Abstract

Tunable propagation properties of graphene asymmetrical bowtie metamaterials (MMs) structures have been investigated in the terahertz regime, including the effects of graphene Fermi levels, structural parameters and operation frequencies. Because of its thin film thickness, the strong resonant curves of the proposed graphene MMs structures are dominated by the plasmonic mode instead of the Fabry-Perot mode for the metal structures. Compared with existing tunable graphene devices, the sharp Fano resonant curve manifests a large Q-factor of more than 40. In addition, as the width of graphene bowtie aperture increases, the resonant frequency dip shifts low frequency, and the resonant amplitude and figure of merit increase. The results are very helpful in order to understand the tunable mechanisms of graphene components and design high sensitivity functional devices, sensors, modulators, and antenna.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]

2018 (4)

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable THz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref] [PubMed]

G. X. Ni, A. S. McLeod, Z. Sun, L. Wang, L. Xiong, K. W. Post, S. S. Sunku, B. Y. Jiang, J. Hone, C. R. Dean, M. M. Fogler, and D. N. Basov, “Fundamental limits to graphene plasmonics,” Nature 557(7706), 530–533 (2018).
[Crossref] [PubMed]

W. J. Wan, H. Li, and J. C. Cao, “Homogeneous spectral broadening of pulsed terahertz quantum cascade lasers by radio frequency modulation,” Opt. Express 26(2), 980–989 (2018).
[Crossref] [PubMed]

2017 (7)

A. Khaleque, E. G. Mironov, J. H. Osório, Z. Li, C. M. B. Cordeiro, L. Liu, M. A. R. Franco, J. L. Liow, and H. T. Hattori, “Integration of bow-tie plasmonic nano-antennas on tapered fibers,” Opt. Express 25(8), 8986–8996 (2017).
[Crossref] [PubMed]

C. G. Wade, N. Sibalic, N. R. de Melo, J. M. Kondo, C. S. Adams, and K. J. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11(1), 40–43 (2017).
[Crossref]

A. M. Tareki, R. G. Lindquist, W. Kim, M. S. Heimbeck, and J. P. Guo, “Terahertz transparent electrode using tripod metal aperture array,” IEEE Trans. THz Sci. Technol. 7(1), 80–85 (2017).

J. B. Pendry, P. A. Huidobro, Y. Luo, and E. Galiffi, “Compacted dimensions and singular plasmonic surfaces,” Science 358(6365), 915–917 (2017).
[Crossref] [PubMed]

K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358(6361), eaan5196 (2017).
[Crossref] [PubMed]

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017).
[Crossref]

M. Morshed, A. Khaleque, and H. T. Hattori, “Multi-layered bowtie nano-antennas,” J. Appl. Phys. 121(13), 133106 (2017).
[Crossref]

2016 (5)

A. Bhattacharya, G. Georgiou, S. Sawallich, C. Matheisen, M. Nagel, and J. Gómez Rivas, “Large near-to-far field spectral shifts for terahertz resonances,” Phys. Rev. B 93(3), 035438 (2016).
[Crossref]

Y. Chen, J. Chu, and X. Xu, “Plasmonic multibowtie aperture antenna with Fano resonance for nanoscale spectral sorting,” ACS Photonics 3(9), 1689–1697 (2016).
[Crossref]

I. C. Huang, J. Holzgrafe, R. A. Jensen, J. T. Choy, M. G. Bawendi, and M. Loncar, “10 nm gap bowtie plasmonic apertures fabricated by modified lift-off process,” Appl. Phys. Lett. 109(13), 133105 (2016).
[Crossref]

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8(19), 10388–10397 (2016).
[Crossref] [PubMed]

X. Y. He, X. Zhong, F. T. Lin, and W. Z. Shi, “Investigation of graphene assisted tunable terahertz metamaterials absorber,” Opt. Mater. Express 6(2), 331–342 (2016).
[Crossref]

