Graphene Based Transmitarray for Terahertz Applications

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1 Progress In Electromagnetics Research M, Vol. 36, , 214 Graphene Based Transmitarra for Terahertz Applications Hend A. Malhat 1, *, Saber H. Zainud-Deen 2, and Shamaa M. Gaber 3 Abstract Circularl polarized graphene based transmitarra for terahertz applications is proposed. The characteristics of the graphene material is eplained. The cell element of the transmitarra is made of square Quartz cell. Dual circular graphene rings are printed on both sides of the Quartz substrate. The graphene ring radius is varied to change the transmission coefficient phase and magnitude. The effect of the graphene chemical potential on the transmission coefficient is demonstrated. Transmitarra is composed of 9 9 unit cell elements. A circularl polarized circular horn is used to feed the transmitarra at f = 6 THz. The left- and right-hand field components in the E- and H-plane are determined. The variation of the gain and the aial-ratio with the frequenc are eplained. The peak gain is db and 1-dB gain bandwidth is 6.8%. The transmitarra produces a circular polarization from 5.5 THz to 6.5 THz. 1. INTRODUCTION Rapidl developing terahertz (THz) science and technolog has attracted a great deal of attention in recent ears due to its enormous potential such as in spectroscop, communication, defense, and biomedical imaging. Graphene, a flat monolaer of carbon atoms tightl packed in a two-dimensional honecomb lattice, has recentl attracted the attention of the research communit due to its novel mechanical, thermal, chemical, electronic and optical properties [1]. Graphene is a promising material for the realization of miniaturized resonant THz antennas [2]. It supports surface plasmon polaritons in the THz range, which are widel tunable b a change of graphene s electrochemical potential via chemical doping, or magnetic field or electrostatic gating. Because of its unique characteristics, graphene is envisaged to enable new potential applications, ranging from ultra-high-speed transistors to transparent solar cells [3]. High gain antennas are desired in various applications, such as satellite communications, radar sstems, and radio astronom observations [4]. Traditionall, large parabolic reflectors and lenses antennas are selected for the sstems mentioned above. However, these antennas are bulk, heav, and their geometrical shape tends to be distorted during the implementation. The use of graphene for dnamicall control the phase of reflectarra and transmitarra antennas at THz frequencies has been proposed for the first time at [5]. Tunable graphene reflective cells for THz reflectarra is proposed in [6]. In this paper, transmitarra antennas are introduced for these applications. In transmitarra, there is no ground plane as in the reflectarra case so, the incident electromagnetic waves pass through the transmitarra structure and converted from spherical wave into a plane wave [7 9]. Consequentl, the feed horn cannot interfere with the transmitted and received waves, and there is no blockage loss. The transmitarra has man surface antenna elements, each of which imparts the necessar phase shift to equalize the path length of ever ra. In this antenna, however, there is no ground plane. Therefore, the feed signal is not reflected, but passes through the structure as it is collimated into a plane wave. The disadvantage with this antenna, however, is that its design is more complicated than that of a reflectarra since both the phase and transmission properties of the element must be considered [1]. Received 7 Ma 214, Accepted 18 June 214, Scheduled 21 June 214 * Corresponding author: Hend Abd Malhat (er honida1@ahoo.com). 1 Facult of Electronic Engineering, Menoufia Universit, Egpt. 2 Facult of Electronic Engineering, Menoufia Universit, Egpt. 3 Egptian Russian Universit, Egpt.

