Portal de Periódicos da CAPES

Graphene‐based low side‐lobe microwave horn antenna

2019; Institution of Engineering and Technology; Volume: 13; Issue: 11 Linguagem: Inglês

10.1049/iet-map.2018.5504

1751-8733

Hadi Balegh, Bijan Abbasi Arand, Leila Yousefi,

Advanced Antenna and Metasurface Technologies

IET Microwaves, Antennas & PropagationVolume 13, Issue 11 p. 1832-1838 Research ArticleFree Access Graphene-based low side-lobe microwave horn antenna Hadi Balegh, Hadi Balegh Department of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, IranSearch for more papers by this authorBijan Abbasi Arand, Corresponding Author Bijan Abbasi Arand abbasi@modares.ac.ir Department of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, IranSearch for more papers by this authorLeila Yousefi, Leila Yousefi School of Electrical and Computer Engineering, Faculty of Engineering, University of Tehran, Tehran, IranSearch for more papers by this author Hadi Balegh, Hadi Balegh Department of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, IranSearch for more papers by this authorBijan Abbasi Arand, Corresponding Author Bijan Abbasi Arand abbasi@modares.ac.ir Department of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, IranSearch for more papers by this authorLeila Yousefi, Leila Yousefi School of Electrical and Computer Engineering, Faculty of Engineering, University of Tehran, Tehran, IranSearch for more papers by this author First published: 26 July 2019 https://doi.org/10.1049/iet-map.2018.5504Citations: 2AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In this study, a novel method is proposed to control and reduce the side-lobe level (SLL) of the pyramidal horn antennas. In this method, graphene sheets are deposited on the antenna walls to taper the aperture field leading to pattern engineering with the goal of the SLL reduction. In essence, graphene sheet acts as a high-impedance surface and hinders electromagnetic power from reaching to the horn antenna aperture edges, in such a way that the diffraction phenomenon could be drastically diminished. The proposed design is numerically analysed and optimised using full-wave three-dimensional simulation methods. Numerical full-wave results illustrate more than 17.6 dB reduction in the SLL of the proposed antenna. 1 Introduction Horn antennas have variety of applications in large radio astronomy, satellite tracking, communication dishes, and phased arrays, due to their interesting features such as high gain, simple construction, ease of excitation, and versatility [[1]]. However, the diffraction from edges of horn antennas distorts their radiation pattern and causes undesired minor lobes [[1]], resulting in a high side-lobe level (SLL). Low SLL is vital for some applications requiring high accuracy such as radar systems, tracking devices, and also applications requiring low electromagnetic interference [[1]–[3]]. In radio links, the SLL of the receiving antenna directly influences the sensitivity of the receiver. Furthermore, the noise figure of a reflector antenna deeply depends on its feed antenna [[4]]. Therefore, for decades, distinctive methods have been suggested to engineer horn antennas patterns mainly with the goal of SLL reduction including corrugated surfaces [[4]–[8]], metamaterials [[9], [10]], wire mediums [[2]], non-uniform slot arrays [[11]], frequency selective surfaces [[3]], bending the edges of aperture [[12]], and manipulating the walls impedance by using lossy materials [[13]–[17]]. Aforementioned avenues have some conspicuous deficiencies such as difficult fabrication and the lack of tunability in the radiation specification of the antenna. Here, we propose a novel method to reduce the SLL in horn antennas and at the same time to engineer the radiation pattern by the aid of graphene sheets. In essence, this approach benefits from high-impedance property of graphene sheets at microwave frequencies. A high-impedance surface (HIS) can reduce the SLL of a horn antenna by suppressing surface currents. By depositing graphene on the inner side of horn walls, the distribution of the antenna aperture field is tapered leading to reduction of the diffraction, which in turn