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Graphene-based patch antenna tunable in the three atmospheric windows
Accepted Manuscript Title: Graphene-based Patch Antenna Tunable in the Three Atmospheric Windows Authors: Amir Hossein Kazemi, Arash Mokhtari PII: DOI: Reference:
S0030-4026(17)30695-2 http://dx.doi.org/doi:10.1016/j.ijleo.2017.05.113 IJLEO 59289
To appear in: Received date: Accepted date:
23-2-2017 22-5-2017
Please cite this article as: Amir Hossein Kazemi, Arash Mokhtari, Graphene-based Patch Antenna Tunable in the Three Atmospheric Windows, Optik - International Journal for Light and Electron Opticshttp://dx.doi.org/10.1016/j.ijleo.2017.05.113 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Graphene-based Patch Antenna Tunable in the Three Atmospheric Windows
Amir Hossein Kazemi 1, Arash Mokhtari1
1
Dept. of Electrical engineering, Shahid Bahonar University of Kerman, Kerman, Iran
[email protected], [email protected] Manuscript received February 20, 2017
Abstract: A graphene microstrip patch antenna is designed to operate in the three bands of the atmospheric windows promising for the future wireless communications. The graphene has a reconfigurable surface conductivity that can be tuned to operate at the desired frequencies. This paper studies the role of chemical potential (ππ ) of the graphene to tune the resonant frequency of a microstrip antenna. The results show that the resonant frequency of a microstrip antenna increases as the chemical potential grows that can be employed to realize a reconfigurable antenna. The proposed resonances for the low-loss 300 GHz, 350 GHz and 410 GHz atmospheric windows can be achieved for ππ = 0.21 eV, ππ = 0.4 eV and ππ = 1.5 eV respectively. Finally, a design process for a multi-band graphene-based antenna has been presented.
Keywords: Reconfigurable Antenna; THz band; Atmospheric windows; Microstrip Patch-antenna; Graphene.
The THz band is a portion of the electromagnetic spectrum includes frequencies in the range of 0.1 THz to 10 THz. Due to important properties of THz band such as the ability to pass through different materials with various levels of attenuation and the non-ionization effect, it has been used in numerous applications including high bitrate to support Tbps links [1], spectroscopy, high-resolution radars and circuit integration [2]. The choice of antenna is crucial to achieving the desired electromagnetic properties in THz regime [3] in some applications like high-performance aircrafts, satellites, space crafts, and missile[4]. The microstrip patch antenna is one of the most widely used antennas due to its simple, robust and low-cost structure readily applicable to planar and non-planar surfaces. Therefore, it is a good choice in order to realize system miniaturization for THz wireless applications [5]. Graphene is a two-dimensional monolayer of carbon atoms firmly arranged in a twodimensional honeycomb lattice [6-8]. Hence, it can be used in a plenty of possible applications such as high-speed transistors, transparent solar cells, metamaterials and antennas [9-15]. The resonant frequency of an antenna plays a key role in the design of a reconfigurable and tunable antenna [9]. A graphene-based microstrip patch antenna with dimensions of micrometers has been predicted to resonate in the THz band [4], [9]. Its resonant frequency can be tuned by the choice of chemical potential of graphene which can be simply controlled by means of either material doping or by applying an external voltage. In a previous work [16], a patch microstrip antenna for 600 GHz with both copper and graphene has been investigated using the simulator ANSYS-HFSS. It is shown that changing the graphene material parameters such as chemical potential and relaxation time can influence radiation characteristics. Moreover, a rough conductivity model of graphene is used. The usability
of the proposed scheme is also highly restricted because of high atmospheric attenuation for 600 GHz band in the wireless communication. In this paper, we exhibit a graphene-based microstrip patch antenna that operates at three atmospheric windows with minimum attenuation at 300 GHz, 350 GHz, 410 GHz bands [17]. Here, the surface conductivity of graphene controls the antenna parameters; input impedance, return loss, VSWR, and radiation pattern. Additionally, the accuracy of the conductivity model of graphene is enhanced. A design algorithm for tunable operation is also introduced at the end. Owing to the two-dimensional structure of graphene, graphene sheet can be modeled by an equivalent surface with a given conductivity Ο, which can be calculated by Kuboβs formula with the Drude-like intraband contribution, the surface conductivity can be represented as[18]:
ο
ο³ο¨ο·ο©ο ο½
2π 2 πβ
π
π
ππ΅ πππ [2πππ β [2πΎ π π]] π+ππβ1ο ο ο¨ο±ο©ο π΅
where e (charge of an electron), Δ§ (reduced Planckβs constant), Ο (relaxation time), T (temperature in Kelvin), ππ (chemical potential of graphene), πΎπ΅ (Boltzmann constant) and π (angular frequency). For the frequency range below 8 THz, this intraband contribution approximation is reasonable. The surface conductivity due to the interband contribution can be calculated by [18], [19]: π2
π
ππ (π) = 4β (π» ( 2 ) + π
4π π
π
β π»(π)βπ»( 2 )
β«0
π 2 β4π 2
ππ)
(2)
which should be evaluated by numerical integration. H(Ξ΅) is also defined as follows: ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο(π) =
Δ§π ) ππ΅ π
π ππβ(
π’ Δ§π ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο¨ο³ο©ο πππ β( π )+πππ β( ) ππ΅ π
ππ΅ π
The total conductivity is π + ππ and ππ = 1/Ο is the surface conductivity of the graphene sheet. It should be noted that at higher frequencies, intraband contribution can be neglected compared to the interband contribution. To increase the accuracy of conductivity model of graphene, interband contribution is calculated numerically. Here we assume π = 1 ππ and π = 300Β° πΎ.
