Abstract

We report new models for out-of-plane focusing and manipulation of terahertz beams based on a silicon/copper grating covered by monolayer graphene. Dependences of focusing and manipulation of terahertz beams on the chemical potential and scattering rate of graphene are investigated. Based on the graphene/silicon grating model, we demonstrate that the focal distance and intensity are sensitively influenced by the chemical potential. Based on the graphene/copper grating model, we show how 2 to 1 and 3 to 1 modulation of terahertz beams can be efficiently realized through tuning the chemical potential of graphene. These tunable beam focusing and manipulation effects are well explained by the diffraction theory of optical images and the surface plasmon polariton theory of graphene. Our proposed devices are of compact structures, high electro-optical tunability and good repeatability, and they are expected to have prospective applications in terahertz communications, imaging, sensing, and so on.

© 2017 Optical Society of America

Full Article  |  PDF Article
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2017 (2)

D. V. Fateev, K. V. Mashinsky, and V. V. Popov, “Terahertz plasmonic rectification in a spatially periodic graphene,” Appl. Phys. Lett. 110(6), 061106 (2017).
[Crossref]

Z. Liu and B. Bai, “Ultra-thin and high-efficiency graphene metasurface for tunable terahertz wave manipulation,” Opt. Express 25(8), 8584–8592 (2017).
[Crossref] [PubMed]

2016 (4)

W. Liu, B. Wang, S. Ke, C. Qin, H. Long, K. Wang, and P. Lu, “Enhanced plasmonic nanofocusing of terahertz waves in tapered graphene multilayers,” Opt. Express 24(13), 14765–14780 (2016).
[Crossref] [PubMed]

L. M. Liu, Y. Zarate, H. T. Hattori, D. N. Neshev, I. V. Shadrivov, and D. A. Powell, “Terahertz focusing of multiple wavelengths by graphene metasurfaces,” Appl. Phys. Lett. 108(3), 031106 (2016).
[Crossref]

X. Yu, X. Gao, W. Qiao, L. Wen, and W. Yang, “Broadband tunable polarization converter realized by graphene-based metamaterial,” IEEE Photonics Technol. Lett. 28(21), 2399–2402 (2016).
[Crossref]

J. S. Li, “Tunable focus graphene-based terahertz lens,” Opt. Commun. 359, 268–271 (2016).
[Crossref]

2015 (5)

D. Wang, L. Zhang, Y. Gu, M. Q. Mehmood, Y. Gong, A. Srivastava, L. Jian, T. Venkatesan, C. W. Qiu, and M. Hong, “Switchable ultrathin quarter-wave plate in terahertz using active phase-change metasurface,” Sci. Rep. 5, 15020 (2015).
[Crossref] [PubMed]

H. W. Zhuang, F. M. Kong, K. Li, and Q. Y. Yue, “A gating tunable planar lens based on graphene,” Opt. Quantum Electron. 47(5), 1139–1150 (2015).
[Crossref]

Z. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. An, Y. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
[Crossref]

Z. Li, K. Yao, F. Xia, S. Shen, J. Tian, and Y. Liu, “Graphene plasmonic metasurfaces to steer infrared light,” Sci. Rep. 5(1), 12423 (2015).
[Crossref] [PubMed]

A. Olivieri, C. Chen, S. Hassan, E. Lisicka-Skrzek, R. N. Tait, and P. Berini, “Plasmonic nanostructured metal-oxide-semiconductor reflection modulators,” Nano Lett. 15(4), 2304–2311 (2015).
[Crossref] [PubMed]

2014 (1)

H. W. Zhuang, F. M. Kong, K. Li, J. Zhao, and S. W. Sheng, “Analysis of graphene-based half Maxwell fish-eye lens using effective index method,” Opt. Eng. 53(12), 127109 (2014).
[Crossref]

2013 (6)

2012 (6)

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Fourier optics on graphene,” Phys. Rev. B 85(7), 075434 (2012).
[Crossref]

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[Crossref] [PubMed]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, and H. G. Xing, “Extraordinary control of terahertz beam reflectance in graphene electro-absorption modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[Crossref] [PubMed]

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100(15), 153111 (2012).
[Crossref] [PubMed]

2011 (3)

