Abstract

Graphene is a good candidate material in designing tunable terahertz devices due to its tunability of sheet conductivity. In this paper, we propose a scheme to design switchable quarter-wave plate for terahertz wave that is composed of graphene based grating and metallic grating structures. The proposed active device can dynamically switch the transmission wave among left-handed, right-handed circular polarization and linear polarization states by electrically controlling the Fermi energy of the graphene grating. The device is analyzed with grating circular polarizer theory and its performance is investigated through full wave simulations on practically realizable geometry. The proposed quarter-wave plate having a subwavelength thickness demonstrates a wide angle of incidence tolerance, and a broad bandwidth operation. This device concept offers a further step in developing tunable polarizers and polarization switchers, which may be applied in practical terahertz image and communication systems.

© 2015 Optical Society of America

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2015 (1)

K. B. Fan and W. J. Padilla, “Dynamic electromagnetic metamaterials,” Mater. Today 18(1), 39–50 (2015).
[Crossref]

2014 (6)

B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4, 4130 (2014).
[PubMed]

Y. Zhang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency,” Opt. Express 22(19), 22743–22752 (2014).
[Crossref] [PubMed]

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G.-B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

J. Ding, B. Arigong, H. Ren, M. Zhou, J. Shao, Y. Lin, and H. Zhang, “Efficient multiband and broadband cross polarization converters based on slotted L-shaped nanoantennas,” Opt. Express 22(23), 29143–29151 (2014).
[Crossref] [PubMed]

X. L. Ma, W. B. Pan, C. Huang, M. B. Pu, Y. Q. Wang, B. Zhao, J. H. Cui, C. T. Wang, and X. G. Luo, “An active metamaterial for polarization manipulating,” Adv. Opt. Mater. 2(10), 945–949 (2014).
[Crossref]

L. Q. Cong, N. N. Xu, J. Q. Gu, R. J. Singh, J. G. Han, and W. L. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photonics Rev. 8(4), 626–632 (2014).
[Crossref]

2013 (6)

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013).
[Crossref]

B. Yang, W. M. Ye, X. D. Yuan, Z. H. Zhu, and C. Zeng, “Design of ultrathin plasmonic quarter-wave plate based on period coupling,” Opt. Lett. 38(5), 679–681 (2013).
[Crossref] [PubMed]

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

P. Tassin, T. Koschny, and C. M. Soukoulis, “Graphene for terahertz applications,” Science 341(6146), 620–621 (2013).
[Crossref] [PubMed]

J. S. Gómez-Díaz and J. Perruisseau-Carrier, “Graphene-based plasmonic switches at near infrared frequencies,” Opt. Express 21(13), 15490–15504 (2013).
[Crossref] [PubMed]

A. Andryieuski and A. V. Lavrinenko, “Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach,” Opt. Express 21(7), 9144–9155 (2013).
[Crossref] [PubMed]

2012 (5)

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]

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[Crossref] [PubMed]

R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012).
[Crossref] [PubMed]

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

2011 (6)

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X. H. Zhou, J. D. Luo, A. K. Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109(4), 043505 (2011).
[Crossref]

J. Y. Kim, C. Lee, S. Bae, K. S. Kim, B. H. Hong, and E. J. Choi, “Far-infrared study of substrate-effect on large scale graphene,” Appl. Phys. Lett. 98(20), 201907 (2011).
[Crossref]

B. S. 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, 113104 (2011).
[Crossref]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

H. J. Song and T. D. Nagatsuma, “Present and future of terahertz communications,” IEEE Trans. Terahertz Sci. Technol. 1(1), 256–263 (2011).
[Crossref]

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

2010 (4)

D. Huang, E. Poutrina, and D. R. Smith, “Analysis of the power dependent tuning of a varactor-loaded metamaterial at microwave frequencies,” Appl. Phys. Lett. 96(10), 104104 (2010).
[Crossref]

B. Zhu, C. Huang, Y. J. Feng, J. M. Zhao, and T. Jiang, “Dual band switchable metamaterial electromagnetic absorber,” Prog. Electromagn. Res. B 24, 121–129 (2010).
[Crossref]

B. Zhu, Y. J. Feng, C. Huang, J. M. Zhao, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

B. Zhu, Y. Feng, J. Zhao, C. Huang, Z. Wang, and T. Jiang, “Polarization modulation by tunable electromagnetic metamaterial reflector/absorber,” Opt. Express 18(22), 23196–23203 (2010).
[Crossref] [PubMed]

2009 (2)

2008 (4)

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: design, fabrication and characterization,” Opt. Express 16(10), 7181–7188 (2008).
[Crossref] [PubMed]

C. M. Bingham, H. Tao, X. Liu, R. D. Averitt, X. Zhang, and W. J. Padilla, “Planar wallpaper group metamaterials for novel terahertz applications,” Opt. Express 16(23), 18565–18575 (2008).
[Crossref] [PubMed]

H. T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93(9), 091117 (2008).
[Crossref]

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]

2007 (1)

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

2006 (3)

G. P. Williams, “Filling the THz gap-high power sources and applications,” Rep. Prog. Phys. 69(2), 301–326 (2006).
[Crossref]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

2004 (1)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

2003 (1)

G. F. Brand, “The strip grating as a circular polarizer,” Am. J. Phys. 71(5), 452 (2003).
[Crossref]

Abbott, D.

