Abstract

Properties of one-dimensional graphene photonic crystals with dual-layer defects are studied. Results show that two defect modes appear within the gaps, and the defect modes shift to the lower frequencies with the chemical potential increasing, the physical mechanism are also given based on the relative dielectric constant of the graphene. It is also found that the frequency, magnitude, and numbers of the defect modes can vary with the symmetrical changes of the dual-defect layers. For oblique incidence, the defect modes of the TE polarization follow a similar trend with the TM polarization, and all the defect modes shift to the higher frequencies and disappear while new defect modes appear at the larger incident angles. These properties of graphene photonic crystals with dual-layer defects have potential applications in tunable terahertz narrow multiband filters.

© 2017 Optical Society of America

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2016 (4)

Y. Liu, X. Xie, L. Xie, Z. Yang, and H. Yang, “Dual-band absorption characteristics of one-dimensional photonic crystal with graphene-based defect,” Optik (Stuttg.) 127(9), 3945–3948 (2016).
[Crossref]

J. Fu, W. Chen, and B. Lv, “Tunable defect mode realized by graphene-based photonic crystal,” Phys. Lett. A 380(20), 1793–1798 (2016).
[Crossref]

A. A. Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6(1), 25442 (2016).
[Crossref] [PubMed]

A. Marini and F. J. García de Abajo, “Graphene-Based Active Random Metamaterials for Cavity-Free Lasing,” Phys. Rev. Lett. 116(21), 217401 (2016).
[Crossref] [PubMed]

2015 (3)

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

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24(11), 118103 (2015).
[Crossref]

Y. Zhang, Z. Wu, Y. Cao, and H. Zhang, “Optical properties of one-dimensional Fibonacci quasi-periodic graphene photonic crystal,” Opt. Commun. 338, 168–173 (2015).
[Crossref]

2014 (2)

A. W. Lima and A. S. B. Sombra, “Graphene-photonic crystal switch,” Opt. Commun. 321, 150–156 (2014).
[Crossref]

L. Qi, L. Shang, and S. Zhang, “One-dimensional plasma photonic crystals with sinusoidal densities,” Phys. Plasmas 21(1), 013501 (2014).
[Crossref]

2013 (8)

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “Tunable metamaterials based on split ring resonators and doped graphene,” Appl. Phys. Lett. 103(1), 011102 (2013).
[Crossref]

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]

B. Zhu, G. Ren, S. Zheng, Z. Lin, and S. Jian, “Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices,” Opt. Express 21(14), 17089–17096 (2013).
[Crossref] [PubMed]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114(3), 033102 (2013).
[Crossref]

M. A. Vincenti, D. de Ceglia, M. Grande, A. D’Orazio, and M. Scalora, “Nonlinear control of absorption in one-dimensional photonic crystal with graphene-based defect,” Opt. Lett. 38(18), 3550–3553 (2013).
[Crossref] [PubMed]

Z. Arefinia and A. Asgari, “Novel attributes in the scaling and performance considerations of the one-dimensional graphene-based photonic crystals for terahertz applications,” Phys. E 54, 34–39 (2013).
[Crossref]

A. Madani and S. R. Entezar, “Optical properties of one-dimensional photonic crystals containing graphene sheets,” Phys. B 431(15), 1–5 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene-dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

2012 (3)

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B 85(24), 245407 (2012).
[Crossref]

L. Huang, D. R. Chowdhury, S. Ramani, and T. Matthew, “Reiten, S. Luo, A. J. Taylor, and H. Chen, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Opt. Express 37(2), 154–156 (2012).

2011 (1)

L. Qi and X. Zhang, “Photonic band gaps of one-dimensional ternary plasma photonic crystals with periodic and periodic-varying structures,” J. Electromagn. Waves Appl. 25(4), 539–552 (2011).
[Crossref]

2010 (1)

L. Qi, Z. Yang, F. Lan, X. Gao, and Z. Shi, “Properties of Obliquely Incident Electromagnetic Wave in 1D Magnetized Plasma Photonic crystals,” Phys. Plasmas 17(4), 042501 (2010).
[Crossref]

2009 (5)

B. Guo, “Transfer matrix for obliquely incident electromagnetic waves propagating in one dimension plasma photonic crystals,” Plasma Sci. Technol. 11(1), 18–22 (2009).
[Crossref]