B. Sensale-Rodriguez, T. Fang, R. Yan, M. M. Kelly, D. Jena, L. Liu, and H. Xing, “Unique prospects for graphene-based terahertz modulators,” Appl. Phys. Lett. 99(11), 113104 (2011).
[Crossref]

R. Yahiaoui, H. Němec, P. Kužel, F. Kadlec, C. Kadlec, and P. Mounaix, “Tunable THz metamaterials based on an array of paraelectric SrTiO3 rods,” Appl. Phys., A Mater. Sci. Process. 103(3), 689–692 (2011).
[Crossref]

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref] [PubMed]

2010 (2)

M. K. Chen, Y. C. Chang, C. E. Yang, Y. H. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, “Tunable terahertz plasmonic lenses based on semiconductor microslits,” Microw. Opt. Technol. Lett. 52(4), 979–981 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

2009 (3)

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B 79(24), 241108 (2009).
[Crossref]

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

2008 (4)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

K. I. Bolotin, K. J. Sikes, J. Hone, H. L. Stormer, and P. Kim, “Temperature-dependent transport in suspended graphene,” Phys. Rev. Lett. 101(9), 096802 (2008).
[Crossref] [PubMed]

G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9–10), 351–355 (2008).
[Crossref]

2007 (3)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

F. T. Vasko and V. Ryzhii, “Voltage and temperature dependencies of conductivity in gated graphene,” Phys. Rev. B 76(23), 233404 (2007).
[Crossref]

2006 (1)

Z. Wang, T. Sang, L. Wang, J. Zhu, Y. Wu, and L. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 251115 (2006).
[Crossref]

2005 (1)

H. C. Lin, P. D. Ye, and G. D. Wilk, “Leakage current and breakdown electric-field studies on ultrathin atomic-layer-deposited Al2O3 on GaAs,” Appl. Phys. Lett. 87(18), 182904 (2005).
[Crossref]

2002 (1)

B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[Crossref] [PubMed]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 29(3), 466–475 (1956).

Alù, A.

P. Y. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alù, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
[Crossref]

An, Z.

Z. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. An, Y. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
[Crossref]

Andryieuski, A.

Bai, B.

Berini, P.

A. Olivieri, C. Chen, S. Hassan, E. Lisicka-Skrzek, R. N. Tait, and P. Berini, “Plasmonic nanostructured metal-oxide-semiconductor reflection modulators,” Nano Lett. 15(4), 2304–2311 (2015).
[Crossref] [PubMed]

Bernety, H. M.

P. Y. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alù, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
[Crossref]

Bolotin, K. I.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9–10), 351–355 (2008).
[Crossref]

K. I. Bolotin, K. J. Sikes, J. Hone, H. L. Stormer, and P. Kim, “Temperature-dependent transport in suspended graphene,” Phys. Rev. Lett. 101(9), 096802 (2008).
[Crossref] [PubMed]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Boudouris, B. W.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref] [PubMed]

Brantley, C.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. H. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, “Tunable terahertz plasmonic lenses based on semiconductor microslits,” Microw. Opt. Technol. Lett. 52(4), 979–981 (2010).
[Crossref]

Brower-Thomas, T.

T. A. Searles, M. Rezaee, A. Shams-Ansari, E. Strickland, T. Brower-Thomas, G. Harris, and R. Yahiaoui, “Graphene-based metasurfaces for multimode tunable terahertz modulators,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2017), paper JW2A.105.
[Crossref]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Cai, W.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100(15), 153111 (2012).
[Crossref] [PubMed]

Chang, Y. C.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. H. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, “Tunable terahertz plasmonic lenses based on semiconductor microslits,” Microw. Opt. Technol. Lett. 52(4), 979–981 (2010).
[Crossref]

Chen, C.

A. Olivieri, C. Chen, S. Hassan, E. Lisicka-Skrzek, R. N. Tait, and P. Berini, “Plasmonic nanostructured metal-oxide-semiconductor reflection modulators,” Nano Lett. 15(4), 2304–2311 (2015).
[Crossref] [PubMed]

Chen, C. F.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref] [PubMed]

Chen, L.