2015 (1)

X. Y. He, “Tunable terahertz graphene metamaterials,” Carbon 82(1), 229–237 (2015).
[Crossref]

2014 (3)

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

P. Fan, Z. Yu, S. Fan, and M. L. Brongersma, “Optical Fano resonance of an individual semiconductor nanostructure,” Nat. Mater. 13(5), 471–475 (2014).
[Crossref] [PubMed]

P. Fan, Z. Yu, S. Fan, M. L. Brongersma, M. Fleischhauer, T. Pfau, and H. Giessen, “Optical Fano resonance of an individual semiconductor nanostructure,” Nat. Mater. 13(5), 471–475 (2014).
[Crossref] [PubMed]

2013 (5)

Z. Y. Tan, T. Zhou, J. C. Cao, and H. C. Liu, “Terahertz imaging with quantum-cascade laser and quantum-well photodetector,” IEEE Photonics Technol. Lett. 25(14), 1344–1346 (2013).
[Crossref]

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. L. Zhang, “Plasmon-induced transparency in metamaterials: active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).
[Crossref]

M. C. Schaafsma, H. Starmans, A. Berrier, and J. G. Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys. 15(1), 015006 (2013).
[Crossref]

S. Koenig, D. L. Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

2012 (1)

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
[Crossref] [PubMed]

2011 (1)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

2010 (1)

A. R. Wright and C. Zhang, “Dynamic conductivity of graphene with electron-LO-phonon interaction,” Phys. Rev. B Condens. Matter Mater. Phys. 81(16), 165413 (2010).
[Crossref]

2009 (1)

A. R. Wright, J. C. Cao, and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime,” Phys. Rev. Lett. 103(20), 207401 (2009).
[Crossref] [PubMed]

2008 (2)

H. Guo, T. P. Meyrath, T. Zentgraf, N. Liu, L. Fu, H. Schweizer, and H. Giessen, “Optical resonances of bowtie slot antennas and their geometry and material dependence,” Opt. Express 16(11), 7756–7766 (2008).
[Crossref] [PubMed]

M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008).
[Crossref] [PubMed]

2007 (3)

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
[Crossref] [PubMed]

N. Yu, E. Cubukcu, L. Diehl, D. Bour, S. Corzine, J. Zhu, G. Höfler, K. B. Crozier, and F. Capasso, “Bowtie plasmonic quantum cascade laser antenna,” Opt. Express 15(20), 13272–13281 (2007).
[Crossref] [PubMed]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

2004 (1)

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[Crossref]

Adams, C. S.

C. G. Wade, N. Sibalic, N. R. de Melo, J. M. Kondo, C. S. Adams, and K. J. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11(1), 40–43 (2017).
[Crossref]

Ambacher, O.

S. Koenig, D. L. Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Antes, J.

S. Koenig, D. L. Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Avouris, P.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

Badolato, A.

M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008).
[Crossref] [PubMed]

Barbour, R.

M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008).
[Crossref] [PubMed]

Barnes, W. L.

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

Basov, D. N.

G. X. Ni, A. S. McLeod, Z. Sun, L. Wang, L. Xiong, K. W. Post, S. S. Sunku, B. Y. Jiang, J. Hone, C. R. Dean, M. M. Fogler, and D. N. Basov, “Fundamental limits to graphene plasmonics,” Nature 557(7706), 530–533 (2018).
[Crossref] [PubMed]

Bawendi, M. G.

I. C. Huang, J. Holzgrafe, R. A. Jensen, J. T. Choy, M. G. Bawendi, and M. Loncar, “10 nm gap bowtie plasmonic apertures fabricated by modified lift-off process,” Appl. Phys. Lett. 109(13), 133105 (2016).
[Crossref]

Berrier, A.

M. C. Schaafsma, H. Starmans, A. Berrier, and J. G. Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys. 15(1), 015006 (2013).
[Crossref]

Bhattacharya, A.