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai, “Narrow graphene nanoribbons from carbon nanotubes,” Nature 458(7240), 877–880 (2009).
[Crossref] [PubMed]

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

2008 (1)

D. Li and R. B. Kaner, “Materials science. Graphene-based materials,” Science 320(5880), 1170–1171 (2008).
[Crossref] [PubMed]

2007 (1)

J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, “The structure of suspended graphene sheets,” Nature 446(7131), 60–63 (2007).
[Crossref] [PubMed]

2006 (1)

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

2002 (1)

L. Hu and S. T. Chui, “Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials,” Phys. Rev. B 66(8), 085108 (2002).
[Crossref]

1993 (1)

Ahn, J.-H.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Andryieuski, A.

Arefinia, Z.

Z. Arefinia and A. Asgari, “Novel attributes in the scaling and performance considerations of the one-dimensional graphene-based photonic crystals for terahertz applications,” Phys. E 54, 34–39 (2013).
[Crossref]

Asgari, A.

Z. Arefinia and A. Asgari, “Novel attributes in the scaling and performance considerations of the one-dimensional graphene-based photonic crystals for terahertz applications,” Phys. E 54, 34–39 (2013).
[Crossref]

Bao, Q.

Booth, T. J.

J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, “The structure of suspended graphene sheets,” Nature 446(7131), 60–63 (2007).
[Crossref] [PubMed]

Brommer, K. D.

Bulovic, V.

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Cao, Y.

Y. Zhang, Z. Wu, Y. Cao, and H. Zhang, “Optical properties of one-dimensional Fibonacci quasi-periodic graphene photonic crystal,” Opt. Commun. 338, 168–173 (2015).
[Crossref]

Chen, W.

J. Fu, W. Chen, and B. Lv, “Tunable defect mode realized by graphene-based photonic crystal,” Phys. Lett. A 380(20), 1793–1798 (2016).
[Crossref]

Choi, J.-Y.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Chowdhury, D. R.

L. Huang, D. R. Chowdhury, S. Ramani, and T. Matthew, “Reiten, S. Luo, A. J. Taylor, and H. Chen, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Opt. Express 37(2), 154–156 (2012).

Chui, S. T.

L. Hu and S. T. Chui, “Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials,” Phys. Rev. B 66(8), 085108 (2002).
[Crossref]

D’Orazio, A.

Dai, H.

L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai, “Narrow graphene nanoribbons from carbon nanotubes,” Nature 458(7240), 877–880 (2009).
[Crossref] [PubMed]

de Ceglia, D.

Diankov, G.

L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai, “Narrow graphene nanoribbons from carbon nanotubes,” Nature 458(7240), 877–880 (2009).
[Crossref] [PubMed]

Dikin, D. A.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Dimiev, A.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Ding, G.

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24(11), 118103 (2015).
[Crossref]

Dommett, G. H.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Dresselhaus, M. S.

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Entezar, S. R.

A. Madani and S. R. Entezar, “Optical properties of one-dimensional photonic crystals containing graphene sheets,” Phys. B 431(15), 1–5 (2013).
[Crossref]

Fu, J.

J. Fu, W. Chen, and B. Lv, “Tunable defect mode realized by graphene-based photonic crystal,” Phys. Lett. A 380(20), 1793–1798 (2016).
[Crossref]

Gajic, R.

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “Tunable metamaterials based on split ring resonators and doped graphene,” Appl. Phys. Lett. 103(1), 011102 (2013).
[Crossref]

Gao, X.

L. Qi, Z. Yang, F. Lan, X. Gao, and Z. Shi, “Properties of Obliquely Incident Electromagnetic Wave in 1D Magnetized Plasma Photonic crystals,” Phys. Plasmas 17(4), 042501 (2010).
[Crossref]

García de Abajo, F. J.

A. Marini and F. J. García de Abajo, “Graphene-Based Active Random Metamaterials for Cavity-Free Lasing,” Phys. Rev. Lett. 116(21), 217401 (2016).
[Crossref] [PubMed]

Geim, A. K.

J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, “The structure of suspended graphene sheets,” Nature 446(7131), 60–63 (2007).
[Crossref] [PubMed]

Godbout, N.

Grande, M.

Guo, B.

