x

## 留言板

Dynamic beam-steering in wide angle range based on tunable graphene metasurface

## Dynamic beam-steering in wide angle range based on tunable graphene metasurface

Li Xiao-Bing, Lu Wei-Bing, Liu Zhen-Guo, Chen Hao
• #### Abstract

Metasurfaces, the two-dimensional counterparts of metamaterials composed of subwavelength building blocks, can be used to control the amplitude, phase, and polarization of the scattered wave in a simple but effective way and thus have a wide range of applications such as lenses, holograms, and beam steering. Among these applications, metasurfacebased beam steering is of great importance for antenna engineering in communication systems, because of its low loss and easy manufacture. The capability of beam steering is mainly controlled by the phase profile which is determined by the phase shift applied to the wave scattered by each of unit cells that constitute the metasurface. It should be noted that the required phase profile achieved by distributing the unit cells with different phase responses can operate well only at a certain frequency. The guidance in determining the required phase profile to steer the beam into a certain direction is the generalized Snell's law. According to this law, the reflection angle of the wave reflected by the metasurface interface depends on the linear phase gradient along the metasurface. Therefore, by forming different linear phase gradients covering the whole phase shift 2 periodically, one can steer the reflected waves to different angles. However, the obtained reflection angles are limited because the phase gradient of a metasurface is limited by the unit cell size, which cannot be infinitely small. Recently, a new pattern shift theory based on the convolution theorem has been proposed to realize wide angle range steering, enabling flexible and continuous manipulation of reflection angle. Because the electric field distribution and the scattering pattern in the far-field region are a Fourier transform pair, we can pattern the electric field of the metasurface to control the scattered waves of far field. Specifically, the multiplication of an electric distribution by a gradient phase sequence leads to a deviation of the scattering pattern from its original direction to a certain extent in the angular coordinate. However, we have not considered the tunability of metasurfaces so far, which is required in applications. The ways to reach tunability in metasurface include diode switches, micro-electro-mechanical system, and the use of tunable materials such as graphene. Graphene, an atomically thin layer of carbon atoms arranged in a honeycomb lattice, has aroused the enormous interest due to its outstanding mechanical, thermal, and electrical properties. With the capability of being electrically tunable, graphene has manifested itself as a promising candidate for designing the tunable metasurfaces. Although the reflection angle can be changed by electrically reconfiguring the graphene Fermi level distribution of the metasurface, the steering angle is still limited. In this paper, we propose and design a tunable graphene metasurface with the capability of dynamically steering the reflection angle in a wide range, which is achieved based on the new pattern shift theory. The theoretical results and the numerically simulated results both show that the reflection angle can be steered from 5 to 70 with an interval less than 10, implying the promising potential in the design of tunable antenna.

#### Authors and contacts

###### Corresponding author: Lu Wei-Bing, wblu@seu.edu.cn
• Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61671150, 61671147) and the Six Talent Peaks Project in Jiangsu Province, China (Grant No. XCL-004).