A. Bhattacharya, G. Georgiou, S. Sawallich, C. Matheisen, M. Nagel, and J. Gómez Rivas, “Large near-to-far field spectral shifts for terahertz resonances,” Phys. Rev. B 93(3), 035438 (2016).
[Crossref]

Biedermann, B.

M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008).
[Crossref] [PubMed]

Boes, F.

S. Koenig, D. L. Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Bour, D.

Boyd, R. W.

K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358(6361), eaan5196 (2017).
[Crossref] [PubMed]

Brongersma, M. L.

P. Fan, Z. Yu, S. Fan, M. L. Brongersma, M. Fleischhauer, T. Pfau, and H. Giessen, “Optical Fano resonance of an individual semiconductor nanostructure,” Nat. Mater. 13(5), 471–475 (2014).
[Crossref] [PubMed]

P. Fan, Z. Yu, S. Fan, and M. L. Brongersma, “Optical Fano resonance of an individual semiconductor nanostructure,” Nat. Mater. 13(5), 471–475 (2014).
[Crossref] [PubMed]

Cao, J. C.

W. J. Wan, H. Li, and J. C. Cao, “Homogeneous spectral broadening of pulsed terahertz quantum cascade lasers by radio frequency modulation,” Opt. Express 26(2), 980–989 (2018).
[Crossref] [PubMed]

Z. Y. Tan, T. Zhou, J. C. Cao, and H. C. Liu, “Terahertz imaging with quantum-cascade laser and quantum-well photodetector,” IEEE Photonics Technol. Lett. 25(14), 1344–1346 (2013).
[Crossref]

A. R. Wright, J. C. Cao, and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime,” Phys. Rev. Lett. 103(20), 207401 (2009).
[Crossref] [PubMed]

Cao, W.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. L. Zhang, “Plasmon-induced transparency in metamaterials: active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).
[Crossref]

Cao, Y.

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref] [PubMed]

Capasso, F.

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Chen, X.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Chen, Y.

Y. Chen, J. Chu, and X. Xu, “Plasmonic multibowtie aperture antenna with Fano resonance for nanoscale spectral sorting,” ACS Photonics 3(9), 1689–1697 (2016).
[Crossref]

Choi, C.

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Rao, Y.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable THz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Remi, S.

M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008).
[Crossref] [PubMed]

Rivas, J. G.

M. C. Schaafsma, H. Starmans, A. Berrier, and J. G. Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys. 15(1), 015006 (2013).
[Crossref]

Rybin, M. V.

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017).
[Crossref]

Sawallich, S.

A. Bhattacharya, G. Georgiou, S. Sawallich, C. Matheisen, M. Nagel, and J. Gómez Rivas, “Large near-to-far field spectral shifts for terahertz resonances,” Phys. Rev. B 93(3), 035438 (2016).
[Crossref]

Schaafsma, M. C.

M. C. Schaafsma, H. Starmans, A. Berrier, and J. G. Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys. 15(1), 015006 (2013).
[Crossref]

Schmogrow, R.

S. Koenig, D. L. Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Schweizer, H.

Seidl, S.

M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008).
[Crossref] [PubMed]

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Shi, W.

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8(19), 10388–10397 (2016).
[Crossref] [PubMed]

Shi, W. Z.

Sibalic, N.

C. G. Wade, N. Sibalic, N. R. de Melo, J. M. Kondo, C. S. Adams, and K. J. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11(1), 40–43 (2017).
[Crossref]

Singh, R.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. L. Zhang, “Plasmon-induced transparency in metamaterials: active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).
[Crossref]

Starmans, H.

M. C. Schaafsma, H. Starmans, A. Berrier, and J. G. Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys. 15(1), 015006 (2013).
[Crossref]

Sun, Z.