W. Withayachumnankul and D. Abbott, “Metamaterials in the terahertz regime,” IEEE Photonics J. 1(2), 99–118 (2009).
[Crossref]

Alaee, R.

Alù, A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[Crossref] [PubMed]

Andryieuski, A.

Arigong, B.

Atwater, H. A.

Averitt, R. D.

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: design, fabrication and characterization,” Opt. Express 16(10), 7181–7188 (2008).
[Crossref] [PubMed]

C. M. Bingham, H. Tao, X. Liu, R. D. Averitt, X. Zhang, and W. J. Padilla, “Planar wallpaper group metamaterials for novel terahertz applications,” Opt. Express 16(23), 18565–18575 (2008).
[Crossref] [PubMed]

H. T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93(9), 091117 (2008).
[Crossref]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

Aydin, K.

Azad, A. K.

N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Bae, S.

J. Y. Kim, C. Lee, S. Bae, K. S. Kim, B. H. Hong, and E. J. Choi, “Far-infrared study of substrate-effect on large scale graphene,” Appl. Phys. Lett. 98(20), 201907 (2011).
[Crossref]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
[Crossref] [PubMed]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Belkin, M. A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized ultrathin broadband circular polarizers,” Nat. Commun. 3, 870 (2012).
[Crossref] [PubMed]

Bingham, C. M.

H. T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93(9), 091117 (2008).
[Crossref]

C. M. Bingham, H. Tao, X. Liu, R. D. Averitt, X. Zhang, and W. J. Padilla, “Planar wallpaper group metamaterials for novel terahertz applications,” Opt. Express 16(23), 18565–18575 (2008).
[Crossref] [PubMed]

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: design, fabrication and characterization,” Opt. Express 16(10), 7181–7188 (2008).
[Crossref] [PubMed]

Boyd, E. M.

Brand, G. F.

G. F. Brand, “The strip grating as a circular polarizer,” Am. J. Phys. 71(5), 452 (2003).
[Crossref]

Cao, W.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013).
[Crossref]

Chen, H. T.

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H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
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S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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J. Y. Kim, C. Lee, S. Bae, K. S. Kim, B. H. Hong, and E. J. Choi, “Far-infrared study of substrate-effect on large scale graphene,” Appl. Phys. Lett. 98(20), 201907 (2011).
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S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

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S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
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N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
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B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4, 4130 (2014).
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L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013).
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L. Q. Cong, N. N. Xu, J. Q. Gu, R. J. Singh, J. G. Han, and W. L. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photonics Rev. 8(4), 626–632 (2014).
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X. L. Ma, W. B. Pan, C. Huang, M. B. Pu, Y. Q. Wang, B. Zhao, J. H. Cui, C. T. Wang, and X. G. Luo, “An active metamaterial for polarization manipulating,” Adv. Opt. Mater. 2(10), 945–949 (2014).
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P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X. H. Zhou, J. D. Luo, A. K. Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109(4), 043505 (2011).
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N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
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Ding, J.

Fal’ko, V. I.

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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T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
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B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
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B. S. 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, 113104 (2011).
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Farhat, M.

Feng, Y.

Feng, Y. J.

B. Zhu, C. Huang, Y. J. Feng, J. M. Zhao, and T. Jiang, “Dual band switchable metamaterial electromagnetic absorber,” Prog. Electromagn. Res. B 24, 121–129 (2010).
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B. Zhu, Y. J. Feng, C. Huang, J. M. Zhao, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
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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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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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H. T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93(9), 091117 (2008).
[Crossref]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref] [PubMed]

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N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
[Crossref] [PubMed]

Gu, J.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013).
[Crossref]

Gu, J. Q.

L. Q. Cong, N. N. Xu, J. Q. Gu, R. J. Singh, J. G. Han, and W. L. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photonics Rev. 8(4), 626–632 (2014).
[Crossref]

Han, J.

