Abstract

A kind of tunable hyperbolic metamaterial (HMM) based on the graphene-dielectric layered structure at near-infrared frequencies is presented, and the engineered surface Bloch waves between graphene-based HMM and isotropic medium are investigated. Our calculations demonstrate that the frequency and frequency range of surface Bloch waves existence can be tuned by varying the Fermi energy of graphene sheets via electrostatic biasing. Moreover, we show that the frequency range of surface Bloch waves existence can be broadened by decreasing the thickness of the dielectric in the graphene-dielectric layered structure or by increasing the layer number of graphene sheets.

© 2014 Optical Society of America

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2013 (8)

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[CrossRef]

M. A. K. Othman, C. Guclu, F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
[CrossRef] [PubMed]

K. V. Sreekanth, A. De Luca, G. Strangi, “Negative refraction in graphene-based metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[CrossRef]

I. S. Nefedov, C. A. Valaginnopoulos, L. A. Melnikov, “Perfect absorption in graphene multilayers,” J. Opt. 15(11), 114003 (2013).
[CrossRef]

T. Zhang, L. Chen, X. Li, “Graphene-based tunable broadband hyperlens for far-field subdiffraction imaging at mid-infrared frequencies,” Opt. Express 21(18), 20888–20899 (2013).
[CrossRef] [PubMed]

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

C. J. Zapata-Rodríguez, J. J. Miret, S. Vuković, M. R. Belić, “Engineered surface waves in hyperbolic metamaterials,” Opt. Express 21(16), 19113–19127 (2013).
[CrossRef] [PubMed]

2012 (7)

A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[CrossRef]

C. Rizza, A. Ciattoni, E. Spinozzi, L. Columbo, “Terahertz active spatial filtering through optically tunable hyperbolic metamaterials,” Opt. Lett. 37(16), 3345–3347 (2012).
[CrossRef] [PubMed]

Z. Jacob, I. Smolyaninov, E. E. Narimanov, “Broadband purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012).
[CrossRef]

Y. He, S. He, X. Yang, “Optical field enhancement in nanoscale slot waveguides of hyperbolic metamaterials,” Opt. Lett. 37(14), 2907–2909 (2012).
[CrossRef] [PubMed]

S. A. Biehs, M. Tschikin, P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett. 109(10), 104301 (2012).
[CrossRef] [PubMed]

Y. H. Wan, Z. Zheng, W. J. Kong, X. Zhao, Y. Liu, Y. S. Bian, J. S. Liu, “Nearly three orders of magnitude enhancement of Goos-Hanchen shift by exciting Bloch surface wave,” Opt. Express 20(8), 8998–9003 (2012).
[CrossRef] [PubMed]

T. U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

2011 (2)

J. A. Polo, A. Lakhtakia, “Surface electromagnetic waves: a review,” Laser Photonics Rev. 5(2), 234–246 (2011).
[CrossRef]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

2010 (5)

G. Naik, A. Boltasseva, “Semiconductors for plasmonics and metamaterials,” Phys. Status Solidi 4, 295–297 (2010).

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, H. P. Herzig, “Two dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[CrossRef]

F. Giorgis, E. Descrovi, C. Summonte, L. Dominici, F. Michelotti, “Experimental determination of the sensitivity of Bloch Surface Waves based sensors,” Opt. Express 18(8), 8087–8093 (2010).
[CrossRef] [PubMed]

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[CrossRef] [PubMed]

2009 (4)

M. A. Noginov, A. Barnakov, G. Zhu, T. Tumkur, H. Li, E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[CrossRef]

S. M. Vukovic, I. V. Shadrivov, Y. S. Kivshar, “Surface Bloch waves in metamaterial and metal-dielectric supperlattices,” Appl. Phys. Lett. 95(4), 041902 (2009).
[CrossRef]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

2008 (1)

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

2007 (5)

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

M. Liscidini, J. E. Sipe, “Enhancement of diffraction for biosensing applications via Bloch surface waves,” Appl. Phys. Lett. 91(25), 253125 (2007).
[CrossRef]

E. Guillermain, V. Lysenko, R. Orobtchouk, T. Benyattou, S. Roux, A. Pillonnet, P. Perriat, “Bragg surface wave device based on porous silicon and its application for sensing,” Appl. Phys. Lett. 90(24), 241116 (2007).
[CrossRef]

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

2006 (1)

2005 (1)

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[CrossRef]

2003 (2)

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

D. R. Smith, D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[CrossRef] [PubMed]

1978 (1)

P. Yeh, A. Yariv, A. Y. Cho, “Optical surface-waves in periodic layered media,” Appl. Phys. Lett. 32(2), 104–105 (1978).
[CrossRef]

1977 (1)

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Alekseyev, L. V.