Antenna Design and Configuration We have designed a copper microstrip patch antenna fed by coaxial probe to operate near 421 GHz as shown in Figure 1. The thickness of the patch is 20 ΞΌm. The side view is also depicted in Figure 2. Dimensions of the antenna are of the order of micrometers as listed in Table 1. The antenna has 40 ΞΌm PTFE substrate with ππ = 2.08 and tan Ξ΄ = 0.0004. The thickness of ground and the patch are the same. The return loss graph for the copper patch antenna is shown in Figure 3. A coaxial feed with radius R = 5 Β΅m is used to excite the antenna. The antenna structure is simulated by the full-wave solver (CST Microwave Studio) and validates by the simulator ANSYS-HFSS. The variation of the input impedance versus frequency is shown in Figure 4. The E-plane (x-z) and H-plane (y-z) radiation pattern at 421 GHz are illustrated in Figure 5. The input impedance of an antenna is an important parameter that always should be noticed as well as other antenna electromagnetic characteristics such as radiation pattern, VSWR and return loss. In general, the input impedance and reactance of an antenna vary as a function of frequency. As a matter of fact, the resistance and reactance diagram have even and odd symmetry respectively near this frequency. This is a good criteria that can be checked to predict the resonant frequency of an antenna [3]. As shown in Figure 4, the resonant frequency is predicted to happen round 421 GHz. By replacing the copper patch by a graphene with the same dimensions but a patch thickness of 10 nm, a graphene-based microstrip patch antenna will be
achieved but with a bit lower resonant frequency. As shown in Equation (1), varying the chemical potential of graphene which affects the electrical conductivity of graphene sheet and hence the resonant frequency value. Therefore, we can tune the resonance frequency in the range 300 GHz to 420 GHz. The desired resonances can be engineered cautiously to occur at 300 GHz, 350 GHz and 410 GHz bands by choosing the proper values of chemical potential (i.e. 0.21 eV, 0.4 eV and 1.5 eV respectively). The variation of the return loss versus frequency for different values of chemical potential ππ for graphene-based patch antenna is shown in Figure 6. It is observed that for ΞΌc = 0.4 eV, the return loss is decreased for the proposed range of frequency. The resonant frequency increases as the chemical potential ππ amplifies. The input resistance and input reactance of graphene based patch antenna versus frequency for different values of chemical potential are shown in Figure 7 and Figure 8 respectively. It is observed that both resistance and reactance exhibit symmetry around the resonant frequency. The maximum values of the input impedance resistance and reactance are increased as the chemical potential rises. The maximum value of the VSWR values for different values of chemical potential are shown in Figure 9 that depicts the respective variations well. The best value of VSWR (nearly complete match) is observed for ΞΌc = 0.4 eV. At first, we have designed a condition that resonant frequency of an antenna occurs in the first window, 300 GHz. The variation of the input impedance versus frequency for 300 GHz frequency is shown in Figure 10. It is observed with reasonable approximation, resonant frequency occurs in 300 GHz. The E-plane (x-z) and H-plane (y-z) far-field radiation pattern for a graphene-based patch antenna at 300 GHz are shown in Figure 11. Then we alter chemical