L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013).
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L. Q. Cong, N. N. Xu, J. Q. Gu, R. J. Singh, J. G. Han, and W. L. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photonics Rev. 8(4), 626–632 (2014).
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B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4, 4130 (2014).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X. H. Zhou, J. D. Luo, A. K. Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109(4), 043505 (2011).
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N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013).
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W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
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J. Y. Kim, C. Lee, S. Bae, K. S. Kim, B. H. Hong, and E. J. Choi, “Far-infrared study of substrate-effect on large scale graphene,” Appl. Phys. Lett. 98(20), 201907 (2011).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G.-B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4(2), 021026 (2014).
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S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G.-B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4(2), 021026 (2014).
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X. L. Ma, W. B. Pan, C. Huang, M. B. Pu, Y. Q. Wang, B. Zhao, J. H. Cui, C. T. Wang, and X. G. Luo, “An active metamaterial for polarization manipulating,” Adv. Opt. Mater. 2(10), 945–949 (2014).
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B. Zhu, Y. J. Feng, C. Huang, J. M. Zhao, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
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B. Zhu, C. Huang, Y. J. Feng, J. M. Zhao, and T. Jiang, “Dual band switchable metamaterial electromagnetic absorber,” Prog. Electromagn. Res. B 24, 121–129 (2010).
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B. Zhu, Y. Feng, J. Zhao, C. Huang, Z. Wang, and T. Jiang, “Polarization modulation by tunable electromagnetic metamaterial reflector/absorber,” Opt. Express 18(22), 23196–23203 (2010).
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B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
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P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X. H. Zhou, J. D. Luo, A. K. Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109(4), 043505 (2011).
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B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

B. S. 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, 113104 (2011).
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Jiang, S. C.

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G.-B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4(2), 021026 (2014).
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Jiang, T.

Y. Zhang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency,” Opt. Express 22(19), 22743–22752 (2014).
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B. Zhu, Y. Feng, J. Zhao, C. Huang, Z. Wang, and T. Jiang, “Polarization modulation by tunable electromagnetic metamaterial reflector/absorber,” Opt. Express 18(22), 23196–23203 (2010).
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B. Zhu, C. Huang, Y. J. Feng, J. M. Zhao, and T. Jiang, “Dual band switchable metamaterial electromagnetic absorber,” Prog. Electromagn. Res. B 24, 121–129 (2010).
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B. Zhu, Y. J. Feng, C. Huang, J. M. Zhao, and T. Jiang, “Switchable metamaterial reflector/absorber for different polarized electromagnetic waves,” Appl. Phys. Lett. 97(5), 051906 (2010).
[Crossref]

Jokerst, N. M.

H. T. Chen, S. Palit, T. Tyler, C. M. Bingham, J. M. O. Zide, J. F. O’Hara, D. R. Smith, A. C. Gossard, R. D. Averitt, W. J. Padilla, N. M. Jokerst, and A. J. Taylor, “Hybrid metamaterials enable fast electrical modulation of freely propagating terahertz waves,” Appl. Phys. Lett. 93(9), 091117 (2008).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Kang, S. B.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Kelly, M. M.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
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B. S. 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, 113104 (2011).
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Kim, J. Y.

J. Y. Kim, C. Lee, S. Bae, K. S. Kim, B. H. Hong, and E. J. Choi, “Far-infrared study of substrate-effect on large scale graphene,” Appl. Phys. Lett. 98(20), 201907 (2011).
[Crossref]

Kim, K.

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]

Kim, K. S.

J. Y. Kim, C. Lee, S. Bae, K. S. Kim, B. H. Hong, and E. J. Choi, “Far-infrared study of substrate-effect on large scale graphene,” Appl. Phys. Lett. 98(20), 201907 (2011).
[Crossref]

Kim, T.-T.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Kim, Y.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
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P. Tassin, T. Koschny, and C. M. Soukoulis, “Graphene for terahertz applications,” Science 341(6146), 620–621 (2013).
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Kwak, M. H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
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Landy, N. I.

Lavrinenko, A. V.

Lederer, F.

Lee, C.

J. Y. Kim, C. Lee, S. Bae, K. S. Kim, B. H. Hong, and E. J. Choi, “Far-infrared study of substrate-effect on large scale graphene,” Appl. Phys. Lett. 98(20), 201907 (2011).
[Crossref]

Lee, M.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref] [PubMed]

Lee, S.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Lee, S. H.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Lee, S. S.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Lee, Y.-H.

M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
[Crossref] [PubMed]

Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Liu, L.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
[Crossref] [PubMed]

B. S. 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, 113104 (2011).
[Crossref]

Liu, M.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref] [PubMed]

Liu, X.

Luo, J. D.

P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X. H. Zhou, J. D. Luo, A. K. Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109(4), 043505 (2011).
[Crossref]

Luo, X. G.

