Abstract

We systematically investigated the tunable dynamic characteristics of a broadband surface plasmon polariton (SPP) wave on a silicon-graded grating structure in the range of 10–40 THz with the aid of single-layer graphene. The theoretical and numerical simulated results demonstrate that the SPPs at different frequencies within a broadband range can be trapped at different positions on the graphene surface, which can be used as a broadband spectrometer and optical switch. Meanwhile, the group velocity of the SPPs can be modulated to be several hundred times smaller than light velocity in vacuum. Based on the theoretical analyses, we have predicted the trapping positions and corresponding group velocities of the SPP waves with different frequencies. By appropriately tuning the gate voltages, the trapped SPP waves can be released to propagate along the surface of graphene or out of the graded grating zone. Thus, we have also investigated the switching characteristics of the slow light system, where the optical switching can be controlled as an “off” or “on” mode by actively adjusting the gate voltage. The slow light system offers advantages, including broadband operation, ultracompact footprint, and tunable ability simultaneously, which holds great promise for applications in optical switches.

© 2017 Chinese Laser Press

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  31. Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
    [Crossref]

2016 (2)

B. Guo, W. Shi, and J. Yao, “Slowing and trapping THz waves system based on plasmonic graded period grating,” J. Opt. 45, 50–57 (2016).
[Crossref]

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmonics based on periodically modulated graphene,” Sci. Rep. 6, 26796 (2016).
[Crossref]

2015 (3)

M. Yarahmadi, M. K. Moravvej-Farshi, and L. Yousefi, “Subwavelength graphene-based plasmonic THz switches and logic gates,” IEEE Trans. Terahertz Sci. Technol. 5, 725–731 (2015).
[Crossref]

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
[Crossref]

H. Nasari and M. S. Abrishamian, “Nonlinear manipulation of surface plasmon polaritons in graphene based bragg reflector,” J. Lightwave Technol. 33, 4071–4078 (2015).
[Crossref]

2014 (1)

2013 (4)

2012 (5)

Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (2012).
[Crossref]

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85, 125431 (2012).
[Crossref]

H. J. Xu, W. B. Lu, Y. Jiang, and Z. G. Dong, “Beam-scanning planar lens based on graphene,” Appl. Phys. Lett. 100, 051903 (2012).
[Crossref]

2011 (4)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2011).
[Crossref]

F. H. Koppens, D. E. Chang, and F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

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

Q. Gan and F. J. Bartoli, “Surface dispersion engineering of planar plasmonic chirped grating for complete visible rainbow trapping,” Appl. Phys. Lett. 98, 251103 (2011).
[Crossref]

2010 (1)

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole‐arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
[Crossref]

2009 (3)

Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

L. Chen, G. P. Wang, Q. Gan, and F. J. Bartoli, “Trapping of surface-plasmon polaritons in a graded Bragg structure: frequency-dependent spatially separated localization of the visible spectrum modes,” Phys. Rev. B 80, 161106 (2009).
[Crossref]

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

2008 (1)

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, “Terahertz photonic crystals based on barium titanate/polymer nanocomposites,” Adv. Mater. 20, 3649–3653 (2008).
[Crossref]

2007 (2)

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007).
[Crossref]

J. Li, J. He, and Z. Hong, “Terahertz wave switch based on silicon photonic crystals,” Appl. Opt. 46, 5034–5037 (2007).
[Crossref]

2006 (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref]

2005 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

2002 (1)

Q. M. Zhang, H. Li, M. Poh, F. Xia, Z. Y. Cheng, H. Xu, and C. Huang, “An all-organic composite actuator material with a high dielectric constant,” Nature 419, 284–287 (2002).
[Crossref]

AbdollahRamezani, S.

F. Zangeneh-Nejad, S. AbdollahRamezani, K. Arik, and A. Khavasi, “Beam focusing using two-dimensional graphene-based meta-reflect-array,” in 24th Iranian Conference on Electrical Engineering (ICEE) (IEEE, 2016), pp. 613–616.

Abrishamian, M. S.