results in lower SLL. Furthermore, the SLL can be engineered to the desired level by tuning the impedance of graphene sheets through an applied external voltage. Graphene is the material, which has opened new horizons in material science and physics [[18]–[21]]. It is truly a monolayer of carbon atoms which packed into a honeycomb lattice. This quasi-two-dimensional (2D) material with unique electronic and crystal characteristic is the thinnest and sturdiest material which has been discovered up to now. These advantages of graphene and its tunable behaviour have engrossed researchers' attention around the world [[18]–[21]]. Nowadays, graphene flakes could be grown on copper or any other arbitrary substrate with the size as big as 30 in by chemical vapour deposition (CVD) method [[22]–[24]]. The possibility of manufacturing graphene in large sizes has provided opportunities for using graphene in devices operating at microwave and millimetre-wave frequencies. Graphene naturally is an HIS surface with relatively high resistance, in the extensive frequency range from microwave to THz, in contrast to metals which obtain the high-impedance property by texturing their surfaces [[25]–[28]]. Moreover, the performance of a metallic HIS could not be controlled somehow, but an external voltage can alter the surface impedance of a graphene sheet. The expansion includes the following elements. First, the method is introduced and verified through numerical analysis. Then, this paper investigates the relation between the radiation specifications of the horn antenna and graphene sheet characteristics, namely its length and surface impedance. After that, the design parameters are opted to have a significant reduction in the SLL without significant gain reduction. 2 Proposed structure and parametric study The configuration of the proposed structure is shown in Fig. 1, where the bias voltage and the length of the graphene sheet are Vb = 0 V and , respectively. As shown in this figure, graphene sheets are deposited on the inner side of the antenna walls. Graphene sheets can be grown on the interior walls of the antenna using a CVD method [[29]]. The antenna is designed to operate at the centre frequency of 10 GHz and a standard X-band waveguide (WR-90) has been used as the antenna feed. Fig. 1Open in figure viewerPowerPoint Schematic representation of the proposed graphene-based horn antenna (a) 3D perspective, (b) Top view: . The dimensions scales are not in proportion In the absence of the magnetic bias field, the surface conductivity of graphene sheets can be modelled by the well known Kubo formula [[30]]. In the microwave regime, intra-band contributions of the graphene conductivity simply prevail over the inter-bnad contributions at the room temperature [[30], [31]]. Consequently, the graphene surface conductivity at the microwave frequencies can be expressed as [[31]] (1) where is the radial frequency; e is the charge of an electron; is the reduced Plank's constant; is the electron scattering rate; is the electron relaxation time; T is the temperature; is the Boltzmann's constant; and is the graphene chemical potential. In this paper, the temperature is set to . Another important characteristic of the graphene is the surface impedance which is related to the graphene conductivity as . As shown in (1), the surface impedance can be dynamically tuned by graphene chemical potential , which may be adapted by initial doping [[21]] or applying an external bias voltage as [[32], [33]] (2) where is calculated from a single capacitor model [[33]] and is the voltage offset caused by natural doping of the graphene and is the Fermi velocity [[33]]. Fig. 2 shows the graphene surface impedance for different chemical potential values calculated using the Kubo formula. As shown in this figure, at microwave frequencies, the real part of the graphene surface impedance is not significantly changed with frequency and could be considered as a constant value. Furthermore, the surface impedance strongly depends on the bias voltage , which controls the charge density inside the graphene. The temperature of the graphene sheets could be changed by applying the external electrical bias. On