#### References

 [1] Holloway C L, Kuester E F, Gordon J A, O'Hara J, Booth J, Smith D R 2012 IEEE Antenn. Propag. M. 54 10 [2] Yu N F, Capasso F 2014 Nat. Mater. 13 139 [3] Meinzer N, Barnes W L, Hooper I R 2014 Nat. Photon. 8 889 [4] Liu C, Hum S V 2010 IEEE Antenn. Wirel. Pr. 9 1241 [5] Geim K, Novoselov K S 2007 Nat. Mater. 6 183 [6] Li C, Cai L, Wang S, Liu B J, Cui H Q, Wei B 2017 Acta Phys. Sin. 66 208501 (in Chinese) [李成, 蔡理, 王森, 刘保军, 崔焕卿, 危波 2017 物理学报 66 208501] [7] Novoselov K S 2004 Science 306 666 [8] Ju L, Geng B S, Horng J, Girit C, Martin M, Hao Z, Bechtel H A, Liang X G, Zettl A, Shen Y R, Wang F 2011 Nat. Nanotechnol. 6 630 [9] Grigorenko A N, Polini M, Novoselov K S 2012 Nat. Photon. 6 749 [10] Wang Z P, Deng Y, Sun L F 2017 Chin. Phys. B 26 114101 [11] Jiang J L, Zhang X, Zhang W, Liang S, Wu H, Jiang L Y, Li X Y 2017 Opt. Express 25 16867 [12] Liu L M, Zarate Y, Hattori H T, Neshev D N, Shadrivov I V, Powell D A 2016 Appl. Phys. Lett. 108 031106 [13] Liu Z, Bai B F 2017 Opt. Express 25 8584 [14] Yu N F, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333 [15] Aieta F, Genevet P, Yu N F, Kats M A, Gaburro Z, Capasso F 2012 Nano Lett. 12 1702 [16] Yatooshi T, Ishikawa A, Tsuruta K 2015 Appl. Phys. Lett. 107 053105 [17] Wang J, Lu W B, Li X B, Liu J L 2016 IEEE Photon. Tech. Lett. 28 971 [18] Liu S, Cui T J, Zhang L, Xu Q, Wang Q, Wan X, Gu J Q, Tang W X, Qi M Q, Han J G, Zhang W L, Zhou X Y, Cheng Q 2016 Adv. Sci. 3 1600156 [19] Falkovsky L A, Pershoguba S S 2007 Phys. Rev. B 76 153410 [20] Novoselov K S, Fal'Ko V I, Colombo L, Gellert P R, Schwab M G, Kim K 2012 Nature 490 192 [21] Brida D, Tomadin A, Manzoni C, Kim Y J, Lombardo A, Milana S, Nair R R, Novoselov K S, Ferrari A C, Cerullo G, Polini M 2013 Nat. Commun. 4 1987 [22] Efetov D K, Kim P 2010 Phys. Rev. Lett. 105 256805 [23] Chen C F, Park C H, Boudouris B W, Horng J, Geng B S, Girit C, Zettl A, Crommie M F, Segalman R A, Louie S G, Wang F 2011 Nature 471 617 [24] Yao Y, Kats M A, Genevet P, Yu N F, Song Y, Kong J, Capasso F 2013 Nano Lett. 13 1257 [25] Lee S H, Choi M, Kim T T, Lee S, Liu M, Yin X B, Choi H K, Lee S S, Choi S Y, Choi C G, Zhang X, Min B K 2012 Nat. Mater. 11 936 [26] Balci O, Polat E O, Kakenov N, Kocabas C 2015 Nat. Commun. 6 6628 [27] Pors A, Bozhevolnyi S I 2013 Opt. Express 21 27438 [28] Vasko F T, Ryzhii V 2007 Phys. Rev. B 76 233404 [29] Sun S L, He Q, Xiao S Y, Xu Q, Li X, Zhou L 2012 Nat. Mater. 11 426

#### Cited By

•  [1] Holloway C L, Kuester E F, Gordon J A, O'Hara J, Booth J, Smith D R 2012 IEEE Antenn. Propag. M. 54 10 [2] Yu N F, Capasso F 2014 Nat. Mater. 13 139 [3] Meinzer N, Barnes W L, Hooper I R 2014 Nat. Photon. 8 889 [4] Liu C, Hum S V 2010 IEEE Antenn. Wirel. Pr. 9 1241 [5] Geim K, Novoselov K S 2007 Nat. Mater. 6 183 [6] Li C, Cai L, Wang S, Liu B J, Cui H Q, Wei B 2017 Acta Phys. Sin. 66 208501 (in Chinese) [李成, 蔡理, 王森, 刘保军, 崔焕卿, 危波 2017 物理学报 66 208501] [7] Novoselov K S 2004 Science 306 666 [8] Ju L, Geng B S, Horng J, Girit C, Martin M, Hao Z, Bechtel H A, Liang X G, Zettl A, Shen Y R, Wang F 2011 Nat. Nanotechnol. 6 630 [9] Grigorenko A N, Polini M, Novoselov K S 2012 Nat. Photon. 6 749 [10] Wang Z P, Deng Y, Sun L F 2017 Chin. Phys. B 26 114101 [11] Jiang J L, Zhang X, Zhang W, Liang S, Wu H, Jiang L Y, Li X Y 2017 Opt. Express 25 16867 [12] Liu L M, Zarate Y, Hattori H T, Neshev D N, Shadrivov I V, Powell D A 2016 Appl. Phys. Lett. 108 031106 [13] Liu Z, Bai B F 2017 Opt. Express 25 8584 [14] Yu N F, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333 [15] Aieta F, Genevet P, Yu N F, Kats M A, Gaburro Z, Capasso F 2012 Nano Lett. 12 1702 [16] Yatooshi T, Ishikawa A, Tsuruta K 2015 Appl. Phys. Lett. 107 053105 [17] Wang J, Lu W B, Li X B, Liu J L 2016 IEEE Photon. Tech. Lett. 28 971 [18] Liu S, Cui T J, Zhang L, Xu Q, Wang Q, Wan X, Gu J Q, Tang W X, Qi M Q, Han J G, Zhang W L, Zhou X Y, Cheng Q 2016 Adv. Sci. 3 1600156 [19] Falkovsky L A, Pershoguba S S 2007 Phys. Rev. B 76 153410 [20] Novoselov K S, Fal'Ko V I, Colombo L, Gellert P R, Schwab M G, Kim K 2012 Nature 490 192 [21] Brida D, Tomadin A, Manzoni C, Kim Y J, Lombardo A, Milana S, Nair R R, Novoselov K S, Ferrari A C, Cerullo G, Polini M 2013 Nat. Commun. 4 1987 [22] Efetov D K, Kim P 2010 Phys. Rev. Lett. 105 256805 [23] Chen C F, Park C H, Boudouris B W, Horng J, Geng B S, Girit C, Zettl A, Crommie M F, Segalman R A, Louie S G, Wang F 2011 Nature 471 617 [24] Yao Y, Kats M A, Genevet P, Yu N F, Song Y, Kong J, Capasso F 2013 Nano Lett. 13 1257 [25] Lee S H, Choi M, Kim T T, Lee S, Liu M, Yin X B, Choi H K, Lee S S, Choi S Y, Choi C G, Zhang X, Min B K 2012 Nat. Mater. 11 936 [26] Balci O, Polat E O, Kakenov N, Kocabas C 2015 Nat. Commun. 6 6628 [27] Pors A, Bozhevolnyi S I 2013 Opt. Express 21 27438 [28] Vasko F T, Ryzhii V 2007 Phys. Rev. B 76 233404 [29] Sun S L, He Q, Xiao S Y, Xu Q, Li X, Zhou L 2012 Nat. Mater. 11 426
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•  Citation:
##### Metrics
• Abstract views:  175
• Cited By: 0
##### Publishing process
• Received Date:  03 April 2018
• Accepted Date:  04 June 2018
• Published Online:  20 September 2018

