Abstract

Extraordinary absorption decrease in graphene superlattices in the visible range is presented. Due to competition between loss and resonant reflection at resonance, the absorption displays non-monotonic behavior. As the period number increases above a certain critical value, absorption decreases with the increase in the period number. This is in contrast to ordinary absorption for a non-resonant condition, which monotonically increases with the period number. Moreover, this extraordinary property can also be controlled by applying a gate voltage to graphene sheets. The results provide not only a new understanding of graphene physics but also an application in nanophotonics and optoelectronics.

© 2015 Optical Society of America

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Corrections

28 October 2015: Corrections were made to the author affiliations and Fig. 2.


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References

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2015 (2)

2014 (3)

C. Cong and T. Yu, “Enhanced ultra-low-frequency interlayer shear modes in folded graphene layers,” Nat. Commun. 5, 4709 (2014).
[Crossref] [PubMed]

T. Stauber, G. Gómez-Santos, and F. J. G. de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014).
[Crossref] [PubMed]

C. W. Tsao, Y. H. Cheng, and W. J. Hsueh, “Localized modes in one-dimensional symmetric Thue-Morse quasicrystals,” Opt. Express 22(20), 24378–24383 (2014).
[Crossref] [PubMed]

2013 (4)

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. H. Cheng and W. J. Hsueh, “High-Q filters with complete transmission by quasi-periodic dielectric multilayers,” Opt. Lett. 38(18), 3631–3634 (2013).
[Crossref] [PubMed]

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

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

2012 (3)

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]

K. V. Sreekanth, S. Zeng, J. Shang, K.-T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

S. Cheon, K. D. Kihm, J. S. Park, J. S. Lee, B. J. Lee, H. Kim, and B. H. Hong, “How to optically count graphene layers,” Opt. Lett. 37(18), 3765–3767 (2012).
[Crossref] [PubMed]

2011 (5)

H. Liu, Y. Liu, and D. Zhu, “Chemical doping of graphene,” J. Mater. Chem. 21(10), 3335–3345 (2011).
[Crossref]

A. Ludwig and K. J. Webb, “Dark materials based on graphene sheet stacks,” Opt. Lett. 36(2), 106–108 (2011).
[Crossref] [PubMed]

W. J. Hsueh and S. J. Wun, “Simple expressions for the maximum omnidirectional bandgap of bilayer photonic crystals,” Opt. Lett. 36(9), 1581–1583 (2011).
[Crossref] [PubMed]

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

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

2010 (3)

F. Schwierz, “Graphene transistors,” Nat. Nanotechnol. 5(7), 487–496 (2010).
[Crossref] [PubMed]

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

A. Ludwig and K. J. Webb, “Accuracy of effective medium parameter extraction procedures for optical metamaterials,” Phys. Rev. B 81(11), 113103 (2010).
[Crossref]

2009 (2)

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 (5)

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism,” Phys. Rev. A 78(1), 013836 (2008).
[Crossref]

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

2007 (2)

M. Bergmair and K. Hingerl, “Band structure and coupled surface states in one-dimensional photonic crystals,” J. Opt. A, Pure Appl. Opt. 9(9), S339–S344 (2007).
[Crossref]

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

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]

Basov, D. N.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Bergmair, M.

M. Bergmair and K. Hingerl, “Band structure and coupled surface states in one-dimensional photonic crystals,” J. Opt. A, Pure Appl. Opt. 9(9), S339–S344 (2007).
[Crossref]

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Bonaccorso, F.

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

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

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]

Carbone, F.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Chen, C. H.

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism,” Phys. Rev. A 78(1), 013836 (2008).
[Crossref]

Chen, C. T.

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism,” Phys. Rev. A 78(1), 013836 (2008).
[Crossref]

Cheng, Y. H.

Cheon, S.

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]

Cong, C.

C. Cong and T. Yu, “Enhanced ultra-low-frequency interlayer shear modes in folded graphene layers,” Nat. Commun. 5, 4709 (2014).
[Crossref] [PubMed]

Crommie, M.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Dai, Y.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

de Abajo, F. J. G.

T. Stauber, G. Gómez-Santos, and F. J. G. de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014).
[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]

Engheta, N.

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

Falkovsky, L. A.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Ferrari, A. C.

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

García de Abajo, F. J.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Geim, A. K.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Girit, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Gómez-Santos, G.