B. Guo, “Transfer matrix for obliquely incident electromagnetic waves propagating in one dimension plasma photonic crystals,” Plasma Sci. Technol. 11(1), 18–22 (2009).
[Crossref]

Hajian, H.

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene-dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114(3), 033102 (2013).
[Crossref]

Hanson, G. W.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B 85(24), 245407 (2012).
[Crossref]

He, X.

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

Higginbotham, A. L.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Ho, J.

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Hong, B. H.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Hu, L.

L. Hu and S. T. Chui, “Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials,” Phys. Rev. B 66(8), 085108 (2002).
[Crossref]

Huang, L.

L. Huang, D. R. Chowdhury, S. Ramani, and T. Matthew, “Reiten, S. Luo, A. J. Taylor, and H. Chen, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Opt. Express 37(2), 154–156 (2012).

Isic, G.

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “Tunable metamaterials based on split ring resonators and doped graphene,” Appl. Phys. Lett. 103(1), 011102 (2013).
[Crossref]

Jahangir, I.

A. A. Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6(1), 25442 (2016).
[Crossref] [PubMed]

Jakovljevic, M. M.

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “Tunable metamaterials based on split ring resonators and doped graphene,” Appl. Phys. Lett. 103(1), 011102 (2013).
[Crossref]

Jang, H.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Jia, X.

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Jian, S.

Jiao, L.

L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai, “Narrow graphene nanoribbons from carbon nanotubes,” Nature 458(7240), 877–880 (2009).
[Crossref] [PubMed]

Joannopoulos, J. D.

Kaipa, C. S. R.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B 85(24), 245407 (2012).
[Crossref]

Kalafi, M.

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene-dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114(3), 033102 (2013).
[Crossref]

Kaner, R. B.

D. Li and R. B. Kaner, “Materials science. Graphene-based materials,” Science 320(5880), 1170–1171 (2008).
[Crossref] [PubMed]

Katsnelson, M. I.

J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, “The structure of suspended graphene sheets,” Nature 446(7131), 60–63 (2007).
[Crossref] [PubMed]

Kim, J. M.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Kim, K. S.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Kim, P.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Kockaert, P.

Kohlhaas, K. M.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Kong, J.

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Kong, X.

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24(11), 118103 (2015).
[Crossref]

Kosynkin, D. V.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Lan, F.

L. Qi, Z. Yang, F. Lan, X. Gao, and Z. Shi, “Properties of Obliquely Incident Electromagnetic Wave in 1D Magnetized Plasma Photonic crystals,” Phys. Plasmas 17(4), 042501 (2010).
[Crossref]

Lavrinenko, A. V.

Lee, S. Y.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Li, B.

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24(11), 118103 (2015).
[Crossref]

Li, D.

D. Li and R. B. Kaner, “Materials science. Graphene-based materials,” Science 320(5880), 1170–1171 (2008).
[Crossref] [PubMed]

Li, H.

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24(11), 118103 (2015).
[Crossref]

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24(11), 118103 (2015).
[Crossref]

Lima, A. W.

A. W. Lima and A. S. B. Sombra, “Graphene-photonic crystal switch,” Opt. Commun. 321, 150–156 (2014).
[Crossref]

Lin, Z.

Liu, S.

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24(11), 118103 (2015).
[Crossref]

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24(11), 118103 (2015).
[Crossref]

Liu, Y.

Y. Liu, X. Xie, L. Xie, Z. Yang, and H. Yang, “Dual-band absorption characteristics of one-dimensional photonic crystal with graphene-based defect,” Optik (Stuttg.) 127(9), 3945–3948 (2016).
[Crossref]

Lomeda, J. R.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Lv, B.

J. Fu, W. Chen, and B. Lv, “Tunable defect mode realized by graphene-based photonic crystal,” Phys. Lett. A 380(20), 1793–1798 (2016).
[Crossref]

Madani, A.

A. Madani and S. R. Entezar, “Optical properties of one-dimensional photonic crystals containing graphene sheets,” Phys. B 431(15), 1–5 (2013).
[Crossref]

Mahdy, M. R. C.

A. A. Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6(1), 25442 (2016).
[Crossref] [PubMed]

Marini, A.

A. Marini and F. J. García de Abajo, “Graphene-Based Active Random Metamaterials for Cavity-Free Lasing,” Phys. Rev. Lett. 116(21), 217401 (2016).
[Crossref] [PubMed]

Massar, S.