potential from ΞΌc = 0.21 eV to ΞΌc = 0.4 eV to achieve 350 GHz resonance frequency. The Eplane (x-z) and H-plane (y-z) radiation pattern at 350 GHz are shown in Figure 12. The variation of the input impedance versus frequency for 350 GHz frequency is shown in Figure 13. As shown, the variation of the input impedance is symmetric around 350 GHz. The value of input impedance compared with the metallic antenna is near 50 Ξ© and can easily match with the proper load. The maximum value of input resistance has been increased by increasing the chemical potential values. Here, this maximum value occurred at ππ = 1.5 eV as shown in Figure 7. In the next step, we change the chemical potential to ππ = 1.5 eV to achieve 410 GHz resonance frequency. The variation of the input impedance versus frequency for 410 GHz frequency is shown in Figure 14. The E-plane (x-z) and H-plane (y-z) radiation pattern at 410 GHz are shown in Figure 15. The input impedance is lower compared to the metallic antenna. Also, we can predict the resonant frequency of antenna from input impedance curve that occurs at 410 GHz. At ππ = 0.4 eV, the minimum value of VSWR has been occurred as shown in Figure 9. The Eplane and H-plane of graphene antennas are nearly the same except for the extra zero in the Efield pattern. The proposed tunable patch antenna based on graphene has been designed and investigated. A brief detail of simulation results is tabulated in Table 2. As mentioned earlier, graphene is a monolayer of carbon atoms arranged in a hexagonal structure. Here, we have used graphene as a patch of the microstrip antenna. Exciting the graphene strip by a time-varying electric current causes surface plasmon polariton (SPP) at the interface with the dielectric layer Graphene layer makes good condition for propagating SPPs. The edges of the patch act as mirror for SPP waves because the interface of air-dielectric doesnβt support SPP wave and patch becomes a resonator. The SPP modes on the patch couple with incident radiations which is the main reason for
resonance of the microstrip patch antenna [20]. Therefore, graphene patch microstrip antenna bahaves as a resonance antenna. We can design a microstrip patch antenna based on graphene operating at any band in the THz band. To achieve the best design, we should stick to some rules. An idea for creating tunable antenna is to change the chemical potential. The value of chemical potential is an analog number between 0 and 2 eV [16]. As previously mentioned, the resonant frequency of antenna increases as chemical potential value amplifies. Surface impedance of graphene decreases as chemical potential of graphene increases. So graphene has similar performance like metal at higher value of chemical potential. 1) Now, we are going to design a tunable microstrip patch antenna based on graphene that resonances at π1 , π2 , and π3 sorted from the lowest to the highest. We should follow this steps: A microstrip patch antenna based on copper should be designed to operate at 2-3% higher thanπ3 . 2) Substitute copper by a thick layer of graphene with chemical potential value higher 1.4 eV. 3) The chemical potential values is reduced to achieve good resonances at π1 and π2 . If the lowest reasonable resonance is higher than the proposed frequency ( π1 ), we should alter our first design dimension to make the antenna have a resonance at lower frequency. We have prepared a block diagram for better understanding of the procedure depicted in Figure 16.
Conclusion In this paper, we have investigated the graphene microstrip patch antenna that can operate at atmospheric windows. The effect of graphene chemical potential tunability on resonant
frequency has been investigated and showed that for ΞΌc = 0.21 eV, ΞΌc = 0.4 eV, and ΞΌc = 1.5 eV proposed resonances occur at 300 GHz, 350 GHz and 410 GHz respectively. Therefore, it can be concluded that proposed antenna can be used in a THz communication circuit to operate at three atmospheric windows with minimum loss simultaneously. Also we have presented a process to design a multi-band antenna for operation in the THz-spectrum. It has been shown the proposed graphene antenna has the potential to operate in multiple bands of the THz spectrum. However, a tunable matching circuit is essential to guarantee maximum performance of the antenna at the frequencies of operation.