Atkinson, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

Bajoni, D.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

Barnakov, A.

M. A. Noginov, A. Barnakov, G. Zhu, T. Tumkur, H. Li, E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[CrossRef]

Barnakov, Y. A.

Barnes, W. L.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Bartal, G.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Belic, M. R.

Belov, P. A.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[CrossRef]

Ben-Abdallah, P.

S. A. Biehs, M. Tschikin, P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett. 109(10), 104301 (2012).
[CrossRef] [PubMed]

Benyattou, T.

E. Guillermain, V. Lysenko, R. Orobtchouk, T. Benyattou, S. Roux, A. Pillonnet, P. Perriat, “Bragg surface wave device based on porous silicon and its application for sensing,” Appl. Phys. Lett. 90(24), 241116 (2007).
[CrossRef]

Bian, Y. S.

Biehs, S. A.

S. A. Biehs, M. Tschikin, P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett. 109(10), 104301 (2012).
[CrossRef] [PubMed]

Boltasseva, A.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

G. Naik, A. Boltasseva, “Semiconductors for plasmonics and metamaterials,” Phys. Status Solidi 4, 295–297 (2010).

Bonner, C. E.

Capolino, F.

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Chen, L.

Cho, A. Y.

P. Yeh, A. Yariv, A. Y. Cho, “Optical surface-waves in periodic layered media,” Appl. Phys. Lett. 32(2), 104–105 (1978).
[CrossRef]

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

Ciattoni, A.

Columbo, L.

Dacarro, G.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

De Luca, A.

K. V. Sreekanth, A. De Luca, G. Strangi, “Negative refraction in graphene-based metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[CrossRef]

Delfan, A.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Descrovi, E.

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, H. P. Herzig, “Two dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[CrossRef]

F. Giorgis, E. Descrovi, C. Summonte, L. Dominici, F. Michelotti, “Experimental determination of the sensitivity of Bloch Surface Waves based sensors,” Opt. Express 18(8), 8087–8093 (2010).
[CrossRef] [PubMed]

Dominici, L.

F. Giorgis, E. Descrovi, C. Summonte, L. Dominici, F. Michelotti, “Experimental determination of the sensitivity of Bloch Surface Waves based sensors,” Opt. Express 18(8), 8087–8093 (2010).
[CrossRef] [PubMed]

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, H. P. Herzig, “Two dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[CrossRef]

Dryden, D.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

Evans, P.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

Franz, K. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Galli, M.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

Geim, A. K.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Geng, B.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Giorgis, F.

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, H. P. Herzig, “Two dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[CrossRef]

F. Giorgis, E. Descrovi, C. Summonte, L. Dominici, F. Michelotti, “Experimental determination of the sensitivity of Bloch Surface Waves based sensors,” Opt. Express 18(8), 8087–8093 (2010).
[CrossRef] [PubMed]

Gmachl, C.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Grigorenko, A. N.

A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[CrossRef]

Gu, L.

T. U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

Guclu, C.

Guillermain, E.

E. Guillermain, V. Lysenko, R. Orobtchouk, T. Benyattou, S. Roux, A. Pillonnet, P. Perriat, “Bragg surface wave device based on porous silicon and its application for sensing,” Appl. Phys. Lett. 90(24), 241116 (2007).
[CrossRef]

Guinea, F.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Guizzetti, G.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

He, S.

He, Y.

Hendren, W.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

Herzig, H. P.

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, H. P. Herzig, “Two dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[CrossRef]

Hoffman, A. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Hong, C. S.

Howard, S. S.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Iorsh, I. V.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[CrossRef]

Jacob, Z.

Z. Jacob, I. Smolyaninov, E. E. Narimanov, “Broadband purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012).
[CrossRef]

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[CrossRef] [PubMed]

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Z. Jacob, L. V. Alekseyev, E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[CrossRef] [PubMed]

Jian, S.

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Kabashin, A. V.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

Kim, J.-Y.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Kitur, J. K.

T. U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

Kivshar, Y. S.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[CrossRef]

S. M. Vukovic, I. V. Shadrivov, Y. S. Kivshar, “Surface Bloch waves in metamaterial and metal-dielectric supperlattices,” Appl. Phys. Lett. 95(4), 041902 (2009).
[CrossRef]

Kong, W. J.

Lakhtakia, A.