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Arik, K.

F. Zangeneh-Nejad, S. AbdollahRamezani, K. Arik, and A. Khavasi, “Beam focusing using two-dimensional graphene-based meta-reflect-array,” in 24th Iranian Conference on Electrical Engineering (ICEE) (IEEE, 2016), pp. 613–616.

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Bartoli, F. J.

Q. Gan and F. J. Bartoli, “Surface dispersion engineering of planar plasmonic chirped grating for complete visible rainbow trapping,” Appl. Phys. Lett. 98, 251103 (2011).
[Crossref]

Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

L. Chen, G. P. Wang, Q. Gan, and F. J. Bartoli, “Trapping of surface-plasmon polaritons in a graded Bragg structure: frequency-dependent spatially separated localization of the visible spectrum modes,” Phys. Rev. B 80, 161106 (2009).
[Crossref]

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Brolo, A. G.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole‐arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
[Crossref]

Buljan, H.

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

Cai, W.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmonics based on periodically modulated graphene,” Sci. Rep. 6, 26796 (2016).
[Crossref]

Chang, D. E.

F. H. Koppens, D. E. Chang, and F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Chang, W.-H.

Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Chen, H. Y.

Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Chen, L.

Chen, L.-J.

Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Cheng, Z. Y.

Q. M. Zhang, H. Li, M. Poh, F. Xia, Z. Y. Cheng, H. Xu, and C. Huang, “An all-organic composite actuator material with a high dielectric constant,” Nature 419, 284–287 (2002).
[Crossref]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2011).
[Crossref]

Chu, H. S.

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85, 125431 (2012).
[Crossref]

Colombelli, R.

D. Gacemi, J. Mangeney, R. Colombelli, and A. Degiron, “Subwavelength metallic waveguides as a tool for extreme confinement of THz surface waves,” Sci. Rep. 3, 1369 (2013).
[Crossref]

Dabidian, N.

Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Degiron, A.

D. Gacemi, J. Mangeney, R. Colombelli, and A. Degiron, “Subwavelength metallic waveguides as a tool for extreme confinement of THz surface waves,” Sci. Rep. 3, 1369 (2013).
[Crossref]

Ding, Y. J.

Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Dong, Z. G.

H. J. Xu, W. B. Lu, Y. Jiang, and Z. G. Dong, “Beam-scanning planar lens based on graphene,” Appl. Phys. Lett. 100, 051903 (2012).
[Crossref]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

Engheta, N.

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

Fei, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

Fogler, M. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Gacemi, D.

D. Gacemi, J. Mangeney, R. Colombelli, and A. Degiron, “Subwavelength metallic waveguides as a tool for extreme confinement of THz surface waves,” Sci. Rep. 3, 1369 (2013).
[Crossref]

Gan, C. H.

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85, 125431 (2012).
[Crossref]

Gan, Q.

Q. Gan and F. J. Bartoli, “Surface dispersion engineering of planar plasmonic chirped grating for complete visible rainbow trapping,” Appl. Phys. Lett. 98, 251103 (2011).
[Crossref]

L. Chen, G. P. Wang, Q. Gan, and F. J. Bartoli, “Trapping of surface-plasmon polaritons in a graded Bragg structure: frequency-dependent spatially separated localization of the visible spectrum modes,” Phys. Rev. B 80, 161106 (2009).
[Crossref]

Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102, 056801 (2009).
[Crossref]

Garcia de Abajo, F. J.

F. H. Koppens, D. E. Chang, and F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

García de Abajo, F. J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2011).
[Crossref]

García-Vidal, F. J.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (2012).
[Crossref]

Gastro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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Geng, J.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmonics based on periodically modulated graphene,” Sci. Rep. 6, 26796 (2016).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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Gu, M.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
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B. Guo, W. Shi, and J. Yao, “Slowing and trapping THz waves system based on plasmonic graded period grating,” J. Opt. 45, 50–57 (2016).
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Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
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Hao, R.

He, J.

Hong, Z.