References [1] [2] [3] [4]
[5]
[6]
[7]
I. F. Akyildiz, J. M. Jornet, and C. Han, "Terahertz band: Next frontier for wireless communications," Physical Communication, vol. 12, pp. 16-32, 2014. K. R. Jha and G. Singh, Terahertz planar antennas for next generation communication: Springer, 2014. C. A. Balanis, Antenna theory: analysis and design: John Wiley & Sons, 2016. M. S. D. Anand Sreekantan Thampy n, Sriram Kumar Dhamodharan, "Analysis_of_graphene_based_optically_transparent_patch_antenna_for_terahert (1)," Elsevier, 2014. A. S. Thampy, M. S. Darak, and S. K. Dhamodharan, "Analysis of graphene based optically transparent patch antenna for terahertz communications," Physica E: Lowdimensional Systems and Nanostructures, vol. 66, pp. 67-73, 2015. O. P. Paola Goria*, Roberto de Lieto Vollaroa, Claudia Guattaria, "Thermophysical properties of the novel 2D materials graphene and silicene: insights from ab-initio calculations," by Elsever, vol. 45, pp. 512-517, 2014. R. T. Renato Iovine, Lucio Vegni, "Electromagnetic Analysis of Graphene
Nanoparticles Operating in the TeraHertz Band," Advances in Nanoparticles, vol. 3, 2014. [8]
M. l.Katsnelson, "Graphene: carbon in two dimensions," Materialstoday, vol. 10, pp. 2027, 2007.
[9]
I. Llatser, C. Kremers, A. Cabellos-Aparicio, J. M. Jornet, E. AlarcΓ³n, and D. N. Chigrin, "Graphene-based nano-patch antenna for terahertz radiation," Photonics and Nanostructures - Fundamentals and Applications, vol. 10, pp. 353-358, 2012.
[10] [11] [12] [13] [14] [15]
[16]
[17]
[18]
[19] [20]
Y. Iyechika, "Application of graphene to high-speed transistors: expectations and challenges," Sci. Technol. Trends, vol. 37, pp. 76-92, 2010. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, et al., "Graphene plasmonics for tunable terahertz metamaterials," Nature nanotechnology, vol. 6, pp. 630-634, 2011. P. Avouris and C. Dimitrakopoulos, "Graphene: synthesis and applications," Materials Today, vol. 15, pp. 86-97, 2012. J.-H. Ahn, B. H. Hong, F. Torrisi, J. Coleman, J. Liu, S. BΓΆhm, et al., "Things you could do with graphene," Nat. Nanotechnol, vol. 9, pp. 737-747, May 6, 2014. P. Tassin, T. Koschny, and C. M. Soukoulis, "Graphene for terahertz applications," Science, vol. 341, pp. 620-621, 2014. P. Avouris, Y. M. Lin, F. Xia, T. Mueller, D. B. Farmer, C. Dimitrakopoulos, et al., "Graphene-based fast electronics and optoelectronics," in 68th Device Research Conference, 2010, pp. 205-206. H. A. E.-A. Malhat and S. H. Zainud-Deen, "Equivalent Circuit with FrequencyIndependent Lumped Elements for Plasmonic Graphene Patch Antenna Using Particle Swarm Optimization Technique," Wireless Personal Communications, vol. 85, pp. 18511867, 2015. T. Kleine-Ostmann and T. Nagatsuma, "A Review on Terahertz Communications Research," Journal of Infrared, Millimeter, and Terahertz Waves, vol. 32, pp. 143-171, 2011. I. Llatser, C. Kremers, A. Cabellos-Aparicio, J. M. Jornet, E. AlarcΓ³n, and D. N. Chigrin, "Graphene-based nano-patch antenna for terahertz radiation," Photonics and Nanostructures-Fundamentals and Applications, vol. 10, pp. 353-358, 2012. G. W. Hanson, "Dyadic Greenβs functions and guided surface waves for a surface conductivity model of graphene," Journal of Applied Physics, vol. 103, 2008. I. Llatser, C. Kremers, A. Cabellos-Aparicio, E. AlarcoΒ΄ n, D. N. Chigrin, and D. N. Chigrin, "Comparison of the resonant frequency in graphene and metallic nanoantennas," in AIP Conference Proceedings-American Institute of Physics, p. 143, 2012.
Ws 2R
Wp
Ls
Lp
Y X
Figure 1. Top view of a coaxial feed based patch antenna. (P and S stand for patch and substrate)
h
Z
X
2R Figure 2. Side view of a coaxial feed based patch antenna.
Figure 3. Return loss versus frequency for the copper patch microstrip antenna
Figure 4. The variation of input impedance versus frequency for copper patch microstrip antenna.
Fig. 5. E-plane (solid line) and H-plane (dash line) far field radiation patterns of the copper based patch antenna at 421 GHz.
Fig. 6. Return loss versus frequency for different values of chemical potential for the graphene based patch antenna.