G. X. Ni, A. S. McLeod, Z. Sun, L. Wang, L. Xiong, K. W. Post, S. S. Sunku, B. Y. Jiang, J. Hone, C. R. Dean, M. M. Fogler, and D. N. Basov, “Fundamental limits to graphene plasmonics,” Nature 557(7706), 530–533 (2018).
[Crossref] [PubMed]

Sunku, S. S.

G. X. Ni, A. S. McLeod, Z. Sun, L. Wang, L. Xiong, K. W. Post, S. S. Sunku, B. Y. Jiang, J. Hone, C. R. Dean, M. M. Fogler, and D. N. Basov, “Fundamental limits to graphene plasmonics,” Nature 557(7706), 530–533 (2018).
[Crossref] [PubMed]

Tan, Z. Y.

Z. Y. Tan, T. Zhou, J. C. Cao, and H. C. Liu, “Terahertz imaging with quantum-cascade laser and quantum-well photodetector,” IEEE Photonics Technol. Lett. 25(14), 1344–1346 (2013).
[Crossref]

Taniguchi, T.

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref] [PubMed]

Tareki, A. M.

A. M. Tareki, R. G. Lindquist, W. Kim, M. S. Heimbeck, and J. P. Guo, “Terahertz transparent electrode using tripod metal aperture array,” IEEE Trans. THz Sci. Technol. 7(1), 80–85 (2017).

Tessmann, A.

S. Koenig, D. L. Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Tonouchi, M.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. L. Zhang, “Plasmon-induced transparency in metamaterials: active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).
[Crossref]

Tsakmakidis, K. L.

K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358(6361), eaan5196 (2017).
[Crossref] [PubMed]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

Wade, C. G.

C. G. Wade, N. Sibalic, N. R. de Melo, J. M. Kondo, C. S. Adams, and K. J. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11(1), 40–43 (2017).
[Crossref]

Wan, W. J.

Wang, L.

G. X. Ni, A. S. McLeod, Z. Sun, L. Wang, L. Xiong, K. W. Post, S. S. Sunku, B. Y. Jiang, J. Hone, C. R. Dean, M. M. Fogler, and D. N. Basov, “Fundamental limits to graphene plasmonics,” Nature 557(7706), 530–533 (2018).
[Crossref] [PubMed]

Warburton, R. J.

M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008).
[Crossref] [PubMed]

Watanabe, K.

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref] [PubMed]

Weatherill, K. J.

C. G. Wade, N. Sibalic, N. R. de Melo, J. M. Kondo, C. S. Adams, and K. J. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11(1), 40–43 (2017).
[Crossref]

Wong, C. W.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable THz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Wright, A. R.

A. R. Wright and C. Zhang, “Dynamic conductivity of graphene with electron-LO-phonon interaction,” Phys. Rev. B Condens. Matter Mater. Phys. 81(16), 165413 (2010).
[Crossref]

A. R. Wright, J. C. Cao, and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime,” Phys. Rev. Lett. 103(20), 207401 (2009).
[Crossref] [PubMed]

Wu, B. I.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

Wu, Y.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable THz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

Xia, F. N.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

Xie, Z.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable THz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Xiong, L.

G. X. Ni, A. S. McLeod, Z. Sun, L. Wang, L. Xiong, K. W. Post, S. S. Sunku, B. Y. Jiang, J. Hone, C. R. Dean, M. M. Fogler, and D. N. Basov, “Fundamental limits to graphene plasmonics,” Nature 557(7706), 530–533 (2018).
[Crossref] [PubMed]

Xu, X.

Y. Chen, J. Chu, and X. Xu, “Plasmonic multibowtie aperture antenna with Fano resonance for nanoscale spectral sorting,” ACS Photonics 3(9), 1689–1697 (2016).
[Crossref]

Yan, H.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

Yao, B.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable THz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Yu, M.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable THz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Yu, N.

Yu, Z.