Z. Wang, T. Sang, L. Wang, J. Zhu, Y. Wu, and L. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 251115 (2006).
[Crossref]

Chen, M. K.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. H. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, “Tunable terahertz plasmonic lenses based on semiconductor microslits,” Microw. Opt. Technol. Lett. 52(4), 979–981 (2010).
[Crossref]

Chen, P. Y.

P. Y. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alù, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
[Crossref]

Colombo, L.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
[Crossref] [PubMed]

Crommie, M. F.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref] [PubMed]

Danaeifar, M.

Ding, K.

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L. M. Liu, Y. Zarate, H. T. Hattori, D. N. Neshev, I. V. Shadrivov, and D. A. Powell, “Terahertz focusing of multiple wavelengths by graphene metasurfaces,” Appl. Phys. Lett. 108(3), 031106 (2016).
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A. Olivieri, C. Chen, S. Hassan, E. Lisicka-Skrzek, R. N. Tait, and P. Berini, “Plasmonic nanostructured metal-oxide-semiconductor reflection modulators,” Nano Lett. 15(4), 2304–2311 (2015).
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D. V. Fateev, K. V. Mashinsky, and V. V. Popov, “Terahertz plasmonic rectification in a spatially periodic graphene,” Appl. Phys. Lett. 110(6), 061106 (2017).
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L. M. Liu, Y. Zarate, H. T. Hattori, D. N. Neshev, I. V. Shadrivov, and D. A. Powell, “Terahertz focusing of multiple wavelengths by graphene metasurfaces,” Appl. Phys. Lett. 108(3), 031106 (2016).
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B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, and H. G. Xing, “Extraordinary control of terahertz beam reflectance in graphene electro-absorption modulators,” Nano Lett. 12(9), 4518–4522 (2012).
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X. Yu, X. Gao, W. Qiao, L. Wen, and W. Yang, “Broadband tunable polarization converter realized by graphene-based metamaterial,” IEEE Photonics Technol. Lett. 28(21), 2399–2402 (2016).
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M. K. Chen, Y. C. Chang, C. E. Yang, Y. H. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, “Tunable terahertz plasmonic lenses based on semiconductor microslits,” Microw. Opt. Technol. Lett. 52(4), 979–981 (2010).
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Z. Li, K. Yao, F. Xia, S. Shen, J. Tian, and Y. Liu, “Graphene plasmonic metasurfaces to steer infrared light,” Sci. Rep. 5(1), 12423 (2015).
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H. W. Zhuang, F. M. Kong, K. Li, J. Zhao, and S. W. Sheng, “Analysis of graphene-based half Maxwell fish-eye lens using effective index method,” Opt. Eng. 53(12), 127109 (2014).
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D. Wang, L. Zhang, Y. Gu, M. Q. Mehmood, Y. Gong, A. Srivastava, L. Jian, T. Venkatesan, C. W. Qiu, and M. Hong, “Switchable ultrathin quarter-wave plate in terahertz using active phase-change metasurface,” Sci. Rep. 5, 15020 (2015).
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T. A. Searles, M. Rezaee, A. Shams-Ansari, E. Strickland, T. Brower-Thomas, G. Harris, and R. Yahiaoui, “Graphene-based metasurfaces for multimode tunable terahertz modulators,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2017), paper JW2A.105.
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A. Olivieri, C. Chen, S. Hassan, E. Lisicka-Skrzek, R. N. Tait, and P. Berini, “Plasmonic nanostructured metal-oxide-semiconductor reflection modulators,” Nano Lett. 15(4), 2304–2311 (2015).
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Z. Li, K. Yao, F. Xia, S. Shen, J. Tian, and Y. Liu, “Graphene plasmonic metasurfaces to steer infrared light,” Sci. Rep. 5(1), 12423 (2015).
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D. Wang, L. Zhang, Y. Gu, M. Q. Mehmood, Y. Gong, A. Srivastava, L. Jian, T. Venkatesan, C. W. Qiu, and M. Hong, “Switchable ultrathin quarter-wave plate in terahertz using active phase-change metasurface,” Sci. Rep. 5, 15020 (2015).
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D. Svintsov, V. Vyurkov, V. Ryzhii, and T. Otsuji, “Voltage-controlled surface plasmon-polaritons in double graphene layer structures,” J. Appl. Phys. 113(5), 053701 (2013).
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Wang, D.