Fig. 7. Input resistance versus frequency for different values of chemical potential for the graphene based patch antenna.
Fig. 8. The variation of input reactance versus frequency for different values of chemical potential for graphene based patch antenna.
Fig. 9. The VSWR curves for different chemical potential values.
Fig. 10. The variation of input impedance versus frequency for graphene patch microstrip antenna. (ππ = 0.21 eV)
Fig. 11. E-plane (solid line) and H-plane (dash line) far field radiation patterns of the graphene based patch antenna at 300 GHz.
Fig. 12. E-plane (solid line) and H-plane (dash line) far field radiation patterns of the graphene based patch antenna at 350 GHz.
Fig. 13. The variation of input impedance versus frequency for graphene patch microstrip antenna. (ππ = 0.4 eV)
Fig. 14. The variation of input impedance versus frequency for graphene patch microstrip antenna. (ππ = 1.5 eV)
Figure 15. E-plane (blue line) and H-plane (red line) far field radiation patterns of the graphene based patch antenna at 410 GHz.
1 2 3 4
β’Select any arbitrary frequency π1, π2 and π3 .
(π1 < π2 < π3 )
β’Design a copper microstrip patch antenna at 2-3% higher than π3 . β’Substitute copper by a graphene layer ( ππ >1.4 eV ). β’Reduce ππ to achieve proposed resonances at π1 and π2 .
Fig. 16. The block-diagram that show steps of designing any arbitrary triple band antenna. Parameters πΏπ Γ ππ
Tab. 1.
Dimensions ( ΞΌm ) 182.86 Γ 233
πΏπ Γ ππ Γ h
500 Γ 500 Γ 40
R
5
Design parameter of the microstrip patch antenna.
Resonant frequency ( GHz)
ππ ( eV )
πΊππ ( dB )
VSWR
πΉππ (Ξ©)
πΏππ (Ξ©)
Directivity (dB)
Band width ( GHz)
300
0.21
12.16
1.65
32.24
-10.50
6.71
41.23
350
0.4
30.67
47.22
-1.53
7.34
410
1.5
13.96
73.9
-4.92
Graphene antenna
Tab. 2.
1.06
1.5
7.73
Simulation results of the graphene microstrip patch antenna.
58.39 37.5
S0030-4026(17)30695-2 http://dx.doi.org/doi:10.1016/j.ijleo.2017.05.113 IJLEO 59289
To appear in: Received date: Accepted date:
23-2-2017 22-5-2017
Please cite this article as: Amir Hossein Kazemi, Arash Mokhtari, Graphene-based Patch Antenna Tunable in the Three Atmospheric Windows, Optik - International Journal for Light and Electron Opticshttp://dx.doi.org/10.1016/j.ijleo.2017.05.113 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Graphene-based Patch Antenna Tunable in the Three Atmospheric Windows
Amir Hossein Kazemi 1, Arash Mokhtari1
1
Dept. of Electrical engineering, Shahid Bahonar University of Kerman, Kerman, Iran
[email protected], [email protected] Manuscript received February 20, 2017
Abstract: A graphene microstrip patch antenna is designed to operate in the three bands of the atmospheric windows promising for the future wireless communications. The graphene has a reconfigurable surface conductivity that can be tuned to operate at the desired frequencies. This paper studies the role of chemical potential (ππ ) of the graphene to tune the resonant frequency of a microstrip antenna. The results show that the resonant frequency of a microstrip antenna increases as the chemical potential grows that can be employed to realize a reconfigurable antenna. The proposed resonances for the low-loss 300 GHz, 350 GHz and 410 GHz atmospheric windows can be achieved for ππ = 0.21 eV, ππ = 0.4 eV and ππ = 1.5 eV respectively. Finally, a design process for a multi-band graphene-based antenna has been presented.
Keywords: Reconfigurable Antenna; THz band; Atmospheric windows; Microstrip Patch-antenna; Graphene.