Matthew, T.

L. Huang, D. R. Chowdhury, S. Ramani, and T. Matthew, “Reiten, S. Luo, A. J. Taylor, and H. Chen, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Opt. Express 37(2), 154–156 (2012).

Meade, D.

Medina, F.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B 85(24), 245407 (2012).
[Crossref]

Mesa, F.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B 85(24), 245407 (2012).
[Crossref]

Meyer, J. C.

J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, “The structure of suspended graphene sheets,” Nature 446(7131), 60–63 (2007).
[Crossref] [PubMed]

Nezich, D.

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Nguyen, S. T.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Novoselov, K. S.

J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, “The structure of suspended graphene sheets,” Nature 446(7131), 60–63 (2007).
[Crossref] [PubMed]

Padooru, Y. R.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B 85(24), 245407 (2012).
[Crossref]

Piner, R. D.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Ping, L. K.

Price, B. K.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Qi, L.

L. Qi, L. Shang, and S. Zhang, “One-dimensional plasma photonic crystals with sinusoidal densities,” Phys. Plasmas 21(1), 013501 (2014).
[Crossref]

L. Qi and X. Zhang, “Photonic band gaps of one-dimensional ternary plasma photonic crystals with periodic and periodic-varying structures,” J. Electromagn. Waves Appl. 25(4), 539–552 (2011).
[Crossref]

L. Qi, Z. Yang, F. Lan, X. Gao, and Z. Shi, “Properties of Obliquely Incident Electromagnetic Wave in 1D Magnetized Plasma Photonic crystals,” Phys. Plasmas 17(4), 042501 (2010).
[Crossref]

Rahman, M. M.

A. A. Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6(1), 25442 (2016).
[Crossref] [PubMed]

Rahman, M. S.

A. A. Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6(1), 25442 (2016).
[Crossref] [PubMed]

Ramani, S.

L. Huang, D. R. Chowdhury, S. Ramani, and T. Matthew, “Reiten, S. Luo, A. J. Taylor, and H. Chen, “Experimental demonstration of terahertz metamaterial absorbers with a broad and flat high absorption band,” Opt. Express 37(2), 154–156 (2012).

Rappe, A. M.

Reina, A.

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Ren, G.

Roth, S.

J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, “The structure of suspended graphene sheets,” Nature 446(7131), 60–63 (2007).
[Crossref] [PubMed]

Ruoff, R. S.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Sayem, A. A.

A. A. Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6(1), 25442 (2016).
[Crossref] [PubMed]

Scalora, M.

Shang, L.

L. Qi, L. Shang, and S. Zhang, “One-dimensional plasma photonic crystals with sinusoidal densities,” Phys. Plasmas 21(1), 013501 (2014).
[Crossref]

Shi, Z.

L. Qi, Z. Yang, F. Lan, X. Gao, and Z. Shi, “Properties of Obliquely Incident Electromagnetic Wave in 1D Magnetized Plasma Photonic crystals,” Phys. Plasmas 17(4), 042501 (2010).
[Crossref]

Sinitskii, A.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Soltani-Vala, A.

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene-dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114(3), 033102 (2013).
[Crossref]

Sombra, A. S. B.

A. W. Lima and A. S. B. Sombra, “Graphene-photonic crystal switch,” Opt. Commun. 321, 150–156 (2014).
[Crossref]

Son, H.

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Stach, E. A.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Stankovich, S.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Tour, J. M.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

Vasic, B.

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “Tunable metamaterials based on split ring resonators and doped graphene,” Appl. Phys. Lett. 103(1), 011102 (2013).
[Crossref]

Vincenti, M. A.

Virally, S.

Wang, X.

L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai, “Narrow graphene nanoribbons from carbon nanotubes,” Nature 458(7240), 877–880 (2009).
[Crossref] [PubMed]

Wu, Z.

Y. Zhang, Z. Wu, Y. Cao, and H. Zhang, “Optical properties of one-dimensional Fibonacci quasi-periodic graphene photonic crystal,” Opt. Commun. 338, 168–173 (2015).
[Crossref]

Xie, L.

Y. Liu, X. Xie, L. Xie, Z. Yang, and H. Yang, “Dual-band absorption characteristics of one-dimensional photonic crystal with graphene-based defect,” Optik (Stuttg.) 127(9), 3945–3948 (2016).
[Crossref]

Xie, X.

