Abstract

Tunable deflection of obliquely incident, linearly polarized terahertz waves is theoretically studied in a wide frequency range around 20 THz, by combining a thin slab of graphene-dielectric metamaterial (with ten layers of graphene), a dielectric grating, and a uniform polar-dielectric slab operating in the epsilon-near-zero (ENZ) regime. The modulation of the deflection intensity and deflection angle is done by varying the chemical potential of graphene, and is realized with or without connection to the asymmetric transmission. It is shown to depend on the location of the graphene-dielectric metamaterial slab, as well as on the incidence angle. Four scenarios of tunable deflection are found, including the ones realizable in two-component structures without an ENZ slab.

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

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References

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2017 (7)

A. N. Morozovska, A. I. Kurchak, and M. V. Strikha, “Graphene Exfoliation at a Ferroelectric Domain Wall Induced by the Piezoelectric Effect: Impact on the Conductance of the Graphene Channel,” Phys. Rev. Appl.  8(5), 054004 (2017).
[Crossref]

D. Rodrigo, A. Tittl, O. Limaj, F. J. Garcia de Abajo, V. Pruneri, and H. Altug, “Double-layer graphene for enhanced tunable infrared plasmonics,” Light: Sci. Appl. 6, e16277 (2017).
[Crossref]

H. Hajian, H. Caglayan, and E. Ozbay, “Long-range Tamm surface plasmons supported by graphene-dielectric metamaterials,” J. Appl. Phys. 121(3), 033101 (2017).
[Crossref]

T. Gric and O. Hess, “Tunable surface waves at the interface separating different graphene-dielectric composite hyperbolic metamaterials,” Opt. Express 25(10), 11466–11476 (2017).
[Crossref] [PubMed]

H. Jiang, W. Zhao, and Y. Jiang, “High-efficiency tunable circular asymmetric transmission using dielectric metasurface integrated with graphene sheet,” Opt. Express 25(17), 19732–19739 (2017).
[Crossref] [PubMed]

Y. Huang, Z. Yao, F. Hu, C. Liu, L. Yu, Y. Lin, and X. Xu, “Tunable circular polarization conversion and asymmetric transmission of planar chiral graphene-metamaterial in terahertz region,” Carbon 119, 305–313 (2017).
[Crossref]

G. C. R. Devarapu and S. Foteinopoulou, “Broadband Near-Unidirectional Absorption Enabled by Phonon-Polariton Resonances in SiC Micropyramid Arrays,” Phys. Rev. Appl.  7 (3), 034001 (2017).
[Crossref]

2016 (8)

Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “Tunable dual-band asymmetric transmission for circularly polarized waves with graphene planar chiral metasurfaces,” Opt. Lett. 41(13), 3142–3145 (2016).
[Crossref] [PubMed]

J. Zhao, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Tunable asymmetric transmission of THz wave through a graphene chiral metasurface,” J. Opt.  18(9), 095001 (2016).
[Crossref]

J. Wu, L. Jiang, J. Guo, X. Dai, Y. Xiang, and S. Wen, “Tunable perfect absorption at infrared frequencies by a graphene-hBN hyper crystal,” Opt. Express 24(15), 17103–17114 (2016).
[Crossref] [PubMed]

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun.  7, 10568 (2016).
[Crossref] [PubMed]

H. Hajian, I. D. Rukhlenko, P. T. Leung, H. Caglayan, and E. Ozbay, “Guided plasmon modes of a graphene-coated Kerr slab,” Plasmonics 11(3), 735–741 (2016).
[Crossref]

T. Gric, “Surface-Plasmon-Polaritons at the Interface of Nanostructured Metamaterials,” Prog. Electromag. Res. M 46, 165–172 (2016).
[Crossref]

T. Xu and H. J. Lezec, “Visible-frequency asymmetric transmission devices incorporating a hyperbolic metamaterial,” Nat. Commun.  5, 4141 (2016).
[Crossref]

B. Orazbayev, M. Beruete, and I. Khromova, “Tunable beam steering enabled by graphene metamaterials,” Opt. Express 24(8), 8848–8861 (2016).
[Crossref] [PubMed]

2015 (5)

F. T. Gundogdu, A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Asymmetric transmission in prisms using structures and materials with isotropic-type dispersion,” Opt. Express 23(19), 24120–24132 (2015).
[Crossref] [PubMed]