The THz band is a portion of the electromagnetic spectrum includes frequencies in the range of 0.1 THz to 10 THz. Due to important properties of THz band such as the ability to pass through different materials with various levels of attenuation and the non-ionization effect, it has been used in numerous applications including high bitrate to support Tbps links [1], spectroscopy, high-resolution radars and circuit integration [2]. The choice of antenna is crucial to achieving the desired electromagnetic properties in THz regime [3] in some applications like high-performance aircrafts, satellites, space crafts, and missile[4]. The microstrip patch antenna is one of the most widely used antennas due to its simple, robust and low-cost structure readily applicable to planar and non-planar surfaces. Therefore, it is a good choice in order to realize system miniaturization for THz wireless applications [5]. Graphene is a two-dimensional monolayer of carbon atoms firmly arranged in a twodimensional honeycomb lattice [6-8]. Hence, it can be used in a plenty of possible applications such as high-speed transistors, transparent solar cells, metamaterials and antennas [9-15]. The resonant frequency of an antenna plays a key role in the design of a reconfigurable and tunable antenna [9]. A graphene-based microstrip patch antenna with dimensions of micrometers has been predicted to resonate in the THz band [4], [9]. Its resonant frequency can be tuned by the choice of chemical potential of graphene which can be simply controlled by means of either material doping or by applying an external voltage. In a previous work [16], a patch microstrip antenna for 600 GHz with both copper and graphene has been investigated using the simulator ANSYS-HFSS. It is shown that changing the graphene material parameters such as chemical potential and relaxation time can influence radiation characteristics. Moreover, a rough conductivity model of graphene is used. The usability
of the proposed scheme is also highly restricted because of high atmospheric attenuation for 600 GHz band in the wireless communication. In this paper, we exhibit a graphene-based microstrip patch antenna that operates at three atmospheric windows with minimum attenuation at 300 GHz, 350 GHz, 410 GHz bands [17]. Here, the surface conductivity of graphene controls the antenna parameters; input impedance, return loss, VSWR, and radiation pattern. Additionally, the accuracy of the conductivity model of graphene is enhanced. A design algorithm for tunable operation is also introduced at the end. Owing to the two-dimensional structure of graphene, graphene sheet can be modeled by an equivalent surface with a given conductivity Ο, which can be calculated by Kuboβs formula with the Drude-like intraband contribution, the surface conductivity can be represented as[18]:
ο
ο³ο¨ο·ο©ο ο½
2π 2 πβ
π
π
ππ΅ πππ [2πππ β [2πΎ π π]] π+ππβ1ο ο ο¨ο±ο©ο π΅
where e (charge of an electron), Δ§ (reduced Planckβs constant), Ο (relaxation time), T (temperature in Kelvin), ππ (chemical potential of graphene), πΎπ΅ (Boltzmann constant) and π (angular frequency). For the frequency range below 8 THz, this intraband contribution approximation is reasonable. The surface conductivity due to the interband contribution can be calculated by [18], [19]: π2
π
ππ (π) = 4β (π» ( 2 ) + π
4π π
π
β π»(π)βπ»( 2 )
β«0
π 2 β4π 2
ππ)
(2)
which should be evaluated by numerical integration. H(Ξ΅) is also defined as follows: ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο(π) =
Δ§π ) ππ΅ π
π ππβ(
π’ Δ§π ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο ο¨ο³ο©ο πππ β( π )+πππ β( ) ππ΅ π
ππ΅ π
The total conductivity is π + ππ and ππ = 1/Ο is the surface conductivity of the graphene sheet. It should be noted that at higher frequencies, intraband contribution can be neglected compared to the interband contribution. To increase the accuracy of conductivity model of graphene, interband contribution is calculated numerically. Here we assume π = 1 ππ and π = 300Β° πΎ.