Y. Liu, X. Xie, L. Xie, Z. Yang, and H. Yang, “Dual-band absorption characteristics of one-dimensional photonic crystal with graphene-based defect,” Optik (Stuttg.) 127(9), 3945–3948 (2016).
[Crossref]

Yakovlev, A. B.

C. S. R. Kaipa, A. B. Yakovlev, G. W. Hanson, Y. R. Padooru, F. Medina, and F. Mesa, “Enhanced transmission with a graphene-dielectric microstructure at low-terahertz frequencies,” Phys. Rev. B 85(24), 245407 (2012).
[Crossref]

Yang, H.

Y. Liu, X. Xie, L. Xie, Z. Yang, and H. Yang, “Dual-band absorption characteristics of one-dimensional photonic crystal with graphene-based defect,” Optik (Stuttg.) 127(9), 3945–3948 (2016).
[Crossref]

Yang, Z.

Y. Liu, X. Xie, L. Xie, Z. Yang, and H. Yang, “Dual-band absorption characteristics of one-dimensional photonic crystal with graphene-based defect,” Optik (Stuttg.) 127(9), 3945–3948 (2016).
[Crossref]

L. Qi, Z. Yang, F. Lan, X. Gao, and Z. Shi, “Properties of Obliquely Incident Electromagnetic Wave in 1D Magnetized Plasma Photonic crystals,” Phys. Plasmas 17(4), 042501 (2010).
[Crossref]

Zhang, H.

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24(11), 118103 (2015).
[Crossref]

Y. Zhang, Z. Wu, Y. Cao, and H. Zhang, “Optical properties of one-dimensional Fibonacci quasi-periodic graphene photonic crystal,” Opt. Commun. 338, 168–173 (2015).
[Crossref]

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

Zhang, L.

L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai, “Narrow graphene nanoribbons from carbon nanotubes,” Nature 458(7240), 877–880 (2009).
[Crossref] [PubMed]

Zhang, S.

L. Qi, L. Shang, and S. Zhang, “One-dimensional plasma photonic crystals with sinusoidal densities,” Phys. Plasmas 21(1), 013501 (2014).
[Crossref]

Zhang, X.

L. Qi and X. Zhang, “Photonic band gaps of one-dimensional ternary plasma photonic crystals with periodic and periodic-varying structures,” J. Electromagn. Waves Appl. 25(4), 539–552 (2011).
[Crossref]

Zhang, Y.

Y. Zhang, Z. Wu, Y. Cao, and H. Zhang, “Optical properties of one-dimensional Fibonacci quasi-periodic graphene photonic crystal,” Opt. Commun. 338, 168–173 (2015).
[Crossref]

Zhao, Y.

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

Zheng, S.

Zhu, B.

Zimney, E. J.

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

B. Vasić, M. M. Jakovljević, G. Isić, and R. Gajić, “Tunable metamaterials based on split ring resonators and doped graphene,” Appl. Phys. Lett. 103(1), 011102 (2013).
[Crossref]

Carbon (1)

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

Chin. Phys. B (1)

G. Ding, S. Liu, H. Zhang, X. Kong, H. Li, B. Li, S. Liu, and H. Li, “Tunable electromagnetically induced transparency at terahertz frequencies in coupled graphene metamaterial,” Chin. Phys. B 24(11), 118103 (2015).
[Crossref]

J. Appl. Phys. (1)

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Optimizing terahertz surface plasmons of a monolayer graphene and a graphene parallel plate waveguide using one-dimensional photonic crystal,” J. Appl. Phys. 114(3), 033102 (2013).
[Crossref]

J. Electromagn. Waves Appl. (1)

L. Qi and X. Zhang, “Photonic band gaps of one-dimensional ternary plasma photonic crystals with periodic and periodic-varying structures,” J. Electromagn. Waves Appl. 25(4), 539–552 (2011).
[Crossref]

J. Opt. Soc. Am. B (1)

Nano Lett. (1)

A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S. Dresselhaus, and J. Kong, “Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition,” Nano Lett. 9(1), 30–35 (2009).
[Crossref] [PubMed]

Nature (5)

K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706–710 (2009).
[Crossref] [PubMed]