Hossain, M. M.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
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Q. M. Zhang, H. Li, M. Poh, F. Xia, Z. Y. Cheng, H. Xu, and C. Huang, “An all-organic composite actuator material with a high dielectric constant,” Nature 419, 284–287 (2002).
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M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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H. J. Xu, W. B. Lu, Y. Jiang, and Z. G. Dong, “Beam-scanning planar lens based on graphene,” Appl. Phys. Lett. 100, 051903 (2012).
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Katsnelson, M. I.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
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R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole‐arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
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F. Zangeneh-Nejad, S. AbdollahRamezani, K. Arik, and A. Khavasi, “Beam focusing using two-dimensional graphene-based meta-reflect-array,” in 24th Iranian Conference on Electrical Engineering (ICEE) (IEEE, 2016), pp. 613–616.

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Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
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J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2011).
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J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, “Terahertz photonic crystals based on barium titanate/polymer nanocomposites,” Adv. Mater. 20, 3649–3653 (2008).
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Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
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Li, E. P.

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Li, J.

Li, X.

Liu, X.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
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J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, “Terahertz photonic crystals based on barium titanate/polymer nanocomposites,” Adv. Mater. 20, 3649–3653 (2008).
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H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
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Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
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H. J. Xu, W. B. Lu, Y. Jiang, and Z. G. Dong, “Beam-scanning planar lens based on graphene,” Appl. Phys. Lett. 100, 051903 (2012).
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Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
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Moravvej-Farshi, M. K.

M. Yarahmadi, M. K. Moravvej-Farshi, and L. Yousefi, “Subwavelength graphene-based plasmonic THz switches and logic gates,” IEEE Trans. Terahertz Sci. Technol. 5, 725–731 (2015).
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Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

Nasari, H.

Novoselov, K. S.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438, 197–200 (2005).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
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Perruisseau-Carrier, J.

Poh, M.

Q. M. Zhang, H. Li, M. Poh, F. Xia, Z. Y. Cheng, H. Xu, and C. Huang, “An all-organic composite actuator material with a high dielectric constant,” Nature 419, 284–287 (2002).
[Crossref]

Qiu, X.

Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
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Reineck, P.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
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Ren, M.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmonics based on periodically modulated graphene,” Sci. Rep. 6, 26796 (2016).
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Rodin, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
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Sanders, C. E.

Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
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Shan, J.

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, “Terahertz photonic crystals based on barium titanate/polymer nanocomposites,” Adv. Mater. 20, 3649–3653 (2008).
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Shi, B.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmonics based on periodically modulated graphene,” Sci. Rep. 6, 26796 (2016).
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Shi, W.

B. Guo, W. Shi, and J. Yao, “Slowing and trapping THz waves system based on plasmonic graded period grating,” J. Opt. 45, 50–57 (2016).
[Crossref]

Shih, C.-K.

Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Shvets, G.

Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Sinton, D.

R. Gordon, A. G. Brolo, D. Sinton, and K. L. Kavanagh, “Resonant optical transmission through hole‐arrays in metal films: physics and applications,” Laser Photon. Rev. 4, 311–335 (2010).
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M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
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B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (2012).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Thongrattanasiri, S.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2011).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

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B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (2012).
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Wang, C.-Y.

Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
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Wang, G. P.

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J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, “Terahertz photonic crystals based on barium titanate/polymer nanocomposites,” Adv. Mater. 20, 3649–3653 (2008).
[Crossref]

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Y. J. Lu, J. Kim, H. Y. Chen, C. Wu, N. Dabidian, C. E. Sanders, C.-Y. Wang, M.-Y. Lu, B.-H. Li, X. Qiu, W.-H. Chang, L.-J. Chen, G. Shvets, C.-K. Shih, and S. Gwo, “Plasmonic nanolaser using epitaxially grown silver film,” Science 337, 450–453 (2012).
[Crossref]

Xia, C.

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, “Terahertz photonic crystals based on barium titanate/polymer nanocomposites,” Adv. Mater. 20, 3649–3653 (2008).
[Crossref]

Xia, F.