2 186 Malhat, Zainud-Deen, and Gaber The unit-cell design in the transmitarra assumes normal incident wave on each element. However, in the real case the incident wave on the elements at the arra edges has an angle different from the normal (which is an approimation). Man transmitarra researches had been proposed using different antenna elements for different applications [11 13]. In this paper, circularl polarized graphene based transmitarra at f = 6 THz is designed. The transmitarra is composed of 9 9 unit-cell elements and is covering an area of µm 2. The radiation characteristics of the transmitarra are demonstrated. Full-wave analsis using the FIT technique for the antenna structure is illustrated [14]. 2. GRAPHENE THEORY The optical properties of the graphene monolaer can be represented b sheet with surface conductivit, σ(ω), which is derived from the Kubo formula [15]. It consists of an intraband contribution: q 2 σ intra (ω, µ c, Γ, T ) j ek B T π (ω j2γ) and an interband contribution: σ(ω) = σ intra (ω) + σ inter (ω) (1) σ inter (ω, µ c, Γ, T ) j q2 e 4π ( µc K B T + 2 ln ( e µ c/k B T + 1) ) (2) ( 2 µc (ω + jτ 1 ) ) 2 µ c + (ω + jτ 1 ) where j is the imaginar unit, q e the electron charge, the reduced Plank constant, K B the Boltzmann s constant, τ the transport relaation time, T the temperature, µ c the chemical potential, ω the operating angular frequenc, and scattering rate Γ = 1/2τ represents loss mechanism. The intraband term of the conductivit given b (2) is a reasonable approimation in the frequenc range below 8 THz [15]. The graphene chemical potential, µ c, depends on carrier densit, which can be controlled b gate voltage, electric bias field, and/or chemical doping. B increasing µ c the graphene surface conductivit is increased, and the resonances are shifted for higher frequencies. Within the randomphase approimation, the surface conductivit of graphene can be represented in a local, Drude-like form. The Drude model assumes that charge carriers in a material scatter frequentl as the move through the medium [16]. This diffusive model of transport reduces the characterization of the transport to two parameters: the number of charge carriers (n) and the ease with which the move through the material (quantied as either mobilit, mean scattering time, or mean free path). However, the Drude model is generall valid for graphene samples because the mean free paths are still significantl shorter than tpical sample sizes. The effective surface conductivit of graphene is generall a comple quantit and can be epressed as σ = σ r + jσ i where σ r and σ i are the real and imaginar parts of the effective conductivit, respectivel. Therefore, from Mawell s equations one can show that the real and imaginar parts of the relative comple permittivit ε = ε + jε can be epressed as [16] ε = 1 + σ i ωε o, and ε = σ i (4) ωε o where ε o is the permittivit of the vacuum and the graphene laer thickness. For the purpose of 3-D simulation, the thickness of graphene is assumed to be = 1 nm, although other etremel small values for this thickness lead to similar results. If the imaginar part of the effective conductivit is assumed to be zero then the real part of the comple permittivit ε is equal to the relative permittivit as in metals such as a copper and gold (low frequenc regime). 3. DESIGN OF UNIT-CELL The configuration of the proposed transmitarra unit cell is shown in Fig. 1. The cell element of the transmitarra consists of square Quartz cell, with length L c = 25 µm, substrate thickness h c = 2 µm with ε r = 3.45, and tan δ =.4. Dual circular graphene rings are printed on both sides of the Quartz substrate. Each circular graphene ring has width t = 1 µm and thickness = 1 nm. The outer graphene ring has radius R o and the inner graphene circular ring have radius of R i with (R i =.5R o ). (3)

Progress In Electromagnetics Research M, Vol. 36, 214 187 Quartz (ε r=3.45, and tanδ=.4) Graphene (τ=.5 psec, T=3 o K,µ c=.

The graphene material parameters are τ = 1 psec, T = 3 K, and µ c =.5 ev which result in surface impedance of 17 + j214.2 Ω.

The unit cell is positioned in the middle of the waveguide simulator as shown in Fig. 1(c).