the basis of Kubo formula, as the temperature varies from 200 to 400 K, the real and imaginary parts of the graphene surface impedance would be changed negligibly in the range of 448.3–448.9 and 2.821–2.817 Ω, respectively. Fig. 2Open in figure viewerPowerPoint Calculated surface impedance (a) Real part, (b) Imaginary part of the graphene surface impedance (Zs) for various chemical potentials. Graphene electron relaxation time () has been considered 0.1 ps At high frequencies, the imaginary part of the graphene surface conductivity plays a critical role in calculations. However, graphene behaves like a lossy material at the microwave frequencies. So, we could ignore the imaginary part of the graphene surface conductivity and consider only its real part. As we know, graphene surface impedance is related to the surface conductivity by the formula. According to Fig. 2b, the imaginary part of the graphene surface impedance in 10 GHz is not comparable with its real part. Consequently, we could ignore the imaginary part without any disruption in our calculations. In the horn antennas, when the surface currents reach to the aperture edges, they cause the undesirable diffraction phenomenon. Graphene as an HIS exerts new boundary conditions on the surfaces and changes them to , where is the unit vector perpendicular to the inner walls of the horn antenna; is the graphene surface conductivity; and is the induced current on the graphene sheet. So, graphene sheets could reduce the surface current amplitude on the antenna walls resulting in the attenuated unwanted radiation and modified SLL in the far-field radiation pattern. We have simulated the proposed structure by 3D full-wave electromagnetic solver CST studio and HFSS software. Graphene layers are modelled as infinitesimally thin sheets (2D sheets), with the surface impedance () achieved from Kubo formula. Compared to the effective dielectric constant method suggested in [[34]], which models graphene as a thin 3D object, simulating graphene as a 2D sheet with specific surface impedance provides more realistic results which are closer to the measured data. The finite element method and surface-based meshing method have been used in the related simulations. The minimum edge length, maximum edge length, and tetrahedrons of the proposed structure's mesh specifications are 0.00085λc, 0.42λc, and 500,000, respectively. In these simulations, we investigate the effect of graphene's different parameters on the radiation pattern of the resultant horn antenna. In this investigation, we perform a parametric study on the length of the graphene sheet and its surface impedance (related to the bias voltage) to achieve an optimised design with highest possible gain and at the same time lowest possible SLL. 2.1 Parametric study on the Graphene's impedance and length The surface impedance () value and the length (L) of the graphene sheets are the pivotal parameters, which play a decisive role in the SLL, the front-to-back ratio (F/B) and gain calculation of the horn antenna. Fig. 3 illustrates the antenna radiation parameters versusthe graphene sheet length and surface impedance. As shown in Fig. 3a, the SLL and F/Breduce as the length of the graphene sheet increases. However, this reductionalmost takes a constant value for the graphene sheets longer than (). Consequently, we choose the graphenelength as in which provides a suitable value to SLLand F/B. For , according to the simulated results at thefrequency of 10 GHz, the SLL is equal to and F/Bis around . Fig. 3Open in figure viewerPowerPoint SLL and F/B as a function of the graphene filmparameters (a) Length (L), wherethe surface impedance is assumed as ,(b) Surface impedance (), where the length is assumedas Another parameter which deserves some investigations is the graphene surfaces impedance (). The influence of the surface impedance on the SLL and F/B ratio of the radiation pattern is illustrated in Fig. 3b. In this paper, the graphene sheet length is assumed to be . As shown in Fig. 3b, SLL is not changed much for surface impedance higher than and F/B ratio insignificantly fluctuates around . According to SLL curve (blue line) in Fig. 3b, SLL takes its