X. L. Ma, W. B. Pan, C. Huang, M. B. Pu, Y. Q. Wang, B. Zhao, J. H. Cui, C. T. Wang, and X. G. Luo, “An active metamaterial for polarization manipulating,” Adv. Opt. Mater. 2(10), 945–949 (2014).
[Crossref]

Ma, G.-B.

S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G.-B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4(2), 021026 (2014).
[Crossref]

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Ma, X. L.

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B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4, 4130 (2014).
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X. L. Ma, W. B. Pan, C. Huang, M. B. Pu, Y. Q. Wang, B. Zhao, J. H. Cui, C. T. Wang, and X. G. Luo, “An active metamaterial for polarization manipulating,” Adv. Opt. Mater. 2(10), 945–949 (2014).
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M. Choi, S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, “A terahertz metamaterial with unnaturally high refractive index,” Nature 470(7334), 369–373 (2011).
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T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303(5663), 1494–1496 (2004).
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S. C. Jiang, X. Xiong, Y. S. Hu, Y. H. Hu, G.-B. Ma, R. W. Peng, C. Sun, and M. Wang, “Controlling the polarization state of light with a dispersion-free metastructure,” Phys. Rev. X 4(2), 021026 (2014).
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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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L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013).
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L. Q. Cong, N. N. Xu, J. Q. Gu, R. J. Singh, J. G. Han, and W. L. Zhang, “Highly flexible broadband terahertz metamaterial quarter-wave plate,” Laser Photonics Rev. 8(4), 626–632 (2014).
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D. Huang, E. Poutrina, and D. R. Smith, “Analysis of the power dependent tuning of a varactor-loaded metamaterial at microwave frequencies,” Appl. Phys. Lett. 96(10), 104104 (2010).
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H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
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L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013).
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B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3, 780 (2012).
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B. Wu, H. M. Tuncer, M. Naeem, B. Yang, M. T. Cole, W. I. Milne, and Y. Hao, “Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz,” Sci. Rep. 4, 4130 (2014).
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L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013).
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L. Cong, W. Cao, X. Zhang, Z. Tian, J. Gu, R. Singh, J. Han, and W. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013).
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Figures (7)

Fig. 1
Fig. 1 Schematic of the unit cell of the graphene based switchable QWP.
Fig. 2
Fig. 2 Amplitude transmissions, phase difference between co- and cross-polarization components, and the corresponding ellipticity χ for LCP QWP in the (a) biased (μc = 0.5 eV) and (b) unbiased (μc = 0 eV) state. The polarization rotation angle of co-polarization transmission wave is also represented in (b).
Fig. 3
Fig. 3 Amplitude transmissions, phase difference and the corresponding ellipticity χ of switchable QWP for RCP in the (a) biased (μc = 0.5 eV) and (b) unbiased (μc = 0 eV) state. The polarization rotation angle of co-polarization transmission wave is also represented in (b).
Fig. 4
Fig. 4 Transmission phase difference (a), as well as the transmission and reflection amplitudes for the first graphene grating layer (b), and the third gold grating layer (c).
Fig. 5
Fig. 5 The ellipticity χ under different oblique incidence angle φ ((a) and (b)), and θ ((c) and (d)). The chemical potential μc is kept as 0.5 eV ((a) and (c)), or 0 eV ((b) and (d)) by different voltage biasing.
Fig. 6
Fig. 6 The graphene based dual-function switchable QWP with three output states.
Fig. 7
Fig. 7 Amplitude transmissions, phase difference and the corresponding ellipticity χ of dual-function switchable QWP at state 1 (a), state 2 (b), and state 3 (c). The polarization rotation angle of the co-polarization transmission wave is also represented in (c).

Tables (1)

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Table 1 Optimal geometrical parameters of the graphene based switchable QWP.

Equations (8)

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σ S = σ i n t r a ( ω , μ c , Γ , T ) + σ i n t e r ( ω , μ c , Γ , T ) ,
σ i n t r a ( ω , μ c , Γ , T ) = j e 2 k B T π 2 ( ω j 2 Γ ) ( μ c k B T + 2 ln ( e μ c / k B T + 1 ) ) ,
σ inter ( ω , μ c , Γ , T ) j e 2 4 π ln ( 2 | μ c | ( ω j 2 Γ ) 2 | μ c | + ( ω j 2 Γ ) ) ,
E F = μ c ν f π ε r ε 0 V g e t s ,
S 0 = | t ˜ y y | 2 + | t ˜ x y | 2 ,
S 1 = | t ˜ y y | 2 | t ˜ x y | 2 ,
S 2 = 2 | t ˜ y y | | t ˜ x y | cos φ d i f f ,
S 3 = 2 | t ˜ y y | | t ˜ x y | sin φ d i f f .

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