J. A. Polo, A. Lakhtakia, “Surface electromagnetic waves: a review,” Laser Photonics Rev. 5(2), 234–246 (2011).
[CrossRef]

Lee, H.

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

Li, H.

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[CrossRef] [PubMed]

M. A. Noginov, A. Barnakov, G. Zhu, T. Tumkur, H. Li, E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[CrossRef]

Li, X.

Lin, Z.

Liscidini, M.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

M. Liscidini, J. E. Sipe, “Enhancement of diffraction for biosensing applications via Bloch surface waves,” Appl. Phys. Lett. 91(25), 253125 (2007).
[CrossRef]

Liu, J. S.

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Liu, Y.

Liu, Y. M.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Liu, Z. W.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

Lysenko, V.

E. Guillermain, V. Lysenko, R. Orobtchouk, T. Benyattou, S. Roux, A. Pillonnet, P. Perriat, “Bragg surface wave device based on porous silicon and its application for sensing,” Appl. Phys. Lett. 90(24), 241116 (2007).
[CrossRef]

Maiti, S.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[CrossRef]

Mayy, M.

Melnikov, L. A.

I. S. Nefedov, C. A. Valaginnopoulos, L. A. Melnikov, “Perfect absorption in graphene multilayers,” J. Opt. 15(11), 114003 (2013).
[CrossRef]

Michelotti, F.

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, H. P. Herzig, “Two dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[CrossRef]

F. Giorgis, E. Descrovi, C. Summonte, L. Dominici, F. Michelotti, “Experimental determination of the sensitivity of Bloch Surface Waves based sensors,” Opt. Express 18(8), 8087–8093 (2010).
[CrossRef] [PubMed]

Miret, J. J.

Mukhin, I. S.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[CrossRef]

Mysore, S.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

Naik, G.

G. Naik, A. Boltasseva, “Semiconductors for plasmonics and metamaterials,” Phys. Status Solidi 4, 295–297 (2010).

Naik, G. V.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Nakagawa, W.

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, H. P. Herzig, “Two dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[CrossRef]

Narimanov, E.

Narimanov, E. E.

Z. Jacob, I. Smolyaninov, E. E. Narimanov, “Broadband purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012).
[CrossRef]

T. U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[CrossRef] [PubMed]

M. A. Noginov, A. Barnakov, G. Zhu, T. Tumkur, H. Li, E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[CrossRef]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Nataraj, G.

Nefedov, I. S.

I. S. Nefedov, C. A. Valaginnopoulos, L. A. Melnikov, “Perfect absorption in graphene multilayers,” J. Opt. 15(11), 114003 (2013).
[CrossRef]

Noginov, M. A.

T. U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[CrossRef] [PubMed]

M. A. Noginov, A. Barnakov, G. Zhu, T. Tumkur, H. Li, E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[CrossRef]

Novoselov, K. S.

A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[CrossRef]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Orobtchouk, R.

E. Guillermain, V. Lysenko, R. Orobtchouk, T. Benyattou, S. Roux, A. Pillonnet, P. Perriat, “Bragg surface wave device based on porous silicon and its application for sensing,” Appl. Phys. Lett. 90(24), 241116 (2007).
[CrossRef]

Othman, M. A. K.

Pastkovsky, S.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

Patrini, M.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

Peres, N. M. R.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Perriat, P.

E. Guillermain, V. Lysenko, R. Orobtchouk, T. Benyattou, S. Roux, A. Pillonnet, P. Perriat, “Bragg surface wave device based on porous silicon and its application for sensing,” Appl. Phys. Lett. 90(24), 241116 (2007).
[CrossRef]

Pillonnet, A.

E. Guillermain, V. Lysenko, R. Orobtchouk, T. Benyattou, S. Roux, A. Pillonnet, P. Perriat, “Bragg surface wave device based on porous silicon and its application for sensing,” Appl. Phys. Lett. 90(24), 241116 (2007).
[CrossRef]

Pirotta, S.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

Podolskiy, V. A.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Polini, M.

A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[CrossRef]

Pollard, R.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[CrossRef] [PubMed]

Polo, J. A.

J. A. Polo, A. Lakhtakia, “Surface electromagnetic waves: a review,” Laser Photonics Rev. 5(2), 234–246 (2011).
[CrossRef]

Quaglio, M.

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, H. P. Herzig, “Two dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[CrossRef]

Ren, G.

Rizza, C.

Roux, S.