L. Zinkiewicz, J. Haberko, and P. Wasylczyk, “Highly asymmetric near infrared light transmission in an all-dielectric grating-on-mirror photonic structure,” Opt. Express 23(4), 4206–4211 (2015).
[Crossref] [PubMed]

P. Rodriguez-Ulibarri, V. Pacheco-Pena, M. Navarro-Cia, A.E. Serebryannikov, and M. Beruete, “Experimental demonstration of deflection angle tuning in unidirectional fishnet metamaterials at millimeter-waves,” Appl. Phys. Lett. 106(6), 061109 (2015).
[Crossref]

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun.  6, 6334 (2015).
[Crossref] [PubMed]

A. E. Serebryannikov, S. Nojima, K. B. Alici, and E. Ozbay, “Effect of in-material losses on terahertz absorption, transmission, and reflection in photonic crystals made of polar dielectrics,” J. Appl. Phys. 118(13), 133101 (2015).
[Crossref]

2014 (9)

A. E. Serebryannikov, S. Nojima, and E. Ozbay, “One-way absorption of terahertz waves in rod-type and multilayer structures containing polar dielectrics,” Phys. Rev. B 90(23), 235126 (2014).
[Crossref]

M. Kafesaki, A. A. Basharin, E. N. Economou, and C. M. Soukoulis, “THz metamaterials made of phonon-polariton materials,” Photon. Nanostr. Fundam. Appl. 12(4), 376–386 (2014).
[Crossref]

R. I. Merino, M. F. Acosta, and V. M. Orera, “New polaritonic materials in the THz range made of directionally solidified halide eutectics,” J. Eur. Ceram. Soc. 34(9), 2061–2069 (2014).
[Crossref]

Y. Fu, L. Xu, Z.H. Hang, and H. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014).
[Crossref]

Y. Zhou, Y.-Q. Dong, R.-H. Fan, Q. Hu, R.-W. Peng, and M. Wang, “Asymmetric transmission of terahertz waves through a graphene-loaded metal grating,” Appl. Phys. Lett. 105(4), 041114 (2014).
[Crossref]

A. E. Serebryannikov, E. Ozbay, and S. Nojima, “Asymmetric transmission of terahertz waves using polar dielectrics,” Opt. Express 22(3), 3075–3088 (2014).
[Crossref] [PubMed]

Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, and D. Tang, “Critical coupling with graphene-based hyperbolic metamaterials,” Sci. Rep.  4, 5483 (2014).
[Crossref] [PubMed]

Y. Xiang, J. Guo, X. Dai, S. Wen, and D. Tang, “Engineered surface Bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express 22(3), 3054–3062 (2014).
[Crossref] [PubMed]

I. Khromova, A. Andryieuski, and A. Lavrinenko, “Ultrasensitive terahertz/infrared waveguide modulators based on multilayer graphene metamaterials,” Laser Photon. Rev. 8(6), 916–923 (2014).
[Crossref]

2013 (8)

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

Y. Yao, M. A. Kats, P. Gevenet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad Electrical Tuning of Graphene-Loaded Plasmonic Antennas,” Nano Lett. 13(3), 12571264 (2013).
[Crossref] [PubMed]

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophoton.  7(1), 073089 (2013).
[Crossref]

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

A. E. Serebryannikov and A. Lakhtakia, “Wideband switchable unidirectional transmission in a photonic crystal with a periodically nonuniform pupil,” Opt. Lett. 38(17), 3279–3282 (2013).
[Crossref] [PubMed]

A. E. Serebryannikov and E. Ozbay, “One-way Rayleigh-Wood anomalies and tunable narrowband transmission in photonic crystal gratings with broken structural symmetry,” Phys. Rev. A 87(5), 053804 (2013).
[Crossref]

P. Rodriguez-Ulibarri, M. Beruete, M. Navarro-Cia, and A. E. Serebryannikov, “Wideband unidirectional transmission with tunable sign-switchable refraction and deflection in nonsymmetric structures,” Phys. Rev. B 88(16), 165137 (2013).
[Crossref]

2012 (4)

A. E. Serebryannikov, K. B. Alici, T. Magath, A. O. Cakmak, and E. Ozbay, “Asymmetric Fabry-Perot-type transmission in photonic-crystal gratings with one-sided corrugations at a two-way coupling,” Phys. Rev. A 86(5), 053835 (2012).
[Crossref]

A. Yu. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-Antenna Sandwich Photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

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

2011 (4)

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single-and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).
[Crossref]

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett. 106(8), 084301 (2011).
[Crossref] [PubMed]

C. Lu, X. Hu, Y. Zhang, Z. Li, X. Xu, and et al.., “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84(3), 035128 (2011).
[Crossref]

2010 (2)

2009 (1)

2008 (1)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129(1), 012004 (2008).