D. Wang, L. Zhang, Y. Gu, M. Q. Mehmood, Y. Gong, A. Srivastava, L. Jian, T. Venkatesan, C. W. Qiu, and M. Hong, “Switchable ultrathin quarter-wave plate in terahertz using active phase-change metasurface,” Sci. Rep. 5, 15020 (2015).
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Wang, L.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100(15), 153111 (2012).
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Z. Wang, T. Sang, L. Wang, J. Zhu, Y. Wu, and L. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 251115 (2006).
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Z. Wang, T. Sang, L. Wang, J. Zhu, Y. Wu, and L. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 251115 (2006).
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X. Yu, X. Gao, W. Qiao, L. Wen, and W. Yang, “Broadband tunable polarization converter realized by graphene-based metamaterial,” IEEE Photonics Technol. Lett. 28(21), 2399–2402 (2016).
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H. C. Lin, P. D. Ye, and G. D. Wilk, “Leakage current and breakdown electric-field studies on ultrathin atomic-layer-deposited Al2O3 on GaAs,” Appl. Phys. Lett. 87(18), 182904 (2005).
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Z. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. An, Y. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
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Z. Wang, T. Sang, L. Wang, J. Zhu, Y. Wu, and L. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 251115 (2006).
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Z. Li, K. Yao, F. Xia, S. Shen, J. Tian, and Y. Liu, “Graphene plasmonic metasurfaces to steer infrared light,” Sci. Rep. 5(1), 12423 (2015).
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B. Sensale-Rodriguez, T. Fang, R. Yan, M. M. Kelly, D. Jena, L. Liu, and H. Xing, “Unique prospects for graphene-based terahertz modulators,” Appl. Phys. Lett. 99(11), 113104 (2011).
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B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, and H. G. Xing, “Extraordinary control of terahertz beam reflectance in graphene electro-absorption modulators,” Nano Lett. 12(9), 4518–4522 (2012).
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Xu, J.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100(15), 153111 (2012).
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Xu, Q.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
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R. Yahiaoui, H. Němec, P. Kužel, F. Kadlec, C. Kadlec, and P. Mounaix, “Tunable THz metamaterials based on an array of paraelectric SrTiO3 rods,” Appl. Phys., A Mater. Sci. Process. 103(3), 689–692 (2011).
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H. Němec, P. Kužel, F. Kadlec, C. Kadlec, R. Yahiaoui, and P. Mounaix, “Tunable terahertz metamaterials with negative permeability,” Phys. Rev. B 79(24), 241108 (2009).
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T. A. Searles, M. Rezaee, A. Shams-Ansari, E. Strickland, T. Brower-Thomas, G. Harris, and R. Yahiaoui, “Graphene-based metasurfaces for multimode tunable terahertz modulators,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2017), paper JW2A.105.
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P. Y. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alù, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
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B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, and H. G. Xing, “Extraordinary control of terahertz beam reflectance in graphene electro-absorption modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[Crossref] [PubMed]

B. Sensale-Rodriguez, T. Fang, R. Yan, M. M. Kelly, D. Jena, L. Liu, and H. Xing, “Unique prospects for graphene-based terahertz modulators,” Appl. Phys. Lett. 99(11), 113104 (2011).
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M. K. Chen, Y. C. Chang, C. E. Yang, Y. H. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, “Tunable terahertz plasmonic lenses based on semiconductor microslits,” Microw. Opt. Technol. Lett. 52(4), 979–981 (2010).
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Yang, W.

X. Yu, X. Gao, W. Qiao, L. Wen, and W. Yang, “Broadband tunable polarization converter realized by graphene-based metamaterial,” IEEE Photonics Technol. Lett. 28(21), 2399–2402 (2016).
[Crossref]

Yao, K.

Z. Li, K. Yao, F. Xia, S. Shen, J. Tian, and Y. Liu, “Graphene plasmonic metasurfaces to steer infrared light,” Sci. Rep. 5(1), 12423 (2015).
[Crossref] [PubMed]

Ye, P. D.

H. C. Lin, P. D. Ye, and G. D. Wilk, “Leakage current and breakdown electric-field studies on ultrathin atomic-layer-deposited Al2O3 on GaAs,” Appl. Phys. Lett. 87(18), 182904 (2005).
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Yin, S.