3 Progress In Electromagnetics Research M, Vol. 36, Quartz (ε r=3.45, and tanδ=.4) Graphene (τ=.5 psec, T=3 o K,µ c=.5 ev) Lc hc Lc z Ri Ro t Electric wall Magnetic wall (a) 3-D view (b) Top view (c) Waveguide simulator Figure 1. Detailed construction of the proposed unit-cell. The graphene material parameters are τ = 1 psec, T = 3 K, and µ c =.5 ev which result in surface impedance of 17 + j214.2 Ω. To calculate the relation between the transmission coefficient phase and the graphene ring radius variation in the unit cell, the unit cell is placed in a waveguide simulator [7]. The unit cell is positioned in the middle of the waveguide simulator as shown in Fig. 1(c). The perfect electric and magnetic wall boundar conditions are applied to the sides of the surrounding waveguide, and result in image planes on all sides of the unit cell to represent an infinite arra approimation. A plane wave was used as the ecitation of the unit cells inside the waveguide simulator and onl normal incidence angle was considered. There are several limitations to the infinite arra approach. First, all elements of the transmitarra are identical; this is clearl not the case in the real transmitarra in which the radii of the graphene rings in each cell element must var according to the required phase compensation. Secondl, the transmitarra itself is not infinite in etent. The relationship between variable circular graphene ring radius and the transmission coefficient at 6 THz was determined using the FIT technique as shown in Fig. 2. The unit cell that having onl ring radius variation from 3 µm to 8.5 µm produce a phase shift ranging from to 355, with the transmission coefficient magnitude changes from 4.8 db to db. The surface conductivit of the graphene material with different chemical potentials µ c at τ = 1 psec and T = 3 K is shown in Fig. 3. Transmission phase (degrees) τ=1 psec, T=3 o K, µ c =.5 ev R o (µ m) (a) Transmission coefficient phase Transmission magnitude (db) τ=1 psec, T=3 o K, µ c =.5 ev -5 R o (µm) (b) Transmission coefficient magnitude Figure 2. Variation of the transmission coefficient phase and magnitude versus the graphene ring radius at f = 6 THz.

4 188 Malhat, Zainud-Deen, and Gaber In the frequenc range of interest, from 2 to 7 THz, the intraband contribution of the conductivit dominates, and the interband contribution can be ignored. B altering the chemical potential from EV to.95 EV, the comple conductivit has been calculated using Eq. (2). The conductivit is decreased with increasing frequenc. At a constant frequenc, the graphene conductivit is increased with increasing the chemical potential µ c. The graphene laer surface impedance Z s = 1/σ, behaves as a constant resistance in series with an inductive reactance that increases with frequenc. At 6 THz the surface impedance (resistance and inductive reactance) is decreased with increasing the chemical potential µ c. A parametric stud on the influence of graphene material parameters µ c at τ = 1 psec and T = 3 K on the variation of the transmission coefficient phase and magnitude versus the graphene ring radius is presented in Fig. 4. As the graphene chemical potential µ c is increased the transmission coefficient phase variation is increased to approach 36 and the transmission magnitude is reduced at some values. There will be a compromise between the transmission coefficient phase and magnitude variation for each value of graphene chemical potential µ c. For µ c = ev and µ c =.19 ev the conductivit of the graphene laer is almost constant with frequenc. So, b changing the graphene ring radius at constant frequenc 6 THz the variation in the phase of the transmitted wave is nearl constant and part of the incident plane wave is reflected back from the graphene laer. B increasing Re (σ) Conductivit (S) -2-4 µ c = ev µ c =.19 ev -6 µ c =.38 ev Im(σ) µ c =.5 ev µ c =.57 ev -8 µ c =.76 ev µ c =.95 ev Frequenc (THz) Figure 3. Graphene comple conductivit versus frequenc with different chemical potentials µ c at τ = 1 psec and T = 3 K. Transmission phase (degrees) µ c = ev µ c =.19 ev µ c =.38 ev µ c =.5 ev µ c =.57 ev µ c =.76 ev µ c =.95 ev τ=1 psec, T=3 o K R o (µm) (a) Transmission coefficient phase Transmission magnitude (db) -5-1 µ c = ev -15 µ c =.19 ev µ c =.38 ev -2 µ c =.5 ev µ c =.57 ev -25 µ c =.76 ev µ c =.95 ev -3 R o (µm) (b) Transmission coefficient magnitude Figure 4. The variation of the transmission coefficient phase and magnitude versus the graphene ring radius for different graphene nobilities at f = 6 THz.