S. Stankovich, D. A. Dikin, G. H. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, “Graphene-based composite materials,” Nature 442(7100), 282–286 (2006).
[Crossref] [PubMed]

J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, “The structure of suspended graphene sheets,” Nature 446(7131), 60–63 (2007).
[Crossref] [PubMed]

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458(7240), 872–876 (2009).
[Crossref] [PubMed]

L. Jiao, L. Zhang, X. Wang, G. Diankov, and H. Dai, “Narrow graphene nanoribbons from carbon nanotubes,” Nature 458(7240), 877–880 (2009).
[Crossref] [PubMed]

Opt. Commun. (3)

H. Hajian, A. Soltani-Vala, and M. Kalafi, “Characteristics of band structure and surface plasmons supported by a one-dimensional graphene-dielectric photonic crystal,” Opt. Commun. 292, 149–157 (2013).
[Crossref]

Y. Zhang, Z. Wu, Y. Cao, and H. Zhang, “Optical properties of one-dimensional Fibonacci quasi-periodic graphene photonic crystal,” Opt. Commun. 338, 168–173 (2015).
[Crossref]

A. W. Lima and A. S. B. Sombra, “Graphene-photonic crystal switch,” Opt. Commun. 321, 150–156 (2014).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Optik (Stuttg.) (1)

Y. Liu, X. Xie, L. Xie, Z. Yang, and H. Yang, “Dual-band absorption characteristics of one-dimensional photonic crystal with graphene-based defect,” Optik (Stuttg.) 127(9), 3945–3948 (2016).
[Crossref]

Phys. B (1)

A. Madani and S. R. Entezar, “Optical properties of one-dimensional photonic crystals containing graphene sheets,” Phys. B 431(15), 1–5 (2013).
[Crossref]

Phys. E (1)

Z. Arefinia and A. Asgari, “Novel attributes in the scaling and performance considerations of the one-dimensional graphene-based photonic crystals for terahertz applications,” Phys. E 54, 34–39 (2013).
[Crossref]

Phys. Lett. A (1)

J. Fu, W. Chen, and B. Lv, “Tunable defect mode realized by graphene-based photonic crystal,” Phys. Lett. A 380(20), 1793–1798 (2016).
[Crossref]

Phys. Plasmas (2)

L. Qi, L. Shang, and S. Zhang, “One-dimensional plasma photonic crystals with sinusoidal densities,” Phys. Plasmas 21(1), 013501 (2014).
[Crossref]

L. Qi, Z. Yang, F. Lan, X. Gao, and Z. Shi, “Properties of Obliquely Incident Electromagnetic Wave in 1D Magnetized Plasma Photonic crystals,” Phys. Plasmas 17(4), 042501 (2010).
[Crossref]

Phys. Rev. B (2)

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[Crossref]

Phys. Rev. Lett. (1)

A. Marini and F. J. García de Abajo, “Graphene-Based Active Random Metamaterials for Cavity-Free Lasing,” Phys. Rev. Lett. 116(21), 217401 (2016).
[Crossref] [PubMed]

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A. A. Sayem, M. M. Rahman, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Negative Refraction with Superior Transmission in Graphene-Hexagonal Boron Nitride (hBN) Multilayer Hyper Crystal,” Sci. Rep. 6(1), 25442 (2016).
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Science (1)

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J. D. Cressler, Silicon Heterostructure Handbook: Materials, Fabrication, Devices, Circuits and Applications of SiGe and Si Strained-Layer Epitaxy (CRC Press 2006).

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Figures (8)