Antenna Design and Configuration We have designed a copper microstrip patch antenna fed by coaxial probe to operate near 421 GHz as shown in Figure 1. The thickness of the patch is 20 ΞΌm. The side view is also depicted in Figure 2. Dimensions of the antenna are of the order of micrometers as listed in Table 1. The antenna has 40 ΞΌm PTFE substrate with ππ = 2.08 and tan Ξ΄ = 0.0004. The thickness of ground and the patch are the same. The return loss graph for the copper patch antenna is shown in Figure 3. A coaxial feed with radius R = 5 Β΅m is used to excite the antenna. The antenna structure is simulated by the full-wave solver (CST Microwave Studio) and validates by the simulator ANSYS-HFSS. The variation of the input impedance versus frequency is shown in Figure 4. The E-plane (x-z) and H-plane (y-z) radiation pattern at 421 GHz are illustrated in Figure 5. The input impedance of an antenna is an important parameter that always should be noticed as well as other antenna electromagnetic characteristics such as radiation pattern, VSWR and return loss. In general, the input impedance and reactance of an antenna vary as a function of frequency. As a matter of fact, the resistance and reactance diagram have even and odd symmetry respectively near this frequency. This is a good criteria that can be checked to predict the resonant frequency of an antenna [3]. As shown in Figure 4, the resonant frequency is predicted to happen round 421 GHz. By replacing the copper patch by a graphene with the same dimensions but a patch thickness of 10 nm, a graphene-based microstrip patch antenna will be
achieved but with a bit lower resonant frequency. As shown in Equation (1), varying the chemical potential of graphene which affects the electrical conductivity of graphene sheet and hence the resonant frequency value. Therefore, we can tune the resonance frequency in the range 300 GHz to 420 GHz. The desired resonances can be engineered cautiously to occur at 300 GHz, 350 GHz and 410 GHz bands by choosing the proper values of chemical potential (i.e. 0.21 eV, 0.4 eV and 1.5 eV respectively). The variation of the return loss versus frequency for different values of chemical potential ππ for graphene-based patch antenna is shown in Figure 6. It is observed that for ΞΌc = 0.4 eV, the return loss is decreased for the proposed range of frequency. The resonant frequency increases as the chemical potential ππ amplifies. The input resistance and input reactance of graphene based patch antenna versus frequency for different values of chemical potential are shown in Figure 7 and Figure 8 respectively. It is observed that both resistance and reactance exhibit symmetry around the resonant frequency. The maximum values of the input impedance resistance and reactance are increased as the chemical potential rises. The maximum value of the VSWR values for different values of chemical potential are shown in Figure 9 that depicts the respective variations well. The best value of VSWR (nearly complete match) is observed for ΞΌc = 0.4 eV. At first, we have designed a condition that resonant frequency of an antenna occurs in the first window, 300 GHz. The variation of the input impedance versus frequency for 300 GHz frequency is shown in Figure 10. It is observed with reasonable approximation, resonant frequency occurs in 300 GHz. The E-plane (x-z) and H-plane (y-z) far-field radiation pattern for a graphene-based patch antenna at 300 GHz are shown in Figure 11. Then we alter chemical
potential from ΞΌc = 0.21 eV to ΞΌc = 0.4 eV to achieve 350 GHz resonance frequency. The Eplane (x-z) and H-plane (y-z) radiation pattern at 350 GHz are shown in Figure 12. The variation of the input impedance versus frequency for 350 GHz frequency is shown in Figure 13. As shown, the variation of the input impedance is symmetric around 350 GHz. The value of input impedance compared with the metallic antenna is near 50 Ξ© and can easily match with the proper load. The maximum value of input resistance has been increased by increasing the chemical potential values. Here, this maximum value occurred at ππ = 1.5 eV as shown in Figure 7. In the next step, we change the chemical potential to ππ = 1.5 eV to achieve 410 GHz resonance frequency. The variation of the input impedance versus frequency for 410 GHz frequency is shown in Figure 14. The E-plane (x-z) and H-plane (y-z) radiation pattern at 410 GHz are shown in Figure 15. The input impedance is lower compared to the metallic antenna. Also, we can predict the resonant frequency of antenna from input impedance curve that occurs at 410 GHz. At ππ = 0.4 eV, the minimum value of VSWR has been occurred as shown in Figure 9. The Eplane and H-plane of graphene antennas are nearly the same except for the extra zero in the Efield pattern. The proposed tunable patch antenna based on graphene has been designed and investigated. A brief detail of simulation results is tabulated in Table 2. As mentioned earlier, graphene is a monolayer of carbon atoms arranged in a hexagonal structure. Here, we have used graphene as a patch of the microstrip antenna. Exciting the graphene strip by a time-varying electric current causes surface plasmon polariton (SPP) at the interface with the dielectric layer Graphene layer makes good condition for propagating SPPs. The edges of the patch act as mirror for SPP waves because the interface of air-dielectric doesnβt support SPP wave and patch becomes a resonator. The SPP modes on the patch couple with incident radiations which is the main reason for
resonance of the microstrip patch antenna [20]. Therefore, graphene patch microstrip antenna bahaves as a resonance antenna. We can design a microstrip patch antenna based on graphene operating at any band in the THz band. To achieve the best design, we should stick to some rules. An idea for creating tunable antenna is to change the chemical potential. The value of chemical potential is an analog number between 0 and 2 eV [16]. As previously mentioned, the resonant frequency of antenna increases as chemical potential value amplifies. Surface impedance of graphene decreases as chemical potential of graphene increases. So graphene has similar performance like metal at higher value of chemical potential. 1) Now, we are going to design a tunable microstrip patch antenna based on graphene that resonances at π1 , π2 , and π3 sorted from the lowest to the highest. We should follow this steps: A microstrip patch antenna based on copper should be designed to operate at 2-3% higher thanπ3 . 2) Substitute copper by a thick layer of graphene with chemical potential value higher 1.4 eV. 3) The chemical potential values is reduced to achieve good resonances at π1 and π2 . If the lowest reasonable resonance is higher than the proposed frequency ( π1 ), we should alter our first design dimension to make the antenna have a resonance at lower frequency. We have prepared a block diagram for better understanding of the procedure depicted in Figure 16.