P. Fan, Z. Yu, S. Fan, M. L. Brongersma, M. Fleischhauer, T. Pfau, and H. Giessen, “Optical Fano resonance of an individual semiconductor nanostructure,” Nat. Mater. 13(5), 471–475 (2014).
[Crossref] [PubMed]

P. Fan, Z. Yu, S. Fan, and M. L. Brongersma, “Optical Fano resonance of an individual semiconductor nanostructure,” Nat. Mater. 13(5), 471–475 (2014).
[Crossref] [PubMed]

Zentgraf, T.

Zhang, C.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. L. Zhang, “Plasmon-induced transparency in metamaterials: active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).
[Crossref]

A. R. Wright and C. Zhang, “Dynamic conductivity of graphene with electron-LO-phonon interaction,” Phys. Rev. B Condens. Matter Mater. Phys. 81(16), 165413 (2010).
[Crossref]

A. R. Wright, J. C. Cao, and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime,” Phys. Rev. Lett. 103(20), 207401 (2009).
[Crossref] [PubMed]

Zhang, W.

M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008).
[Crossref] [PubMed]

Zhang, W. L.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. L. Zhang, “Plasmon-induced transparency in metamaterials: active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).
[Crossref]

Zhang, X.

K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358(6361), eaan5196 (2017).
[Crossref] [PubMed]

Zheludev, N. I.

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
[Crossref] [PubMed]

Zhong, X.

Zhou, T.

Z. Y. Tan, T. Zhou, J. C. Cao, and H. C. Liu, “Terahertz imaging with quantum-cascade laser and quantum-well photodetector,” IEEE Photonics Technol. Lett. 25(14), 1344–1346 (2013).
[Crossref]

Zhu, J.

Zhu, W.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

Zwick, T.

S. Koenig, D. L. Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

ACS Photonics (1)

Y. Chen, J. Chu, and X. Xu, “Plasmonic multibowtie aperture antenna with Fano resonance for nanoscale spectral sorting,” ACS Photonics 3(9), 1689–1697 (2016).
[Crossref]

Appl. Phys. Lett. (2)

I. C. Huang, J. Holzgrafe, R. A. Jensen, J. T. Choy, M. G. Bawendi, and M. Loncar, “10 nm gap bowtie plasmonic apertures fabricated by modified lift-off process,” Appl. Phys. Lett. 109(13), 133105 (2016).
[Crossref]

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. L. Zhang, “Plasmon-induced transparency in metamaterials: active near field coupling between bright superconducting and dark metallic mode resonators,” Appl. Phys. Lett. 103(10), 101106 (2013).
[Crossref]

Carbon (1)

X. Y. He, “Tunable terahertz graphene metamaterials,” Carbon 82(1), 229–237 (2015).
[Crossref]

IEEE Photonics Technol. Lett. (1)

Z. Y. Tan, T. Zhou, J. C. Cao, and H. C. Liu, “Terahertz imaging with quantum-cascade laser and quantum-well photodetector,” IEEE Photonics Technol. Lett. 25(14), 1344–1346 (2013).
[Crossref]

IEEE Trans. THz Sci. Technol. (1)

A. M. Tareki, R. G. Lindquist, W. Kim, M. S. Heimbeck, and J. P. Guo, “Terahertz transparent electrode using tripod metal aperture array,” IEEE Trans. THz Sci. Technol. 7(1), 80–85 (2017).

J. Appl. Phys. (1)

M. Morshed, A. Khaleque, and H. T. Hattori, “Multi-layered bowtie nano-antennas,” J. Appl. Phys. 121(13), 133106 (2017).
[Crossref]

J. Phys. Condens. Matter (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Magneto-optical conductivity in graphene,” J. Phys. Condens. Matter 19(2), 026222 (2007).
[Crossref]

Nanoscale (1)

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8(19), 10388–10397 (2016).
[Crossref] [PubMed]

Nat. Mater. (3)