5 Progress In Electromagnetics Research M, Vol. 36, the chemical potential, the variance of the graphene conductivit is remarkable from the beginning to the remnant of the frequenc band which results in a noteworth variet of the transmitted wave phase. The slope of the transmission coefficient phase variation curve is reduced b increasing the chemical potential which improves the final transmitarra bandwidth. While the fluctuation of the transmission coefficient magnitude didn t follow a specific blueprint. 4. TRANSMITARRAY ANTENNA Generall, the transmitarra transforms the spherical wave emanating from the feed into a plane wave at the output, as conventional parabolic reflector antenna. Consider an arra on the - plane illuminated b a feed horn as shown in Fig. 5(a). The required phase compensation distribution ϕ o at each unit cell element in the transmitarra to collimate a beam in the (θ o, φ o ) direction is obtained b [7]: ϕ o ( cij, cij ) = k o [d ij cij sin(θ o ) cos(φ o ) cij sin(θ o ) sin(φ o )] (5) d ij = ( cij f ) 2 + ( cij f ) 2 + zf 2 (6) where k o = 2π/λ o is the propagation constant in free space; ( cij, cij, ) are the coordinates of transmitarra unit cell element; ( f, f, z f ) are the coordinates of the phase centre of the feed horn. This equation depends on estimating the etra distance travelled b the incident plane wave and transmitted back from a planar reflector than that transmitted back from a parabolic reflector to transform the spherical wave to a plane wave collimating the beam in the required direction. L d Beam Direction (θ o, ϕ o ) L (a) 3-D view F (,,-z f ) ( cij, cij,) -z - ais ais (b) Phase distribution Figure 5. Configuration of 9 9 graphene based transmitarra fed b circularl polarized circular horn and the required phase compensation for each element. The phase of the transmitted wave of each element is achieved b varing the element dimensions. The phase shift of each cell element in the transmitarra should between and 36 with magnitude variation from to 4 db. The transmitarra used in this analsis is composed of 9 9 unit cell elements and is covering an area of µm 2 in - plane. Of course, larger number of cells can be used to get higher gain. However, it is the computing facilities which limited the number of cells to 9 9. A common voltage is applied to all the graphene rings to obtain a tpical chemical potential (µ c =.5 ev) to be the same for all the rings. The compensation phase distribution for the 9 9 transmitarra elements is shown in Fig. 5(b). The transmitarra is smmetrical around both the -ais and -ais with phase distribution varies from to 36. A circular horn is used to feed the transmitarra with radius R h = 4 µm, and length L h = 56 µm at 6 THz as shown in Fig. 6(a). The horn is fed via two orthogonal coaial probes with 9 phase shift to produce circular polarization (CP) field from the horn. The horn is located at a distance of 225 µm from the transmitarra aperture. The 3-D radiation pattern of the circular horn is shown in Fig. 6(b) at 6 THz. The left-hand (LHCP) and right-hand (RHCP) circular polarization far-fields for the circular horn and the transmitarra in E-plane and H-plane are shown in Fig. 7 at f = 6 THz. The program used in computations is based on full-wave analsis of the problem and is taking into consideration the effect of the mutual coupling between the elements

The side lobe levels (SLL) in the E- and H-planes are approimatel 15 db. The gain of the transmitarra against the frequenc is shown in Fig. 8(a). The peak gain is 18.63 db. The 1 db gain bandwidth is.

6 19 Malhat, Zainud-Deen, and Gaber and the edge effects of the arra. The cross-polar (right-hand circular polarization) level is lower than 5 db relative to the copolar in the H-plane aial direction at the designed frequenc. The side lobe levels (SLL) in the E- and H-planes are approimatel 15 db. The gain of the transmitarra against the frequenc is shown in Fig. 8(a). The peak gain is db. The 1 db gain bandwidth is.41 THz R g z Coaial feeding probes (a) 3-D view R h (b) 3-D radiation pattern of the horn at f=6 THz Figure 6. Detailed construction of a circularl polarized circular horn antenna and its 3-D gain pattern at f = 6 THz transmitarra fed b horn LHCP RHCP transmitarra fed b horn LHCP RHCP Gain (db) -1 Gain (db) Elevation angles (degrees) (a) E-plane Elevation angles (degrees) (b) H-plane Figure 7. The configuration of 9 9 graphene based transmitarra fed b circularl polarized horn at f = 6 THz. Gain (db) transmitarra fed b horn Frequenc (THz) (a) Gain Aial Ratio (db) transmitarra fed b horn Frequenc (THz) (b) Aial ratio Figure 8. The gain and aial ratio variation versus frequenc for 9 9 graphene based transmitarra fed b circularl polarized horn at θ = ϕ =.