M. K. Chen, Y. C. Chang, C. E. Yang, Y. H. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, “Tunable terahertz plasmonic lenses based on semiconductor microslits,” Microw. Opt. Technol. Lett. 52(4), 979–981 (2010).
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Yu, X.

X. Yu, X. Gao, W. Qiao, L. Wen, and W. Yang, “Broadband tunable polarization converter realized by graphene-based metamaterial,” IEEE Photonics Technol. Lett. 28(21), 2399–2402 (2016).
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H. W. Zhuang, F. M. Kong, K. Li, and Q. Y. Yue, “A gating tunable planar lens based on graphene,” Opt. Quantum Electron. 47(5), 1139–1150 (2015).
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L. M. Liu, Y. Zarate, H. T. Hattori, D. N. Neshev, I. V. Shadrivov, and D. A. Powell, “Terahertz focusing of multiple wavelengths by graphene metasurfaces,” Appl. Phys. Lett. 108(3), 031106 (2016).
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Zettl, A.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref] [PubMed]

Zhang, L.

D. Wang, L. Zhang, Y. Gu, M. Q. Mehmood, Y. Gong, A. Srivastava, L. Jian, T. Venkatesan, C. W. Qiu, and M. Hong, “Switchable ultrathin quarter-wave plate in terahertz using active phase-change metasurface,” Sci. Rep. 5, 15020 (2015).
[Crossref] [PubMed]

Zhang, X.

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100(15), 153111 (2012).
[Crossref] [PubMed]

Zhang, X. C.

B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
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Zhang, Y.

Z. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. An, Y. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
[Crossref]

Zhao, J.

H. W. Zhuang, F. M. Kong, K. Li, J. Zhao, and S. W. Sheng, “Analysis of graphene-based half Maxwell fish-eye lens using effective index method,” Opt. Eng. 53(12), 127109 (2014).
[Crossref]

Zhou, L.

Z. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. An, Y. Zhang, and L. Zhou, “Widely tunable terahertz phase modulation with gate-controlled graphene metasurfaces,” Phys. Rev. X 5(4), 041027 (2015).
[Crossref]

Zhu, J.

Z. Wang, T. Sang, L. Wang, J. Zhu, Y. Wu, and L. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 251115 (2006).
[Crossref]

Zhu, M.

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, and H. G. Xing, “Extraordinary control of terahertz beam reflectance in graphene electro-absorption modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[Crossref] [PubMed]

Zhuang, H. W.

H. W. Zhuang, F. M. Kong, K. Li, and Q. Y. Yue, “A gating tunable planar lens based on graphene,” Opt. Quantum Electron. 47(5), 1139–1150 (2015).
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H. W. Zhuang, F. M. Kong, K. Li, J. Zhao, and S. W. Sheng, “Analysis of graphene-based half Maxwell fish-eye lens using effective index method,” Opt. Eng. 53(12), 127109 (2014).
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ACS Nano (1)

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (6)

P. Liu, W. Cai, L. Wang, X. Zhang, and J. Xu, “Tunable terahertz optical antennas based on graphene ring structures,” Appl. Phys. Lett. 100(15), 153111 (2012).
[Crossref] [PubMed]

B. Sensale-Rodriguez, T. Fang, R. Yan, M. M. Kelly, D. Jena, L. Liu, and H. Xing, “Unique prospects for graphene-based terahertz modulators,” Appl. Phys. Lett. 99(11), 113104 (2011).
[Crossref]

L. M. Liu, Y. Zarate, H. T. Hattori, D. N. Neshev, I. V. Shadrivov, and D. A. Powell, “Terahertz focusing of multiple wavelengths by graphene metasurfaces,” Appl. Phys. Lett. 108(3), 031106 (2016).
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D. V. Fateev, K. V. Mashinsky, and V. V. Popov, “Terahertz plasmonic rectification in a spatially periodic graphene,” Appl. Phys. Lett. 110(6), 061106 (2017).
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H. C. Lin, P. D. Ye, and G. D. Wilk, “Leakage current and breakdown electric-field studies on ultrathin atomic-layer-deposited Al2O3 on GaAs,” Appl. Phys. Lett. 87(18), 182904 (2005).
[Crossref]