## Dynamic beam-steering in wide angle range based on tunable graphene metasurface

###### Corresponding author: Lu Wei-Bing, wblu@seu.edu.cn;
• 1. State Key Laboratory of Millimetre Waves, School of Information Science and Engineering, Southeast University, Nanjing 210096, China;
• 2. Synergetic Innovation Center of Wireless Communication Technology, Southeast University, Nanjing 210096, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 61671150, 61671147) and the Six Talent Peaks Project in Jiangsu Province, China (Grant No. XCL-004).

Abstract: Metasurfaces, the two-dimensional counterparts of metamaterials composed of subwavelength building blocks, can be used to control the amplitude, phase, and polarization of the scattered wave in a simple but effective way and thus have a wide range of applications such as lenses, holograms, and beam steering. Among these applications, metasurfacebased beam steering is of great importance for antenna engineering in communication systems, because of its low loss and easy manufacture. The capability of beam steering is mainly controlled by the phase profile which is determined by the phase shift applied to the wave scattered by each of unit cells that constitute the metasurface. It should be noted that the required phase profile achieved by distributing the unit cells with different phase responses can operate well only at a certain frequency. The guidance in determining the required phase profile to steer the beam into a certain direction is the generalized Snell's law. According to this law, the reflection angle of the wave reflected by the metasurface interface depends on the linear phase gradient along the metasurface. Therefore, by forming different linear phase gradients covering the whole phase shift 2 periodically, one can steer the reflected waves to different angles. However, the obtained reflection angles are limited because the phase gradient of a metasurface is limited by the unit cell size, which cannot be infinitely small. Recently, a new pattern shift theory based on the convolution theorem has been proposed to realize wide angle range steering, enabling flexible and continuous manipulation of reflection angle. Because the electric field distribution and the scattering pattern in the far-field region are a Fourier transform pair, we can pattern the electric field of the metasurface to control the scattered waves of far field. Specifically, the multiplication of an electric distribution by a gradient phase sequence leads to a deviation of the scattering pattern from its original direction to a certain extent in the angular coordinate. However, we have not considered the tunability of metasurfaces so far, which is required in applications. The ways to reach tunability in metasurface include diode switches, micro-electro-mechanical system, and the use of tunable materials such as graphene. Graphene, an atomically thin layer of carbon atoms arranged in a honeycomb lattice, has aroused the enormous interest due to its outstanding mechanical, thermal, and electrical properties. With the capability of being electrically tunable, graphene has manifested itself as a promising candidate for designing the tunable metasurfaces. Although the reflection angle can be changed by electrically reconfiguring the graphene Fermi level distribution of the metasurface, the steering angle is still limited. In this paper, we propose and design a tunable graphene metasurface with the capability of dynamically steering the reflection angle in a wide range, which is achieved based on the new pattern shift theory. The theoretical results and the numerically simulated results both show that the reflection angle can be steered from 5 to 70 with an interval less than 10, implying the promising potential in the design of tunable antenna.

Reference (29)

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