T. Stauber, G. Gómez-Santos, and F. J. G. de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014).
[Crossref] [PubMed]

Grigorenko, A. N.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

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]

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]

Hao, Z.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Hasan, T.

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

He, X.

Henriksen, E. A.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Hingerl, K.

M. Bergmair and K. Hingerl, “Band structure and coupled surface states in one-dimensional photonic crystals,” J. Opt. A, Pure Appl. Opt. 9(9), S339–S344 (2007).
[Crossref]

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.

S. Cheon, K. D. Kihm, J. S. Park, J. S. Lee, B. J. Lee, H. Kim, and B. H. Hong, “How to optically count graphene layers,” Opt. Lett. 37(18), 3765–3767 (2012).
[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]

Hsueh, W. J.

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]

Jiang, Z.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

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]

Kihm, K. D.

Kim, H.

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]

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

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]

Koppens, F. H. L.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Koschny, T.

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

Kuzmenko, A. B.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

Lee, B. J.

Lee, J. S.

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, Z. Q.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Liu, H.

H. Liu, Y. Liu, and D. Zhu, “Chemical doping of graphene,” J. Mater. Chem. 21(10), 3335–3345 (2011).
[Crossref]

Liu, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Liu, Y.

H. Liu, Y. Liu, and D. Zhu, “Chemical doping of graphene,” J. Mater. Chem. 21(10), 3335–3345 (2011).
[Crossref]

Ludwig, A.

A. Ludwig and K. J. Webb, “Dark materials based on graphene sheet stacks,” Opt. Lett. 36(2), 106–108 (2011).
[Crossref] [PubMed]

A. Ludwig and K. J. Webb, “Accuracy of effective medium parameter extraction procedures for optical metamaterials,” Phys. Rev. B 81(11), 113103 (2010).
[Crossref]

Martin, M. C.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

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]

Nair, R. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[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]

Novoselov, K. S.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[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]

Park, J. S.

Peres, N. M. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Pershoguba, S. S.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

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]

Schwierz, F.

F. Schwierz, “Graphene transistors,” Nat. Nanotechnol. 5(7), 487–496 (2010).
[Crossref] [PubMed]

Shang, J.

K. V. Sreekanth, S. Zeng, J. Shang, K.-T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Shen, Y. R.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Shi, W.

Shi, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[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]

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]

Soukoulis, C. M.

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

Sreekanth, K. V.

K. V. Sreekanth, S. Zeng, J. Shang, K.-T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Stauber, T.

T. Stauber, G. Gómez-Santos, and F. J. G. de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014).
[Crossref] [PubMed]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Stormer, H. L.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Sun, Z.

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

Tassin, P.

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

Tian, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Tsao, C. W.

Vakil, A.

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

van der Marel, D.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

van Heumen, E.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

Wang, F.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Webb, K. J.

A. Ludwig and K. J. Webb, “Dark materials based on graphene sheet stacks,” Opt. Lett. 36(2), 106–108 (2011).
[Crossref] [PubMed]

A. Ludwig and K. J. Webb, “Accuracy of effective medium parameter extraction procedures for optical metamaterials,” Phys. Rev. B 81(11), 113103 (2010).
[Crossref]

Wun, S. J.

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]

Yong, K.-T.

K. V. Sreekanth, S. Zeng, J. Shang, K.-T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Yu, T.

C. Cong and T. Yu, “Enhanced ultra-low-frequency interlayer shear modes in folded graphene layers,” Nat. Commun. 5, 4709 (2014).
[Crossref] [PubMed]

K. V. Sreekanth, S. Zeng, J. Shang, K.-T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Zeng, S.

K. V. Sreekanth, S. Zeng, J. Shang, K.-T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Zettl, A.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Zhan, T.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Zhang, Y.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

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]

Zhao, Z.-Y.

Zhu, D.