P. Fan, Z. Yu, S. Fan, M. L. Brongersma, M. Fleischhauer, T. Pfau, and H. Giessen, “Optical Fano resonance of an individual semiconductor nanostructure,” Nat. Mater. 13(5), 471–475 (2014).
[Crossref] [PubMed]

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
[Crossref] [PubMed]

P. Fan, Z. Yu, S. Fan, and M. L. Brongersma, “Optical Fano resonance of an individual semiconductor nanostructure,” Nat. Mater. 13(5), 471–475 (2014).
[Crossref] [PubMed]

Nat. Photonics (6)

S. Koenig, D. L. Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

N. Meinzer, W. L. Barnes, and I. R. Hooper, “Plasmonic meta-atoms and metasurfaces,” Nat. Photonics 8(12), 889–898 (2014).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. N. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7(5), 394–399 (2013).
[Crossref]

C. G. Wade, N. Sibalic, N. R. de Melo, J. M. Kondo, C. S. Adams, and K. J. Weatherill, “Real-time near-field terahertz imaging with atomic optical fluorescence,” Nat. Photonics 11(1), 40–43 (2017).
[Crossref]

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017).
[Crossref]

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable THz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Nature (3)

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref] [PubMed]

G. X. Ni, A. S. McLeod, Z. Sun, L. Wang, L. Xiong, K. W. Post, S. S. Sunku, B. Y. Jiang, J. Hone, C. R. Dean, M. M. Fogler, and D. N. Basov, “Fundamental limits to graphene plasmonics,” Nature 557(7706), 530–533 (2018).
[Crossref] [PubMed]

M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008).
[Crossref] [PubMed]

New J. Phys. (1)

M. C. Schaafsma, H. Starmans, A. Berrier, and J. G. Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys. 15(1), 015006 (2013).
[Crossref]

Opt. Express (4)

Opt. Mater. Express (1)

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
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Phys. Rev. B (1)

A. Bhattacharya, G. Georgiou, S. Sawallich, C. Matheisen, M. Nagel, and J. Gómez Rivas, “Large near-to-far field spectral shifts for terahertz resonances,” Phys. Rev. B 93(3), 035438 (2016).
[Crossref]

Phys. Rev. B Condens. Matter Mater. Phys. (1)

A. R. Wright and C. Zhang, “Dynamic conductivity of graphene with electron-LO-phonon interaction,” Phys. Rev. B Condens. Matter Mater. Phys. 81(16), 165413 (2010).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
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Phys. Rev. Lett. (2)

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
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A. R. Wright, J. C. Cao, and C. Zhang, “Enhanced optical conductivity of bilayer graphene nanoribbons in the terahertz regime,” Phys. Rev. Lett. 103(20), 207401 (2009).
[Crossref] [PubMed]

Science (3)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358(6361), eaan5196 (2017).
[Crossref] [PubMed]