2007 (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mat. 6, 183–191 (2007).
[Crossref]

2006 (1)

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles,,“One-way diffraction grating,” Phys. Rev. E 74(5), 056611 (2006).
[Crossref]

2005 (1)

Acosta, M. F.

R. I. Merino, M. F. Acosta, and V. M. Orera, “New polaritonic materials in the THz range made of directionally solidified halide eutectics,” J. Eur. Ceram. Soc. 34(9), 2061–2069 (2014).
[Crossref]

Ajayan, P. M.

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-Antenna Sandwich Photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Alici, K. B.

A. E. Serebryannikov, S. Nojima, K. B. Alici, and E. Ozbay, “Effect of in-material losses on terahertz absorption, transmission, and reflection in photonic crystals made of polar dielectrics,” J. Appl. Phys. 118(13), 133101 (2015).
[Crossref]

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A. E. Serebryannikov, S. Nojima, K. B. Alici, and E. Ozbay, “Effect of in-material losses on terahertz absorption, transmission, and reflection in photonic crystals made of polar dielectrics,” J. Appl. Phys. 118(13), 133101 (2015).
[Crossref]

A. E. Serebryannikov, E. Ozbay, and S. Nojima, “Asymmetric transmission of terahertz waves using polar dielectrics,” Opt. Express 22(3), 3075–3088 (2014).
[Crossref] [PubMed]

A. E. Serebryannikov, S. Nojima, and E. Ozbay, “One-way absorption of terahertz waves in rod-type and multilayer structures containing polar dielectrics,” Phys. Rev. B 90(23), 235126 (2014).
[Crossref]

Nordlander, P.

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-Antenna Sandwich Photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Norris, T. B.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun.  7, 10568 (2016).
[Crossref] [PubMed]

Novoselov, K. S.

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

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mat. 6, 183–191 (2007).
[Crossref]

Orazbayev, B.

Orera, V. M.

R. I. Merino, M. F. Acosta, and V. M. Orera, “New polaritonic materials in the THz range made of directionally solidified halide eutectics,” J. Eur. Ceram. Soc. 34(9), 2061–2069 (2014).
[Crossref]

Ostler, M.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single-and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).
[Crossref]

Othman, M. A. K.

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

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophoton.  7(1), 073089 (2013).
[Crossref]

Ozbay, E.

H. Hajian, H. Caglayan, and E. Ozbay, “Long-range Tamm surface plasmons supported by graphene-dielectric metamaterials,” J. Appl. Phys. 121(3), 033101 (2017).
[Crossref]

H. Hajian, I. D. Rukhlenko, P. T. Leung, H. Caglayan, and E. Ozbay, “Guided plasmon modes of a graphene-coated Kerr slab,” Plasmonics 11(3), 735–741 (2016).
[Crossref]

F. T. Gundogdu, A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Asymmetric transmission in prisms using structures and materials with isotropic-type dispersion,” Opt. Express 23(19), 24120–24132 (2015).
[Crossref] [PubMed]

A. E. Serebryannikov, S. Nojima, K. B. Alici, and E. Ozbay, “Effect of in-material losses on terahertz absorption, transmission, and reflection in photonic crystals made of polar dielectrics,” J. Appl. Phys. 118(13), 133101 (2015).
[Crossref]

A. E. Serebryannikov, E. Ozbay, and S. Nojima, “Asymmetric transmission of terahertz waves using polar dielectrics,” Opt. Express 22(3), 3075–3088 (2014).
[Crossref] [PubMed]

A. E. Serebryannikov, S. Nojima, and E. Ozbay, “One-way absorption of terahertz waves in rod-type and multilayer structures containing polar dielectrics,” Phys. Rev. B 90(23), 235126 (2014).
[Crossref]

A. E. Serebryannikov and E. Ozbay, “One-way Rayleigh-Wood anomalies and tunable narrowband transmission in photonic crystal gratings with broken structural symmetry,” Phys. Rev. A 87(5), 053804 (2013).
[Crossref]

A. E. Serebryannikov, K. B. Alici, T. Magath, A. O. Cakmak, and E. Ozbay, “Asymmetric Fabry-Perot-type transmission in photonic-crystal gratings with one-sided corrugations at a two-way coupling,” Phys. Rev. A 86(5), 053835 (2012).
[Crossref]

A. E. Serebryannikov and E. Ozbay, “Unidirectional transmission in non-symmetric gratings containing metallic layers,” Opt. Express 17(16), 13335–13345 (2009).
[Crossref] [PubMed]

Pacheco-Pena, V.