lowest value at corresponding to , where and F/B ratio is equal to . Now, we study the effect of the graphene surface impedance (or surface resistance) and its length on the antenna gain. Figs. 4a–c illustrate the results of this paper. As shown in these figures, the gain is changed significantly in the range of −18 to +21 dB by the variation of the length and surface impedance of the graphene sheet. According to the results of Fig. 4a, for a specific value of the surface impedance, the gain does not change significantly for the graphene lengths smaller than . Also, for a specific value of the graphene length, the gain is decreased by the increase of the surface impedance. However, for lengths more than , the gain variation is significant. Fig. 4Open in figure viewerPowerPoint Results of this paper (a) Variation of the proposed antenna's gain by changing the graphene sheet length (L) and surface resistance (Rs), (b) E-plane radiation pattern for the different chemical potential values and . The insets illustrate the antenna SLL and gain variations, (c) Curves of the gain and SLL under different bias and On the other hand, since there is a trade-off between the SLL and the gain of the antenna, these two parameters can be arbitrarily adapted in a wide range by applying an external bias voltage to the graphene sheet. Therefore, the applied voltage to the graphene sheet can be used to control the radiation pattern of the antenna. Fig. 4b demonstrates the E-plane radiation pattern of the proposed antenna for various graphene film's chemical potential. As shown in this figure, we could adapt the SLL of the radiation pattern to make it suitable for different applications. The large variation of the SLL with the bias voltage is the interesting feature of the proposed method, which is depicted in the left inset of Fig. 4b. Besides, the gain variation of the main lobe is shown in the right inset of this figure. Using the results of the parametric study, we opt the graphene length and surface resistance equal to ( is the central wavelength) and , corresponding to . It should be noted that here we design a structure with the highest possible gain and at the same time lowest possible SLL but these parameters could be changed by the designers to achieve their desired radiation characteristic, for example, by reducing the external voltage, SLL will be modified but the gain comes down and vice versa, so the parameter selection is completely related to the purpose of the antenna design. 2.2 Parametric study on the position of the graphene sheets According to the numerically calculated surface current distribution on the antenna walls, most of the surface currents exist on the upper and lower walls of the horn and the side walls do not hold any considerable current. Fig. 5 shows the surface current distribution, where graphene sheets are deposited on the side, top, and bottom walls. Hence, it seems that graphene sheets deposited on the side walls cause extra losses in the proposed structure without any significant effect on the SLL. The results show that the gain is increased around 0.5 dB and side-lobes of the radiation pattern are reduced around by eliminating the graphene sheets from the side walls of the horn antenna. Fig. 5Open in figure viewerPowerPoint Numerically calculated surface currents on the lower wall of the horn antenna (a) Metallic horn antenna, (b) Proposed structure with and Finally, graphene sheets are deposited just on the upper and lower walls. Also, the length and surface impedance of the graphene sheets on the upper and lower walls remain unchanged as and . This structure is termed as optimised structure. 