Z. Wang, T. Sang, L. Wang, J. Zhu, Y. Wu, and L. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 251115 (2006).
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Appl. Phys., A Mater. Sci. Process. (1)

R. Yahiaoui, H. Němec, P. Kužel, F. Kadlec, C. Kadlec, and P. Mounaix, “Tunable THz metamaterials based on an array of paraelectric SrTiO3 rods,” Appl. Phys., A Mater. Sci. Process. 103(3), 689–692 (2011).
[Crossref]

IEEE Photonics Technol. Lett. (1)

X. Yu, X. Gao, W. Qiao, L. Wen, and W. Yang, “Broadband tunable polarization converter realized by graphene-based metamaterial,” IEEE Photonics Technol. Lett. 28(21), 2399–2402 (2016).
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J. Appl. Phys. (2)

G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
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D. Svintsov, V. Vyurkov, V. Ryzhii, and T. Otsuji, “Voltage-controlled surface plasmon-polaritons in double graphene layer structures,” J. Appl. Phys. 113(5), 053701 (2013).
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J. Phys. Conf. Ser. (1)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
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Microw. Opt. Technol. Lett. (1)

M. K. Chen, Y. C. Chang, C. E. Yang, Y. H. Guo, J. Mazurowski, S. Yin, P. Ruffin, C. Brantley, E. Edwards, and C. Luo, “Tunable terahertz plasmonic lenses based on semiconductor microslits,” Microw. Opt. Technol. Lett. 52(4), 979–981 (2010).
[Crossref]

Nano Lett. (2)

A. Olivieri, C. Chen, S. Hassan, E. Lisicka-Skrzek, R. N. Tait, and P. Berini, “Plasmonic nanostructured metal-oxide-semiconductor reflection modulators,” Nano Lett. 15(4), 2304–2311 (2015).
[Crossref] [PubMed]

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, and H. G. Xing, “Extraordinary control of terahertz beam reflectance in graphene electro-absorption modulators,” Nano Lett. 12(9), 4518–4522 (2012).
[Crossref] [PubMed]

Nat. Mater. (2)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[Crossref] [PubMed]

Nat. Photonics (3)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
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A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
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Nature (2)

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012).
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C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011).
[Crossref] [PubMed]

New J. Phys. (1)

P. Y. Chen, J. Soric, Y. R. Padooru, H. M. Bernety, A. B. Yakovlev, and A. Alù, “Nanostructured graphene metasurface for tunable terahertz cloaking,” New J. Phys. 15(12), 123029 (2013).
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Opt. Commun. (1)

J. S. Li, “Tunable focus graphene-based terahertz lens,” Opt. Commun. 359, 268–271 (2016).
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Opt. Eng. (1)

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Figures (10)