P. Rodriguez-Ulibarri, V. Pacheco-Pena, M. Navarro-Cia, A.E. Serebryannikov, and M. Beruete, “Experimental demonstration of deflection angle tuning in unidirectional fishnet metamaterials at millimeter-waves,” Appl. Phys. Lett. 106(6), 061109 (2015).
[Crossref]

Peng, R.-W.

Y. Zhou, Y.-Q. Dong, R.-H. Fan, Q. Hu, R.-W. Peng, and M. Wang, “Asymmetric transmission of terahertz waves through a graphene-loaded metal grating,” Appl. Phys. Lett. 105(4), 041114 (2014).
[Crossref]

Perruisseau-Carrier, J.

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun.  6, 6334 (2015).
[Crossref] [PubMed]

Polini, M.

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

Pruneri, V.

D. Rodrigo, A. Tittl, O. Limaj, F. J. Garcia de Abajo, V. Pruneri, and H. Altug, “Double-layer graphene for enhanced tunable infrared plasmonics,” Light: Sci. Appl. 6, e16277 (2017).
[Crossref]

Qin, S.

J. Zhao, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Tunable asymmetric transmission of THz wave through a graphene chiral metasurface,” J. Opt.  18(9), 095001 (2016).
[Crossref]

Ren, G.

Rodrigo, D.

D. Rodrigo, A. Tittl, O. Limaj, F. J. Garcia de Abajo, V. Pruneri, and H. Altug, “Double-layer graphene for enhanced tunable infrared plasmonics,” Light: Sci. Appl. 6, e16277 (2017).
[Crossref]

Rodriguez-Ulibarri, P.

P. Rodriguez-Ulibarri, V. Pacheco-Pena, M. Navarro-Cia, A.E. Serebryannikov, and M. Beruete, “Experimental demonstration of deflection angle tuning in unidirectional fishnet metamaterials at millimeter-waves,” Appl. Phys. Lett. 106(6), 061109 (2015).
[Crossref]

P. Rodriguez-Ulibarri, M. Beruete, M. Navarro-Cia, and A. E. Serebryannikov, “Wideband unidirectional transmission with tunable sign-switchable refraction and deflection in nonsymmetric structures,” Phys. Rev. B 88(16), 165137 (2013).
[Crossref]

Romeu, J.

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun.  6, 6334 (2015).
[Crossref] [PubMed]

Rotenberg, E.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single-and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).
[Crossref]

Rukhlenko, I. D.

H. Hajian, I. D. Rukhlenko, P. T. Leung, H. Caglayan, and E. Ozbay, “Guided plasmon modes of a graphene-coated Kerr slab,” Plasmonics 11(3), 735–741 (2016).
[Crossref]

Sambles, J. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles,,“One-way diffraction grating,” Phys. Rev. E 74(5), 056611 (2006).
[Crossref]

Serebryannikov, A. E.

F. T. Gundogdu, A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Asymmetric transmission in prisms using structures and materials with isotropic-type dispersion,” Opt. Express 23(19), 24120–24132 (2015).
[Crossref] [PubMed]

A. E. Serebryannikov, S. Nojima, K. B. Alici, and E. Ozbay, “Effect of in-material losses on terahertz absorption, transmission, and reflection in photonic crystals made of polar dielectrics,” J. Appl. Phys. 118(13), 133101 (2015).
[Crossref]

A. E. Serebryannikov, E. Ozbay, and S. Nojima, “Asymmetric transmission of terahertz waves using polar dielectrics,” Opt. Express 22(3), 3075–3088 (2014).
[Crossref] [PubMed]

A. E. Serebryannikov, S. Nojima, and E. Ozbay, “One-way absorption of terahertz waves in rod-type and multilayer structures containing polar dielectrics,” Phys. Rev. B 90(23), 235126 (2014).
[Crossref]