7 Progress In Electromagnetics Research M, Vol. 36, (6.8%). The aial ratio versus frequenc is shown in Fig. 8(b). The arra produces circular polarization in the aial direction with aial ratio, AR < 1 db and covers a range from 5.5 THz to 6.5 THz. 5. CONCLUSION In this paper, terahertz transmitarra with graphene ring elements has been proposed. Circularl polarized horn antenna is used to feed the transmitarra. The effect of changing the radius of the ring element and the graphene chemical potential on the transmission coefficient of the cell element has been eplained. The circularl polarized field components are calculated using the full-wave analsis of the antenna structure. The gain of the antenna at the boresight direction has been found db with gain bandwidth equal to 6.8%. REFERENCES 1. Choi, W. and J. Lee, Graphene: Snthesis and Applications, CRC Press Talor & Francis Group, NW, USA, Bao, W., Electrical and mechanical properties of graphene, Ph.D Thesis, Universit of California Riverside, USA, Jian, L., Graphene and its hbrid nanostructures for nanoelectronics and energ applications, Ph.D Thesis, Universit of California Riverside, USA, Hansen, R. C., Phased Arra Antennas, John Wile & Sons, Inc., Hoboken, NJ, USA, Hum, S. V. and J. Perruisseau-Carrier, Reconfigurable reflectarra and arra lenses for dnamic antenna beam control: A review, IEEE Transactions on Antennas and Propagation, Vol. 62, No. 1, , Jan Rodrigo, D., L. Jofre, and J. Perruisseau-Carrier, Unit cell for frequenc-tunable beamscanning reflectarras, IEEE Transactions on Antennas and Propagation, Vol. 61, No. 12, , Gaber, S. M., Analsis and design of reflectarras/transmitarras antennas, Ph.D Thesis, Minoufia Universit, Huang, J. and J. A. Encinar, Reflectarra Antennas, Wile-IEEE Press, Pisatawa, NJ, Zainud-Deen, S. H., H. A. Malhat, S. M. Gaber, and K. H. Awadalla, Perforated nanoantenna reflectarra, Progress In Electromagnetics Research M, Vol. 29, , Zainud-Deen, S. H., H. A. Malhat, S. M. Gaber, and K. H. Awadalla, Plasma reflectarra, Plasmonic Journal, Vol. 8, , Zainud-Deen, S. H., H. A. Malhat, S. M. Gaber, and K. H. Awadalla, Beam steering plasma reflectarra/transmitarra antennas, Plasmonic Journal, DOI 1.17/s , Lau, J. Y. and S. V. Hum, Reconfigurable transmitarra design approaches for beamforming applications, IEEE Transactions on Antennas and Propagation, Vol. 6, No. 12, , Dec Lau, J. Y. and S. V. Hum, A wideband reconfigurable transmitarra element, IEEE Transactions on Antennas and Propagation, Vol. 6, No. 3, , Mar Cooke, S. J., R. Shtokhamer, A. A. Mondelli, and B. Levush, A finite integration method for conformal, structure-grid, electromagnetic simulation, Journal of Computational Phsics, Vol. 215, , Rouhi, N., S. Capdevila, D. Jain, K. Zand, Y. Wang, E. Brown, L. Jofre, and P. Burke, Terahertz graphene optics, Nano Research Journal, Vol. 5, No. 1, , Oct Kadhom, M. J., J. S. Aziz, and R. S. Fath, Performance investigation of loop and helical carbon nanotube antennas, Journal of Emerging Trends in Computing and Information Sciences, Vol. 3, No. 12, , Dec. 212.

Bi-Function Multi-Beam Graphene Lens Antenna for Terahertz Applications

Wireless Engineering and Technology, 2016, 7, 36-45 Published Online January 2016 in SciRes. http://www.scirp.org/journal/wet http://dx.doi.org/10.4236/wet.2016.71004 Bi-Function Multi-Beam Graphene Lens