E. Guillermain, V. Lysenko, R. Orobtchouk, T. Benyattou, S. Roux, A. Pillonnet, P. Perriat, “Bragg surface wave device based on porous silicon and its application for sensing,” Appl. Phys. Lett. 90(24), 241116 (2007).
[CrossRef]

Schurig, D.

D. R. Smith, D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[CrossRef] [PubMed]

Sfez, T.

T. Sfez, E. Descrovi, L. Yu, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, H. P. Herzig, “Two dimensional optics on silicon nitride multilayer: refraction of Bloch surface waves,” Appl. Phys. Lett. 96(15), 151101 (2010).
[CrossRef]

Shadrivov, I. V.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[CrossRef]

S. M. Vukovic, I. V. Shadrivov, Y. S. Kivshar, “Surface Bloch waves in metamaterial and metal-dielectric supperlattices,” Appl. Phys. Lett. 95(4), 041902 (2009).
[CrossRef]

Shalaev, V. M.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Silkin, V. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritons,” Rep. Prog. Phys. 70(1), 1–87 (2007).
[CrossRef]

Sipe, J. E.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013).
[CrossRef]

M. Liscidini, J. E. Sipe, “Enhancement of diffraction for biosensing applications via Bloch surface waves,” Appl. Phys. Lett. 91(25), 253125 (2007).
[CrossRef]

Sivco, D. L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith, D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[CrossRef] [PubMed]

Smolyaninov, I.

Z. Jacob, I. Smolyaninov, E. E. Narimanov, “Broadband purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[CrossRef]

Spinozzi, E.

Sreekanth, K. V.

K. V. Sreekanth, A. De Luca, G. Strangi, “Negative refraction in graphene-based metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[CrossRef]

Stacy, A. M.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Strangi, G.

K. V. Sreekanth, A. De Luca, G. Strangi, “Negative refraction in graphene-based metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[CrossRef]

Summonte, C.

Sun, C.

J. Yao, Z. W. Liu, Y. M. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[CrossRef] [PubMed]

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[CrossRef] [PubMed]

Tschikin, M.

S. A. Biehs, M. Tschikin, P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett. 109(10), 104301 (2012).
[CrossRef] [PubMed]

Tumkur, T.

M. A. Noginov, A. Barnakov, G. Zhu, T. Tumkur, H. Li, E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[CrossRef]

Tumkur, T. U.

T. U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[CrossRef] [PubMed]

Valaginnopoulos, C. A.

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Figures (4)

Fig. 1
Fig. 1

(a) Scheme of the interface of the semi-infinite graphene-based hyperbolic metamaterial and the semi-infinite isotropic dielectric; (b) effective permittivity of the graphene-based layered metamaterial; (c) dispersion curve of the graphene-based hyperbolic metamaterial.

Fig. 2
Fig. 2

The influences of (a) Fermi energy EF, (b) thickness of dielectric td, and (c) number of graphene sheets N on the real part of ε||. Where N = 1, td = 10nm in (a), N = 1, EF = 0.50eV in (b), and td = 10nm, EF = 0.50eV in (c), the gray line is the free-space light line.

Fig. 3
Fig. 3

The dispersion of p-polarized surface Bloch wave at different Fermi energy, where N = 1, td = 10nm, and the gray line is the free-space light line.

Fig. 4
Fig. 4

The dependences of dispersion of p-polarized surface Bloch wave on (a) the thickness of dielectric t d and (b) the number of graphene sheets. Where N = 1, EF = 0.50eV in (a) and td = 10nm, EF = 0.50eV in (b).

Equations (7)

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

σ intra = i e 2 k B T π 2 ( ω + i / τ ) ( E F k B T + 2 ln ( e E F k B T + 1 ) ) , σ inter = i e 2 4 π ln | 2 E F ( ω + i τ 1 ) 2 E F + ( ω + i τ 1 ) | ,
cos( k z t )=cos( k g t g )cos( k d t d ) 1 2 ( F 1 F 2 + F 2 F 1 )sin( k g t g )sin( k d t d ),
sin 2 ( k z t /2 ) ε + t 2 4 k 2 ε || = t 2 4 k 0 2 ,
sin 2 ( k z t /2 )+ t 2 4 k 2 = k 0 2 ε t 2 4 ,
sin 2 ( k z t /2 ) ε + t 2 4 k x 2 ε || = t 2 4 k 0 2 .
ε || ε sin 2 ( k z t /2 ) t 2 /4 ε || k 0 2 / ε || + k z 2 ε s k 0 2 ε s =0,
ε || k z 2 / ε ε || k 0 2 / ε || + k z 2 ε d k 0 2 / ε d =0,

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