J. B. Pendry, P. A. Huidobro, Y. Luo, and E. Galiffi, “Compacted dimensions and singular plasmonic surfaces,” Science 358(6365), 915–917 (2017).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 The side view of the graphene MMs structure, the bowtie unit cell structure deposits on the SiO2/Si layers, the thickness of dielectric layer is 10 nm, the doped Si layer is used to apply the gate voltage. The substrate is made from polymer layer. Figure 1(b) shows the top view of geometry of graphene MMs structures.
Fig. 2
Fig. 2 2(a)-2(c) show the transmission, reflection and absorption curves of complementary graphene bowtie MMs structures at different lengths of upper triangular ribbons. The top (TR) and bottom (BR) widths of graphene patterns are 60 μm and 2 μm, respectively. The length of bottom triangular ribbon (LB) is 30 μm, and the lengths of upper triangular ribbons (LT) are 35, 40, 45, 50, 55, and 60 μm, respectively. The gap distance is 2 μm. Figure 2(d) shows Q-factor and FOM of transmission curves versus upper graphene ribbon length (LT).
Fig. 3
Fig. 3 3(a)-3(c) show the transmission curves of complementary graphene bowtie MMs structures at different width of upper triangular ribbons. The width of bottom graphene triangular ribbons is 2 μm. The gap distance is 2 μm. The bottom and top lengths of triangular ribbons are 30 and 45 μm. The length of top triangular graphene ribbons are 20, 25, 30, 35, 40, 45, 50, 55, and 60 μm, respectively. The period lengths along x and y directions are both 140 μm. Figure 3(d) shows Q-factor and FOM of transmission curves versus upper graphene ribbon width.
Fig. 4
Fig. 4 4(a)-4(c) show the transmission curves of the graphene complementary bowtie MMs structures at different Fermi levels. Figure 4(d) The Q-factor and FOM of transmission curves varies with graphene Fermi level. The top and bottom widths are 60 μm and 2 μm. The bottom and top lengths of are 30 μm and 45 μm, respectively. The period lengths along x and y directions are both 140 μm.
Fig. 5
Fig. 5 5(a)-5(b) The group indices and time delays of the complementary bowtie graphene ribbons structures. The structural parameters are the same to those in Fig. 4.
Fig. 6
Fig. 6 6(a)-6(c) show the transmission, reflection, and absorption curves of the graphene ribbon unit cell structure at different period number. 6(d) The Q-factor and FOM of the transmission curves versus different number. The top and bottom widths are 60 μm and 2 μm, respectively. The bottom and top lengths of are 30 μm and 45 μm, respectively. The period lengths along x and y directions are both 140 μm.
Fig. 7
Fig. 7 The surface current density and magnetic fields of Hz for the graphene bowtie structures at resonant frequencies. The according resonant frequencies are 1.202, 1.360, and 1.463 THz. The polarization direction of the incident light is along y direction. The Fermi level of graphene is 1.0 eV.
Fig. 8
Fig. 8 Fig. 8 show the surface current density and magnetic fields of Hz for the graphene bowtie structures at different Fermi levels, respectively. The Fermi levels of graphene are 0.3 eV (Fig. 8(a), 8(b)), 0.6 eV (Fig. 8(c), 8(d)), 1.0 eV (Figs. 8(e), 8(f)), and the according resonant frequencies are 1.281, 1.334, and 1.360 THz, respectively. The polarization direction of the incident light is along y direction.

Equations (10)

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σ( Ω )= e 2 N f 4 π 2 Ω + dω [ [ f 0 ( ω ) f 0 ( ω' ) ]×{ 2B Δ 2 ( ω+iΓ ) 2 [ Ξ 1 ( B ) Ξ 2 ( B ) ]+ [ Ξ 1 ( B ) Ξ 2 ( +B ) Ξ 2 ( B ) Ξ 2 ( +B ) ] ×ψ( Δ 2 ( ω+iΓ ) 2 2B )+( ωω',ΓΓ' ) } ]
Ξ 1 ( ±B )= ( ω+iΓ )( ω'+iΓ' ) Δ 2 [ ( ωω' )+i( ΓΓ' ) ][ ( ω+ω' )+i( Γ+Γ' ) ]±2B
Ξ 2 ( ±B )= ( ω+iΓ )( ω'iΓ' ) Δ 2 [ ( ωω' )+i( Γ+Γ' ) ][ ( ω+ω' )+i( ΓΓ' ) ]±2B
σ( ω )= 2ω π 0 σ( ω' ) ω ' 2 ω 2 dω'
ε g =1+j σ g ω ε 0 δ
Q= f res FWHM
n eff = 1 k 0 d cos 1 [ ( 1 S 11 2 + S 21 2 )/( 2 S 21 ) ]
z= ( 1+ S 11 ) 2 S 21 2 ( 1 S 11 ) 2 S 21 2
n g ( ω )= n eff ( ω )+ω n eff ( ω ) ω
τ g = ϕ ω