Fig. 1
Fig. 1 One-dimensional graphene photonic crystal with (a) Period, (b) Single-layer defect and (c) Dual-layer structure.
Fig. 2
Fig. 2 Transmission and absorption curves of the period, single-defect and dual-defect structures in Fig. 1 with εA = 2.2, εB = 3.2, dA = 100 μm, dB = 150 μm, dG = 0.34 nm, T = 300 K, Γ = 1 THz, μ c = 0.9 eV.
Fig. 3
Fig. 3 Transmission and absorption curves under different chemical potential μ c = 0.5 and 0.9 eV for the dual-layer defect structure with εA = 2.2, εB = 3.2, dA = 100 μm, dB = 150 μm, dG = 0.34 nm, T = 300 K, Γ = 1 THz.
Fig. 4
Fig. 4 Color map of transmission and absorption under varying from 0.1 and 1.0 eV for the dual-layer defect structure with εA = 2.2, εB = 3.2, dA = 100 μm, dB = 150 μm, dG = 0.34 nm, T = 300 K, Γ = 1 THz.
Fig. 5
Fig. 5 (a) The real part (solid line) and the imaginary part (dot-dash line) of the tangential permittivity εG, t of single-layer graphene for different chemical potential μ c = 0.1, 0.3, 0.5, 0.7 and 0.9 eV with dG = 0.34 nm, T = 300 K and Γ = 1 THz. (b) The enlarged imaginary part valued from 0 to 500.
Fig. 6
Fig. 6 Transmission versus location for the dual-defect layer structure with εA = 2.2, εB = 3.2, dA = 100 μm, dB = 150 μm, dG = 0.34 nm, T = 300 K, Γ = 1 THz and. μ c = 0.9 eV.
Fig. 7
Fig. 7 Color map of the transmission versus the frequency and the incidence angle for (a) TM and (b) TE polarization, where εA = 2.2, εB = 3.2, dA = 100 μm, dB = 150 μm, dG = 0.34 nm, T = 300 K, Γ = 1 THz, and. μ c = 0.9 eV.
Fig. 8
Fig. 8 Electromagnetic field distribution of TM polarization in 1D graphene and dielectric A.

Tables (1)

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Table 1 Transmission (T), absorption (A) and refection (R) magnitude of the four peaks

Equations (28)

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ε G = [ ε G , t 0 0 0 ε G , t 0 0 0 ε G , ] .
ε G , t = 1 + j σ ( ω ) ε 0 ω d G .
σ i n t r a = j e 2 k B T π 2 ( ω j Γ ) ( μ c k B T + 2 ln ( e μ c k B T + 1 ) ) .
σ i n t r a = j e 2 k B T π 2 ( ω j Γ ) ( μ c k B T + 2 ln ( e μ c k B T + 1 ) ) .
k x 2 + k z 2 = ε G , t k 0 2 (TE) .
k x 2 ε G , + k z 2 ε G , t = k 0 2 .
M i = ( cos k i z d i j p i sin k i z d i j p i sin k i z d i cos k i z d i ) .
M = ( M G M A ) N = ( m 11 m 12 m 21 m 22 ) .
M = ( M G M A ) N 1 M G M B M A ( M G M A ) N 3 = ( m 11 m 12 m 21 m 22 ) .
M = ( M G M A ) N 1 M B ( M G M A ) N 2 M B ( M G M A ) N 3 = ( m 11 m 12 m 21 m 22 ) .
R = | r | 2 .
T = { | t | 2 For TE p 0 p N + 1 | t | 2 For TM .
A = 1 T R .
{ r = ( m 11 + m 12 p N + 1 ) p 0 m 21 m 22 p N + 1 ( m 11 + m 12 p N + 1 ) p 0 + m 21 + m 22 p N + 1 t = 2 p 0 ( m 11 + m 12 p N + 1 ) p 0 + m 21 + m 22 p N + 1 .
p 0 = { ε 0 / μ 0 cos θ 0 For TE ε 0 / μ 0 / cos θ 0 For TM , p N + 1 = { ε 0 / μ 0 cos θ N + 1 For TE ε 0 / μ 0 / cos θ N + 1 For TM
ε G = [ ε G , t 0 0 0 ε G , t 0 0 0 ε G , ] .
× E = μ 0 H t .
× H = ε 0 ε G E t .
E z x E x z = j ω μ 0 H y .
H y z = j ω ε 0 ε G , t E x .
H y x = j ω ε 0 ε G , E z .
1 ε G , t 2 H y z 2 + 1 ε G , 2 H y x 2 + k 0 2 H y = 0.
k G x 2 ε G , + k G z 2 ε G , t = k 0 2 .
H y I = ( A + e j k G z z + A e j k G z z ) e j ( ω t k G x x ) = H y t I + H y r I I ' .
E x I = E x t I + E x r I I ' H y I = H y t I + H y r I I ' .
E x I I = E x i I I + E x r I I H y I I = H y i I I + H y r I I .
( H y i I I H y r I I ) = ( e j k G z d G 0 0 e j k G z d G ) ( H y t I H y r II' ) .
( E x I H y I ) = M ( E x I I H y I I ) .

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