A. E. Serebryannikov and E. Ozbay, “One-way Rayleigh-Wood anomalies and tunable narrowband transmission in photonic crystal gratings with broken structural symmetry,” Phys. Rev. A 87(5), 053804 (2013).
[Crossref]

A. E. Serebryannikov and A. Lakhtakia, “Wideband switchable unidirectional transmission in a photonic crystal with a periodically nonuniform pupil,” Opt. Lett. 38(17), 3279–3282 (2013).
[Crossref] [PubMed]

P. Rodriguez-Ulibarri, M. Beruete, M. Navarro-Cia, and A. E. Serebryannikov, “Wideband unidirectional transmission with tunable sign-switchable refraction and deflection in nonsymmetric structures,” Phys. Rev. B 88(16), 165137 (2013).
[Crossref]

A. E. Serebryannikov, K. B. Alici, T. Magath, A. O. Cakmak, and E. Ozbay, “Asymmetric Fabry-Perot-type transmission in photonic-crystal gratings with one-sided corrugations at a two-way coupling,” Phys. Rev. A 86(5), 053835 (2012).
[Crossref]

A. E. Serebryannikov and E. Ozbay, “Unidirectional transmission in non-symmetric gratings containing metallic layers,” Opt. Express 17(16), 13335–13345 (2009).
[Crossref] [PubMed]

T. Magath and A. E. Serebryannikov, “Fast iterative, coupled-integral-equation technique for inhomogeneous profiled and periodic slabs,” J. Opt. Soc. Am. A 22(11), 2405–2418 (2005).
[Crossref]

Serebryannikov, A.E.

P. Rodriguez-Ulibarri, V. Pacheco-Pena, M. Navarro-Cia, A.E. Serebryannikov, and M. Beruete, “Experimental demonstration of deflection angle tuning in unidirectional fishnet metamaterials at millimeter-waves,” Appl. Phys. Lett. 106(6), 061109 (2015).
[Crossref]

Seyller, T.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single-and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).
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Shadrinov, I. V.

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

Y. Yao, M. A. Kats, P. Gevenet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad Electrical Tuning of Graphene-Loaded Plasmonic Antennas,” Nano Lett. 13(3), 12571264 (2013).
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Soukoulis, C. M.

M. Kafesaki, A. A. Basharin, E. N. Economou, and C. M. Soukoulis, “THz metamaterials made of phonon-polariton materials,” Photon. Nanostr. Fundam. Appl. 12(4), 376–386 (2014).
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S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84(3), 035128 (2011).
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A. N. Morozovska, A. I. Kurchak, and M. V. Strikha, “Graphene Exfoliation at a Ferroelectric Domain Wall Induced by the Piezoelectric Effect: Impact on the Conductance of the Graphene Channel,” Phys. Rev. Appl.  8(5), 054004 (2017).
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Sun, Z.

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

Tang, D.

Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, and D. Tang, “Critical coupling with graphene-based hyperbolic metamaterials,” Sci. Rep.  4, 5483 (2014).
[Crossref] [PubMed]

Y. Xiang, J. Guo, X. Dai, S. Wen, and D. Tang, “Engineered surface Bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express 22(3), 3054–3062 (2014).
[Crossref] [PubMed]

Tian, J.

Tittl, A.

D. Rodrigo, A. Tittl, O. Limaj, F. J. Garcia de Abajo, V. Pruneri, and H. Altug, “Double-layer graphene for enhanced tunable infrared plasmonics,” Light: Sci. Appl. 6, e16277 (2017).
[Crossref]

van der Marel, D.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single-and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).
[Crossref]

Walter, A. L.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single-and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).
[Crossref]

Wang, M.

Y. Zhou, Y.-Q. Dong, R.-H. Fan, Q. Hu, R.-W. Peng, and M. Wang, “Asymmetric transmission of terahertz waves through a graphene-loaded metal grating,” Appl. Phys. Lett. 105(4), 041114 (2014).
[Crossref]

Wang, Y.

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-Antenna Sandwich Photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Wasylczyk, P.

Wen, S.

White, K. R.

M. J. Lockyear, A. P. Hibbins, K. R. White, and J. R. Sambles,,“One-way diffraction grating,” Phys. Rev. E 74(5), 056611 (2006).
[Crossref]

Wu, J.

Xiang, Y.

Xu, L.

