmitting beam is 18.5 dB and for reflecting beam is 19 dB. The HPBW is 8˚ for transmitarray and reflectarray respectively. The same structure, but at different angles θ = 30˚ (transmitarray mode) and θ = −150˚ (reflectarray mode). Maximum gain at θ = 30˚ is 16.5 dB and at θ = −150˚ is 14.5 dB. Transmitarray and reflectarray HPBW are 6.6˚ and 9˚, respectively. As proven in this paper, the calculation method can be successfully used for reflectarray and transmitarray in the same structure and in the same time. The tunability of grapheme conductivity introduces the bi-function characteristics of a single array structure in the THz band. The design depends on changing the graphene DC biasing voltage to transform the transmitting antenna to reflecting antenna. The compact structure of the antenna array saves the cost and the allocation area for the terahertz communication applications.

Saber H.Zainud-Deen,Walaa M.Hassan,Hend A.Malhat, (2016) Bi-Function Multi-Beam Graphene Lens Antenna for Terahertz Applications. Wireless Engineering and Technology,07,36-45. doi: 10.4236/wet.2016.71004