H. Liu, Y. Liu, and D. Zhu, “Chemical doping of graphene,” J. Mater. Chem. 21(10), 3335–3345 (2011).
[Crossref]

Zi, J.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Carbon (1)

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

J. Mater. Chem. (1)

H. Liu, Y. Liu, and D. Zhu, “Chemical doping of graphene,” J. Mater. Chem. 21(10), 3335–3345 (2011).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

M. Bergmair and K. Hingerl, “Band structure and coupled surface states in one-dimensional photonic crystals,” J. Opt. A, Pure Appl. Opt. 9(9), S339–S344 (2007).
[Crossref]

J. Phys. Condens. Matter (1)

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Nano Lett. (2)

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]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Nat. Commun. (1)

C. Cong and T. Yu, “Enhanced ultra-low-frequency interlayer shear modes in folded graphene layers,” Nat. Commun. 5, 4709 (2014).
[Crossref] [PubMed]

Nat. Nanotechnol. (1)

F. Schwierz, “Graphene transistors,” Nat. Nanotechnol. 5(7), 487–496 (2010).
[Crossref] [PubMed]

Nat. Photonics (1)

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

Nat. Phys. (1)

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Nature (1)

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]

Opt. Commun. (1)

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]

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. A (1)

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystals with metamaterials using a band-edge formalism,” Phys. Rev. A 78(1), 013836 (2008).
[Crossref]

Phys. Rev. B (3)

A. Ludwig and K. J. Webb, “Accuracy of effective medium parameter extraction procedures for optical metamaterials,” Phys. Rev. B 81(11), 113103 (2010).
[Crossref]

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. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Phys. Rev. Lett. (2)

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

T. Stauber, G. Gómez-Santos, and F. J. G. de Abajo, “Extraordinary absorption of decorated undoped graphene,” Phys. Rev. Lett. 112(7), 077401 (2014).
[Crossref] [PubMed]

Sci. Rep. (1)

K. V. Sreekanth, S. Zeng, J. Shang, K.-T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Science (4)

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

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

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

Other (1)

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

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Figures (4)

Fig. 1
Fig. 1 (a) The structure of the system. Transmission spectra of a free-standing graphene superlattice for period numbers: (a) N = 20, (b) N = 88, and (c) N = 200, with nD = nC = nS = n0, d = 315nm, T = 300K, and μc = 0.15, under normal incidence. The blue dotted lines, red dashed lines, and green solid lines denote the transmittance, absorptance, and reflectance of the system, respectively.
Fig. 2
Fig. 2 (a) The value of |Im(qd)/π| for a graphene superlattice versus normalized frequency. Note that the sharp peak at Ω = 0.5 is the center of Bloch pass band. The transmission spectra and the period number for a superlattice when (b) Ω = 0.500, (c) Ω = 0.501 and (d) Ω = 0.600. The blue dotted lines, red dashed lines, and green solid lines respectively denote the transmittance, absorptance, and reflectance of the system. All parameters in the system are the same as those for Fig. 1. The wavelength of the system is 630nm.
Fig. 3
Fig. 3 The normalized total power dissipation for a graphene superlattice with (a) Ω = 0.5 versus period number N. The squared electric field of (a) corresponding to (b) point A with N = 6 and (c) point B with N = 88. The normalized total power dissipation for a graphene superlattice with (d) Ω = 0.6 versus period number. The squared electric field of (d) corresponding to (e) point C with N = 6 and (f) point D with N = 88. All of the parameters in the system are the same as those for Fig. 1. The green line is the boundary between the cover medium and the graphene superlattice. The grey lines denote the graphene layers. The red circles in (b) and (c) mark the position where the light enters the different layers. The red dotted lines in (e) and (f) connect the positions where the light enters the different layers.
Fig. 4
Fig. 4 (a) Period number at which extraordinary absorption occurs (green) and the corresponding absorptance (blue) in a graphene superlattice versus chemical potential. (b) The absorption and period number for different chemical potentials in the superlattice. The blue and green crosses in (a) each denote A = 0.5 and NT = 88 for μc = 0.15ev, respectively. The blue thick line and arrows in (b) mark the variation in the absorptance where N = NT, when the chemical potential is increased. Here, nD = nC = nS = n0, d = 315nm, T = 300K, and the wavelength is 630nm.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

σ int r a ( ω ) = e 2 4 i 2 π { 16 k B T ω ln ( cosh ( μ c 2 k B T ) ) } ,
σ int e r ( ω ) = e 2 4 { 1 2 + 1 π arc tan ω 2 μ c 2 k B T i 2 π ln ( ω + 2 μ c ) 2 ( ω 2 μ c ) 2 + ( 2 k B T ) 2 } ,
A = 8 n C N σ ˜ R ( n S + n C + 2 N σ ˜ R ) 2 + ( 2 N σ ˜ I ) 2 ,
N T = n C + n S 2 | σ ˜ R + j σ ˜ I | .

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