Y. Fu, L. Xu, Z.H. Hang, and H. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014).
[Crossref]

Xu, T.

T. Xu and H. J. Lezec, “Visible-frequency asymmetric transmission devices incorporating a hyperbolic metamaterial,” Nat. Commun.  5, 4141 (2016).
[Crossref]

Xu, X.

Y. Huang, Z. Yao, F. Hu, C. Liu, L. Yu, Y. Lin, and X. Xu, “Tunable circular polarization conversion and asymmetric transmission of planar chiral graphene-metamaterial in terahertz region,” Carbon 119, 305–313 (2017).
[Crossref]

C. Lu, X. Hu, Y. Zhang, Z. Li, X. Xu, and et al.., “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

Yao, Y.

Y. Yao, M. A. Kats, P. Gevenet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad Electrical Tuning of Graphene-Loaded Plasmonic Antennas,” Nano Lett. 13(3), 12571264 (2013).
[Crossref] [PubMed]

Yao, Z.

Y. Huang, Z. Yao, F. Hu, C. Liu, L. Yu, Y. Lin, and X. Xu, “Tunable circular polarization conversion and asymmetric transmission of planar chiral graphene-metamaterial in terahertz region,” Carbon 119, 305–313 (2017).
[Crossref]

Ye, W.-M.

Yu, L.

Y. Huang, Z. Yao, F. Hu, C. Liu, L. Yu, Y. Lin, and X. Xu, “Tunable circular polarization conversion and asymmetric transmission of planar chiral graphene-metamaterial in terahertz region,” Carbon 119, 305–313 (2017).
[Crossref]

Yu, N.

Y. Yao, M. A. Kats, P. Gevenet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad Electrical Tuning of Graphene-Loaded Plasmonic Antennas,” Nano Lett. 13(3), 12571264 (2013).
[Crossref] [PubMed]

Yuan, X.

J. Zhao, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Tunable asymmetric transmission of THz wave through a graphene chiral metasurface,” J. Opt.  18(9), 095001 (2016).
[Crossref]

Yuan, X.-D.

Zen, C.

Zhang, H.

Y. Xiang, X. Dai, J. Guo, H. Zhang, S. Wen, and D. Tang, “Critical coupling with graphene-based hyperbolic metamaterials,” Sci. Rep.  4, 5483 (2014).
[Crossref] [PubMed]

Zhang, J.

J. Zhao, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Tunable asymmetric transmission of THz wave through a graphene chiral metasurface,” J. Opt.  18(9), 095001 (2016).
[Crossref]

Zhang, S.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun.  7, 10568 (2016).
[Crossref] [PubMed]

Zhang, Y.

C. Lu, X. Hu, Y. Zhang, Z. Li, X. Xu, and et al.., “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

Zhao, J.

J. Zhao, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Tunable asymmetric transmission of THz wave through a graphene chiral metasurface,” J. Opt.  18(9), 095001 (2016).
[Crossref]

Zhao, W.

Zheng, S.

Zhong, Z.

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun.  7, 10568 (2016).
[Crossref] [PubMed]

Zhou, Y.

Y. Zhou, Y.-Q. Dong, R.-H. Fan, Q. Hu, R.-W. Peng, and M. Wang, “Asymmetric transmission of terahertz waves through a graphene-loaded metal grating,” Appl. Phys. Lett. 105(4), 041114 (2014).
[Crossref]

Zhu, B.

Zhu, Z.

J. Zhao, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Tunable asymmetric transmission of THz wave through a graphene chiral metasurface,” J. Opt.  18(9), 095001 (2016).
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Zinkiewicz, L.

Appl. Phys. Lett. (5)

A. Yu. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

C. Lu, X. Hu, Y. Zhang, Z. Li, X. Xu, and et al.., “Ultralow power all-optical diode in photonic crystal heterostructures with broken spatial inversion symmetry,” Appl. Phys. Lett. 99(5), 051107 (2011).
[Crossref]

P. Rodriguez-Ulibarri, V. Pacheco-Pena, M. Navarro-Cia, A.E. Serebryannikov, and M. Beruete, “Experimental demonstration of deflection angle tuning in unidirectional fishnet metamaterials at millimeter-waves,” Appl. Phys. Lett. 106(6), 061109 (2015).
[Crossref]