3 Optimised structure Fig. 6 shows the 3D schematic representation of the optimised structure. The structure is simulated by CST and HFSS software to verify that the simulated results obtained from both of the software are consistent with each other. Fig. 6Open in figure viewerPowerPoint Optimised structure with the deposition of the graphene sheets ( and ) on the upper and lower walls of the metallic horn antenna In the proposed method, graphene sheets can be supposed as an HIS, so HIS analysis could be used in the theory of the suggested design. As an approximation, formulas which have been used in [[1]] for corrugated antennas' field distribution at the aperture, can be used to show the effect of the graphene sheets on the conventional pyramidal horn's aperture field distribution as below: (3) Fig. 7 shows the effect of the graphene sheets on the horn's aperture field distribution. Fig. 7a illustrates the electrical field distribution before inserting the graphene at the conventional pyramidal horn and Fig. 7b shows the electrical field distribution on the optimised structure. These figures show how graphene could taper the aperture field of the horn antenna with the goal of the SLL reduction. Fig. 7Open in figure viewerPowerPoint Antenna aperture electrical field distribution (a) Metallic horn, (b) Optimised structure The numerically calculated electric field distribution inside the graphene-based horn is illustrated and compared with that of the conventional horn antenna in Fig. 8. As can be observed in this figure, for the optimised graphene-based antenna, the amplitude of the electric field is mostly concentrated on the central part of the antenna and is drastically decreased on the edges of the antenna aperture. This figure also shows that the radiation in the minor lobes for the optimised antenna has been rooted out significantly and the radiation pattern has only one main lobe (see yellow-dashed lines in Fig. 8b). However, as Fig. 8a shows, in the case of the metallic horn, due to the high-density energy at the edges, it radiates notably in different directions (yellow-dashed line in Fig. 8a) and produces an unwanted high SLL. Fig. 8Open in figure viewerPowerPoint Numerically calculated electric field inside the horn antenna (a) Metallic horn antenna, (b) Optimised structure The optimised structure has been simulated in CST and HFSS software to prove the dependability of the results. Figs. 9a–c illustrate the radiation patterns of the optimised structure and metallic horn antenna at f = 8, 10, and 12 GHz. These figures show that the optimised structure could suppress the SLL of the horn antenna at the operating bandwidth (8–12 GHz). Furthermore, the 3D radiation pattern of the optimised structure is displayed and compared with that of the conventional metal-based horn antenna in Fig. 10. As clearly shown in this figure, high side-lobes are removed from the antenna radiation pattern by using the proposed method. Fig. 9Open in figure viewerPowerPoint Comparison between the radiation patterns of the metallic horn and optimised structure, which have been simulated in CST and HFSS (a) f = 8 GHz, (b) f = 10 GHz, (c) f = 12 GHz Fig. 10Open in figure viewerPowerPoint 3D radiation pattern of the antenna (a) Metallic horn, (b) Optimised structure To obtain the operating bandwidth of the optimised structure, the numerically calculated return loss (S11) is shown at Fig. 11 and compared with the conventional metallic horn antenna. According to the results of this figure, the operation bandwidth of the optimised graphene-based antenna is almost the same as that of the metallic one. Therefore, the proposed method does not limit the operation bandwidth. Fig. 11Open in figure viewerPowerPoint Numerically calculated for metallic and optimised graphene-based horn antenna The far-field radiation patterns of the traditional metallic horn antenna, the primary structure studied in Section 2 (bias voltage = 0 and ) and optimised structure ( and ) are all depicted and compared with each other in Fig. 12. As shown in Fig. 12, adding the graphene sheets improves the SLL and F/B by 17.6 and 7 dB, respectively, and increases the beamwidth of the antenna by 4°. However, as a drawback, the gain is reduced by 3 dB because of the lossy nature of the graphene. Also, it should be mentioned that X-pol of the optimised structure is around 20 dB better than the conventional metallic horn at . Fig. 12Open in figure viewerPowerPoint Comparison between the radiation patterns of the traditional metallic horn, optimised graphene-based antenna ( and ) and primary proposed structure (bias voltage = 0 and ) (a) E-plane radiation pattern, (b) H-plane radiation pattern Concerning the fabrication process of the