Q. M. Zhang, H. Li, M. Poh, F. Xia, Z. Y. Cheng, H. Xu, and C. Huang, “An all-organic composite actuator material with a high dielectric constant,” Nature 419, 284–287 (2002).
[Crossref]

Xiang, Y.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmonics based on periodically modulated graphene,” Sci. Rep. 6, 26796 (2016).
[Crossref]

Xu, H.

Q. M. Zhang, H. Li, M. Poh, F. Xia, Z. Y. Cheng, H. Xu, and C. Huang, “An all-organic composite actuator material with a high dielectric constant,” Nature 419, 284–287 (2002).
[Crossref]

Xu, H. J.

H. J. Xu, W. B. Lu, Y. Jiang, and Z. G. Dong, “Beam-scanning planar lens based on graphene,” Appl. Phys. Lett. 100, 051903 (2012).
[Crossref]

Xu, J.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmonics based on periodically modulated graphene,” Sci. Rep. 6, 26796 (2016).
[Crossref]

Yao, J.

B. Guo, W. Shi, and J. Yao, “Slowing and trapping THz waves system based on plasmonic graded period grating,” J. Opt. 45, 50–57 (2016).
[Crossref]

Yarahmadi, M.

M. Yarahmadi, M. K. Moravvej-Farshi, and L. Yousefi, “Subwavelength graphene-based plasmonic THz switches and logic gates,” IEEE Trans. Terahertz Sci. Technol. 5, 725–731 (2015).
[Crossref]

Yousefi, L.

M. Yarahmadi, M. K. Moravvej-Farshi, and L. Yousefi, “Subwavelength graphene-based plasmonic THz switches and logic gates,” IEEE Trans. Terahertz Sci. Technol. 5, 725–731 (2015).
[Crossref]

Yuan, X.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (2012).
[Crossref]

Zangeneh-Nejad, F.

F. Zangeneh-Nejad, S. AbdollahRamezani, K. Arik, and A. Khavasi, “Beam focusing using two-dimensional graphene-based meta-reflect-array,” in 24th Iranian Conference on Electrical Engineering (ICEE) (IEEE, 2016), pp. 613–616.

Zeng, C.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
[Crossref]

Zhan, Y.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmonics based on periodically modulated graphene,” Sci. Rep. 6, 26796 (2016).
[Crossref]

Zhang, L. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

Zhang, Q.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
[Crossref]

Zhang, Q. M.

Q. M. Zhang, H. Li, M. Poh, F. Xia, Z. Y. Cheng, H. Xu, and C. Huang, “An all-organic composite actuator material with a high dielectric constant,” Nature 419, 284–287 (2002).
[Crossref]

Zhang, T.

Zhang, X.

B. Shi, W. Cai, X. Zhang, Y. Xiang, Y. Zhan, J. Geng, M. Ren, and J. Xu, “Tunable band-stop filters for graphene plasmonics based on periodically modulated graphene,” Sci. Rep. 6, 26796 (2016).
[Crossref]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109, 073901 (2012).
[Crossref]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref]

Zhao, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Gastro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[Crossref]

ACS Nano (1)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2011).
[Crossref]

Adv. Mater. (1)

J. Lott, C. Xia, L. Kosnosky, C. Weder, and J. Shan, “Terahertz photonic crystals based on barium titanate/polymer nanocomposites,” Adv. Mater. 20, 3649–3653 (2008).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

H. J. Xu, W. B. Lu, Y. Jiang, and Z. G. Dong, “Beam-scanning planar lens based on graphene,” Appl. Phys. Lett. 100, 051903 (2012).
[Crossref]

Q. Gan and F. J. Bartoli, “Surface dispersion engineering of planar plasmonic chirped grating for complete visible rainbow trapping,” Appl. Phys. Lett. 98, 251103 (2011).
[Crossref]

IEEE Trans. Terahertz Sci. Technol. (1)

M. Yarahmadi, M. K. Moravvej-Farshi, and L. Yousefi, “Subwavelength graphene-based plasmonic THz switches and logic gates,” IEEE Trans. Terahertz Sci. Technol. 5, 725–731 (2015).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. (1)