Fig. 1
Fig. 1 (a) Focusing model of terahertz beams based on a simple silicon grating covered by monolayer graphene. (b) Manipulation model of terahertz beams based on a triple-slit copper grating covered by monolayer graphene. The graphene and Si/Cu substrate are separated by a thin Al2O3 gate dielectric film for applying a gate voltage on graphene.
Fig. 2
Fig. 2 Spatial distributions of normalized Poynting vector energy flux |P| in x-z plane for the optimized focusing model in Fig. 1(a) at 3 THz under different conditions. (a) Pure silicon grating without graphene. (b)-(d) Graphene covered silicon grating when Γ is 0.17 meV and μc is 0.1 eV, 0.5 eV, and 0.9 eV, respectively.
Fig. 3
Fig. 3 (a) Dependences of focal distance and intensity on the chemical potential when Γ is fixed to be 0.17 meV. (b) Dependences of focal distance and intensity on the scattering rate when μc is fixed to be 0.5 eV.
Fig. 4
Fig. 4 (a) and (b) Calculated conductivity of graphene and effective refractive index of SPP as a function of the chemical potential when Γ is fixed to be 0.17 meV. (c) and (d) Calculated conductivity of graphene and effective refractive index of SPP as a function of the scattering rate when μc is fixed to be 0.5 eV.
Fig. 5
Fig. 5 The broadband frequency response of the optimized focusing model in Fig. 2. (a) Dependences of the focal distance and the corresponding tunable length Δf on the effective working frequency. (b) Dependences of the normalized focal intensity and the corresponding variation ratio of focal intensity on the effective working frequency.
Fig. 6
Fig. 6 Tunable beam focusing effect for the model in Fig. 1(a) when the optimal working frequency is shifted from 3 THz to about 2 THz [(a) and (b)] and 4 THz [(c) and (d)], respectively. As compared with Fig. 2, the structural parameters of gratings are magnified by 1.5 times in the 2 THz case and shrunk by 0.75 times in the 4 THz case.
Fig. 7
Fig. 7 Evolution of 2 to 1 beam manipulation effect at 3 THz based on the manipulation model in Fig. 1(b) with structural parameters of Λg = 65 μm, hCu = 36 μm, wc = 8 μm, ws = 14 μm, l = 93 μm, wg = 11 μm, and tg = 14 μm under different conditions. (a) Pure copper grating without graphene. (b)-(f) Graphene covered copper grating when Γ is 0.17 meV and μc is 0.1 eV, 0.3 eV, 0.5 eV, 0.7 eV, and 0.9 eV, respectively. The cross-section profile of |P| along the dashed line (z = 350 μm) is shown on the top of each sub figure.
Fig. 8
Fig. 8 Evolution of 3 to 1 beam manipulation effect at 3 THz based on the manipulation model in Fig. 1(b) with structural parameters of Λg = 85 μm, hCu = 36 μm, wc = 8 μm, ws = 14 μm, l = 93 μm, wg = 11 μm, and tg = 14 μm under different conditions. (a) Pure copper grating without graphene. (b)-(f) Graphene covered copper grating when Γ is 0.17 meV and μc is 0.1 eV, 0.3 eV, 0.5 eV, 0.7 eV, and 0.9 eV, respectively. The cross-section profile of |P| along the dashed line (z = 350 μm) is shown on the top of each sub figure.
Fig. 9
Fig. 9 Dependences of 2 to 1 and 3 to 1 beam conversion efficiencies on the chemical potential. The beam conversion efficiency is defined as the intensity ratio of the central beam to side beams at z = 350 μm in Figs. 7 and 8.
Fig. 10
Fig. 10 2 to 1 and 3 to 1 beam manipulation effects at optimal working frequency of about 2 THz [(a) and (b)] and 4 THz [(c) and (d)] based on the model in Fig. 1(b). As compared with Figs. 7 and 8, the structural parameters of gratings are magnified by 1.5 times in the 2 THz case and shrunk by 0.75 times in the 4 THz case.

Tables (1)

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Table 1 Comparison of the tunable out-of-plane focusing devices in THz region

Equations (9)

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σ( ω,Γ, μ c ,T )= σ intra ( ω,Γ, μ c ,T )+ σ inter ( ω,Γ, μ c ,T )
σ intra ( ω,Γ, μ c ,T )=i e 2 k B T π 2 (ω+i2Γ) [ μ c k B T +2ln( e μ c k B T +1 )]
σ inter ( ω,Γ, μ c ,T )=i e 2 4π 2 ln[ 2| μ c |(ω+i2Γ) 2| μ c |+(ω+i2Γ) ]
ε xx = ε yy = ε r +i σ intra ( ω,Γ, μ c ,T ) ε 0 ωt and ε zz = ε r
Δ Ψ x = 2π f 2 + x 2 λ 2πf λ = Ψ c 2mπ
Ψ SPP =Re( n SPP ) k 0 x
ε r1 n 2 SPP - ε r1 + ε r2 n 2 SPP - ε r2 = i σ intra ( ω,Γ, μ c ,T ) ε 0 c  
ε r2 = ϵ eff,TM = ϵ air ϵ Si F ϵ air +( 1F ) ϵ Si + π 2 3 F 2 ( 1F ) 2 ( 1 ϵ air 1 ϵ Si ) 2 ϵ air 3 ϵ Si 3 [ F ϵ Si +( 1F ) ϵ air ] [ F ϵ air +( 1F ) ϵ Si ] 3 ( Λ Si λ ) 2
  ν 0 = c Λ[Re( n SPP )sinθ]

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