proposed device, the following procedure could be carried out. After the manufacturing procedure of the metallic horn antenna, the graphene layer is grown by means of CVD method, and then mechanically transferred to the upper and lower walls of the antenna [[29], [35]]. Graphene can be biased by using the method introduced in [[33], [36], [37]]. As shown in Fig. 13, the gold and platinum have been deposited on the graphene sheets as electrodes widths of WAu = 2 mm and WPt = 4 mm, respectively. Fig. 13Open in figure viewerPowerPoint Perspective view of the optimised structure's biasing method with WAu = 2 mm and WPt = 4 mm Previous methods which have been used to suppress the SLL of the horn antenna have some conspicuous deficiencies such as difficult fabrication and the lack of tunability in the radiation specification of the antenna. Here, we proposed a novel method to reduce the SLL of the horn antennas and engineer the radiation pattern by the aid of graphene sheets at the same time. The proposed method benefits from a simple structure and fabrication that graphene sheets simply can be grown on the inside walls of the conventional metallic horn antenna by various methods such as CVD. As indicated in Table 1, the SLL and F/B of the proposed structure has been compared with suggested structures in [[10], [38]]. Despite the simple structure of the optimised structure in comparison with two other references, it could reduce the SLL and F/B ratio of the conventional horn antenna suitably. Table 1. Comparison of the optimised structure S11 and F/B with previous methods Researches SLL, dB F/B, dB [[10]] ∼10 ∼5 [[38]] ∼22 ∼5 optimised structure ∼18 ∼8 4 Conclusion We have presented a novel graphene-based method to suppress the side-lobes of the pyramidal horn antenna at the microwave frequencies. Thanks to the graphene HIS nature, it eliminates diffractions from the edges, resulting in lower side-lobes. In the first design, numerical results show a significant SLL reduction but also a remarkable gain reduction. We performed a parametric study, and using its results optimised the length and impedance of the graphene sheets to achieve a low SLL but at the same time acceptable gain. It was observed that putting the graphene sheets on the upper and lower walls and eliminating them from the side walls could reduce the SLL of the antenna radiation pattern without any extra losses. The final graphene-based antenna was numerically studied and numerical results show an SLL of −31 dB and gain of 18.5 dB for the optimised structure. 5 References [1]Balanis, C.: ' Antenna theory' ( Wiley, Hoboken, 2005, 1st edn.) [2]Tomaz, A., Barroso, J., Hasar, U.: 'Side lobe reduction in an X-band horn antenna loaded by a wire medium', J. Aerosp. Technol. Manage., 2015, 7, (3), pp. 307– 313 [3]Wang, M., Huang, C., Pu, M., et al.: 'Reducing side lobe level of antenna using frequency selective surface superstrate', Microw. Opt. Technol. Lett., 2015, 57, (8), pp. 1971– 1975 [4]Teniente, J., Gonzalo, R., Río, C.D.: 'Low sidelobe corrugated horn antennas for radio telescopes to maximize G/T-s', IEEE Trans. Antennas Propag., 2011, 59, (6), pp. 1886– 1893 [5]Granet, C., James, G.: 'Design of corrugated horns: a primer', IEEE Antennas Propag. Mag., 2005, 47, (2), pp. 76– 84 [6]Elliott, R.: 'On the theory of corrugated plane surfaces', Trans. IRE Prof. Group Antennas Propag., 1954, 2, (2), pp. 71– 81 [7]Mentzer, C., Peters, L.: 'Pattern analysis of corrugated horn antennas', IEEE Trans. Antennas Propag., 1976, 24, (3), pp. 304– 309 [8]Thomas, B., Greene, K.: 'A curved-aperture corrugated horn having very low cross-polar performance', IEEE Trans. Antennas Propag., 1982, 30, (6), pp. 1068– 1072 [9]Lier, E., Werner, D., Scarborough, C., et al.: 'An octave-bandwidth negligible-loss radiofrequency metamaterial', Nat. Mater., 2011, 10, (3), pp. 216– 222 [10]Qi, M., Tang, W., Ma, H., et al.: 'Suppressing side-lobe radiations of horn antenna by loading metamaterial lens', Sci. Rep., 2015, 5, p. 9113 [11]Tae, H., Oh, K., Hong, S., et al.: 'Low side-lobe horn antenna with non-uniform slot array', Microw. Opt. Technol. Lett., 2014, 56, (8), pp. 1860– 1862 [12]Burnside, W., Chuang, C.: 'An