B. Guo, W. Shi, and J. Yao, “Slowing and trapping THz waves system based on plasmonic graded period grating,” J. Opt. 45, 50–57 (2016).
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Figures (8)

Fig. 1.
Fig. 1. Schematic of a uniform graphene-based grating structure: a graphene monolayer on a uniform silicon grating structure with PMMA as the interlayer. p is the grating period, w 1 and w 2 denote the widths of nongroove parts and groove parts of the grating, w 2 is fixed at 30 nm in our work, and d 1 and d 2 are the depths of graphene sheet to nongroove and groove parts, respectively.
Fig. 2.
Fig. 2. Real parts of the effective refractive index (neff) of SPP modes supported by the graphene monolayer, (a) as the function of frequency and the PMMA spacer depth d = d 1 = d 2 with a constant gate voltage of V b = 60    V , and (b) as the function of frequency and the influence of the gate voltage V b with constant PMMA spacer ( d = d 1 = d 2 = 50    nm ).
Fig. 3.
Fig. 3. (a) Dispersion curves for different nongroove parts’ widths in the graphene-based uniform grating structure. (b) Dependence of slow-down factor S on the excitation frequencies for different nongroove widths. In the calculations, d 1 = 50    nm , d 2 = 250    nm , w 2 = 30    nm , V b = 60    V .
Fig. 4.
Fig. 4. Schematic illustration of the graphene-based graded grating structure. Here, d 1 = 50    nm , d 2 = 250    nm , w 2 = 30    nm , and V b = 60    V . The nongroove width increases linearly from 30 to 65 nm with a step of Δ = 1    nm ; in our simulations, the width of the whole structure along the x axis is 2760 nm.
Fig. 5.
Fig. 5. (a) Trapping position as a function of cutoff frequency. (b) Electric field distributions of | E y | 2 in the x y plane of the graphene graded grating structure in Fig. 4 for incident wavelengths of 9, 9.5, and 10 μm, respectively. (c) Corresponding normalized field intensities distribution 2 nm above the graphene surface. (d) The slow-down factor S as a function of trapping position for different operating wavelength.
Fig. 6.
Fig. 6. (a) Dispersion curves for w 1 = 30    nm and w 1 = 65    nm with different gate voltages ( V b = 60    V and V b = 80    V ). (b) Trapping position as a function of frequency for different gate voltages. (c) Electric field distributions of | E y | 2 in the x y plane of the structure in Fig. 4 for 10 μm of V b = 40 , 60, and 80 V, respective.
Fig. 7.
Fig. 7. Theoretical critical gate voltages needed to turn on the optical switching as a function of frequency at the position x = 2760    nm (output position).
Fig. 8.
Fig. 8. Electric field distributions of | E y | 2 in the x y plane of the modified structure for 10 μm at V b = 40 , 60, and 80 V, respectively. White lines mark the material boundaries of the modified structure. The nongroove width increases linearly from 30 to 37 nm with a step of Δ = 1    nm , and the groove width is fixed at 30 nm.

Equations (5)

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σ intra = i e 2 K B T π 2 ( ω + i τ 1 ) { μ c K B T + 2 ln [ exp ( μ c K B T ) + 1 ] } .
σ inter = i e 2 4 π 2 ln [ 2 | μ c | ( ω + i τ 1 ) 2 | μ c | + ( ω + i τ 1 ) ] ,
ϵ g = 1 + i σ g ω ϵ 0 Δ .
ϵ c k 0 n eff 2 ϵ c + ϵ p k 0 n eff 2 ϵ p + i σ g ω ϵ 0 = 0 ,
cos ( K p ) = ( n eff , 1 + n eff , 2 ) 4 n eff , 1 n eff , 2 cos ( φ 1 + φ 2 ) ( n eff , 1 n eff , 2 ) 4 n eff , 1 n eff , 2 cos ( φ 1 φ 2 ) ,

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