Conclusion In this paper, we have investigated the graphene microstrip patch antenna that can operate at atmospheric windows. The effect of graphene chemical potential tunability on resonant
frequency has been investigated and showed that for ΞΌc = 0.21 eV, ΞΌc = 0.4 eV, and ΞΌc = 1.5 eV proposed resonances occur at 300 GHz, 350 GHz and 410 GHz respectively. Therefore, it can be concluded that proposed antenna can be used in a THz communication circuit to operate at three atmospheric windows with minimum loss simultaneously. Also we have presented a process to design a multi-band antenna for operation in the THz-spectrum. It has been shown the proposed graphene antenna has the potential to operate in multiple bands of the THz spectrum. However, a tunable matching circuit is essential to guarantee maximum performance of the antenna at the frequencies of operation.
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Ws 2R
Wp
Ls
Lp
Y X
Figure 1. Top view of a coaxial feed based patch antenna. (P and S stand for patch and substrate)
h
Z
X
2R Figure 2. Side view of a coaxial feed based patch antenna.
Figure 3. Return loss versus frequency for the copper patch microstrip antenna
Figure 4. The variation of input impedance versus frequency for copper patch microstrip antenna.
Fig. 5. E-plane (solid line) and H-plane (dash line) far field radiation patterns of the copper based patch antenna at 421 GHz.
Fig. 6. Return loss versus frequency for different values of chemical potential for the graphene based patch antenna.
Fig. 7. Input resistance versus frequency for different values of chemical potential for the graphene based patch antenna.
Fig. 8. The variation of input reactance versus frequency for different values of chemical potential for graphene based patch antenna.
Fig. 9. The VSWR curves for different chemical potential values.
Fig. 10. The variation of input impedance versus frequency for graphene patch microstrip antenna. (ππ = 0.21 eV)
Fig. 11. E-plane (solid line) and H-plane (dash line) far field radiation patterns of the graphene based patch antenna at 300 GHz.
Fig. 12. E-plane (solid line) and H-plane (dash line) far field radiation patterns of the graphene based patch antenna at 350 GHz.
Fig. 13. The variation of input impedance versus frequency for graphene patch microstrip antenna. (ππ = 0.4 eV)
Fig. 14. The variation of input impedance versus frequency for graphene patch microstrip antenna. (ππ = 1.5 eV)
Figure 15. E-plane (blue line) and H-plane (red line) far field radiation patterns of the graphene based patch antenna at 410 GHz.
1 2 3 4
β’Select any arbitrary frequency π1, π2 and π3 .
(π1 < π2 < π3 )
β’Design a copper microstrip patch antenna at 2-3% higher than π3 . β’Substitute copper by a graphene layer ( ππ >1.4 eV ). β’Reduce ππ to achieve proposed resonances at π1 and π2 .
Fig. 16. The block-diagram that show steps of designing any arbitrary triple band antenna. Parameters πΏπ Γ ππ
Tab. 1.
Dimensions ( ΞΌm ) 182.86 Γ 233
πΏπ Γ ππ Γ h
500 Γ 500 Γ 40
R
5
Design parameter of the microstrip patch antenna.
Resonant frequency ( GHz)
ππ ( eV )
πΊππ ( dB )
VSWR
πΉππ (Ξ©)
πΏππ (Ξ©)
Directivity (dB)
Band width ( GHz)
300
0.21
12.16
1.65
32.24
-10.50
6.71
41.23
350
0.4
30.67
47.22
-1.53
7.34
410
1.5
13.96
73.9
-4.92
Graphene antenna
Tab. 2.
1.06
1.5
7.73
Simulation results of the graphene microstrip patch antenna.
58.39 37.5