aperture-matched horn design', IEEE Trans. Antennas Propag., 1982, 30, (4), pp. 790– 796 [13]Knop, C., Cheng, Y., Ostertag, E.: 'On the fields in a conical horn having an arbitrary wall impedance', IEEE Trans. Antennas Propag., 1986, 34, (9), pp. 1092– 1098 [14]Lee, C., Lee, S., Justice, D.: 'A simple circular-polarized antenna: circular waveguide horn coated with lossy magnetic material', IEEE Trans. Antennas Propag., 1988, 36, (2), pp. 297– 300 [15]Liu, K., Balanis, C.: 'Analysis of horn antennas with impedance walls'. Antennas Propagation Society Int. Symp., Dallas, TX, USA, May 1990, pp. 1184– 1187 [16]Liu, K., Balanis, C., Barber, G.: 'Low-loss material coating for horn antenna beam shaping'. Antennas Propagation Society Int. Symp., London, Ontario, Canada, June 1991, pp. 1664– 1667 [17]Wang, J., Tripp, V., Tehan, J.: 'The magnetically coated conducting surface as a dual conductor and its application to antennas and microwaves', IEEE Trans. Antennas Propag., 1990, 38, (7), pp. 1069– 1077 [18]Geim, A.: 'Graphene: status and prospects', Science, 2009, 324, (5934), pp. 1530– 1534 [19]Geim, A.K., Novoselov, K.S.: 'The rise and rise of graphene', Nat. Nanotech., 2010, 5, (11), p. 755 [20]Novoselov, K.: 'Electric field effect in atomically thin carbon films', Science, 2004, 306, (5696), pp. 666– 669 [21]Sounas, D., Caloz, C.: 'Gyrotropy and nonreciprocity of graphene for microwave applications', IEEE Trans. Microw. Theory, 2012, 60, (4), pp. 901– 914 [22]Bae, S., Kim, H., Lee, Y., et al.: 'Roll-to-roll production of 30 in graphene films for transparent electrodes', Nat. Nanotech., 2010, 5, (8), pp. 574– 578 [23]Li, X., Cai, W., An, J., et al.: 'Large-area synthesis of high-quality and uniform graphene films on copper foils', Science, 2009, 324, (5932), pp. 1312– 1314 [24]Skulason, H., Nguyen, H., Guermoune, A., et al.: '110 GHz measurement of large-area graphene integrated in low-loss microwave structures', Appl. Phys. Lett., 2011, 99, (15), p. 153504 [25]Gómez-Díaz, J., Perruisseau-Carrier, J., Sharma, P., et al.: 'Non-contact characterization of graphene surface impedance at micro and millimeter waves', J. Appl. Phys., 2012, 111, (11), p. 114908 [26]Hanson, G.: 'Dyadic Green's functions and guided surface waves for a surface conductivity model of graphene', J. Appl. Phys., 2008, 103, (6), p. 064302 [27]Sensale-Rodriguez, B., Yan, R., Liu, L., et al.: 'Graphene for reconfigurable terahertz optoelectronics', Proc. IEEE, 2013, 101, (7), pp. 1705– 1716 [28]Balegh, H., Abbasi Arand, B., Yousefi, L.: 'Side lobe level reduction in horn antennas using graphene'. 24th Iranian Conf. Electrical Engineering, Shiraz, Iran, May 2016, pp. 1937– 1941 [29]Zhang, Y., Zhang, L., Zhou, C.: 'Review of chemical vapor deposition of graphene and related applications', Acc. Chem. Res., 2013, 46, (10), pp. 2329– 2339 [30]Scharf, B., Perebeinos, V., Fabian, J., et al.: 'Magneto-optical conductivity of graphene on polar substrates', Phys. Rev. B, 2013, 88, (12), pp. 1– 12 [31]Gusynin, V., Sharapov, S., Carbotte, J.: 'On the universal ac optical background in graphene', New J. Phys., 2009, 11, (9), p. 1– 18 [32]Xu, C., Jin, Y., Yang, L., et al.: 'Characteristics of electro-refractive modulating based on graphene-oxide-silicon waveguide', Opt. Express, 2012, 20, (20), p. 22398 [33]Liu, M., Yin, X., Ulin-Avila, E., et al.: 'A graphene-based broadband optical modulator', Nature, 2011, 474, (7349), pp. 64– 67 [34]Vakil, A., Engheta, N.: 'Transformation optics using graphene', Science, 2011, 332, (6035), pp. 1291– 1294 [35]Reina, A., Jia, X., Ho, J., et al.: 'Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition', Nano Lett., 2009, 9, (1), pp. 30– 35 [36]Sensale-Rodriguez, B., Yan, R., Kelly, M., et al.: 'Broadband graphene terahertz modulators enabled by intraband transitions', Nat. Commun., 2012, 3, p. 780 [37]Dragoman, M., Neculoiu, D., Dragoman, D., et al.: 'Graphene for microwaves', IEEE Microw. Mag., 2010, 11, (7), pp. 81– 86 [38]Lawrie, R., Peters, L.: 'Modifications of horn antennas for low sidelobe levels', IEEE Trans. Antennas Propag., 1966, 14, (5), pp. 605– 610 Citing Literature Volume13, Issue11September 2019Pages 1832-1838 FiguresReferencesRelatedInformation