Y. Fu, L. Xu, Z.H. Hang, and H. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014).
[Crossref]

Y. Zhou, Y.-Q. Dong, R.-H. Fan, Q. Hu, R.-W. Peng, and M. Wang, “Asymmetric transmission of terahertz waves through a graphene-loaded metal grating,” Appl. Phys. Lett. 105(4), 041114 (2014).
[Crossref]

Carbon (1)

Y. Huang, Z. Yao, F. Hu, C. Liu, L. Yu, Y. Lin, and X. Xu, “Tunable circular polarization conversion and asymmetric transmission of planar chiral graphene-metamaterial in terahertz region,” Carbon 119, 305–313 (2017).
[Crossref]

J. Appl. Phys. (2)

A. E. Serebryannikov, S. Nojima, K. B. Alici, and E. Ozbay, “Effect of in-material losses on terahertz absorption, transmission, and reflection in photonic crystals made of polar dielectrics,” J. Appl. Phys. 118(13), 133101 (2015).
[Crossref]

H. Hajian, H. Caglayan, and E. Ozbay, “Long-range Tamm surface plasmons supported by graphene-dielectric metamaterials,” J. Appl. Phys. 121(3), 033101 (2017).
[Crossref]

J. Eur. Ceram. Soc. (1)

R. I. Merino, M. F. Acosta, and V. M. Orera, “New polaritonic materials in the THz range made of directionally solidified halide eutectics,” J. Eur. Ceram. Soc. 34(9), 2061–2069 (2014).
[Crossref]

J. Nanophoton (1)

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophoton.  7(1), 073089 (2013).
[Crossref]

J. Opt (1)

J. Zhao, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Tunable asymmetric transmission of THz wave through a graphene chiral metasurface,” J. Opt.  18(9), 095001 (2016).
[Crossref]

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

J. Phys.: Conf. Ser. (1)

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Laser Photon. Rev. (1)

I. Khromova, A. Andryieuski, and A. Lavrinenko, “Ultrasensitive terahertz/infrared waveguide modulators based on multilayer graphene metamaterials,” Laser Photon. Rev. 8(6), 916–923 (2014).
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Light: Sci. Appl. (1)

D. Rodrigo, A. Tittl, O. Limaj, F. J. Garcia de Abajo, V. Pruneri, and H. Altug, “Double-layer graphene for enhanced tunable infrared plasmonics,” Light: Sci. Appl. 6, e16277 (2017).
[Crossref]

Nano Lett. (2)

Y. Yao, M. A. Kats, P. Gevenet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad Electrical Tuning of Graphene-Loaded Plasmonic Antennas,” Nano Lett. 13(3), 12571264 (2013).
[Crossref] [PubMed]

Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-Antenna Sandwich Photodetector,” Nano Lett. 12(7), 3808–3813 (2012).
[Crossref] [PubMed]

Nat. Commun (3)

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun.  6, 6334 (2015).
[Crossref] [PubMed]

Y.-C. Chang, C.-H. Liu, C.-H. Liu, S. Zhang, S. R. Marder, E. E. Narimanov, Z. Zhong, and T. B. Norris, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun.  7, 10568 (2016).
[Crossref] [PubMed]

T. Xu and H. J. Lezec, “Visible-frequency asymmetric transmission devices incorporating a hyperbolic metamaterial,” Nat. Commun.  5, 4141 (2016).
[Crossref]

Nat. Mat. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mat. 6, 183–191 (2007).
[Crossref]

Nat. Photon. (2)

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

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

Nat. Phys. (1)

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. van der Marel, and A. B. Kuzmenko, “Giant Faraday rotation in single-and multilayer graphene,” Nat. Phys. 7, 48–51 (2011).
[Crossref]

Opt. Express (12)

A. E. Serebryannikov and E. Ozbay, “Unidirectional transmission in non-symmetric gratings containing metallic layers,” Opt. Express 17(16), 13335–13345 (2009).
[Crossref] [PubMed]

W.-M. Ye, X.-D. Yuan, C.-C. Guo, and C. Zen, “Unidirectional transmission in non-symmetric gratings made of isotropic material,” Opt. Express 18(8), 7590–7595 (2010).
[Crossref] [PubMed]

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

Y. Xiang, J. Guo, X. Dai, S. Wen, and D. Tang, “Engineered surface Bloch waves in graphene-based hyperbolic metamaterials,” Opt. Express 22(3), 3054–3062 (2014).
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A. E. Serebryannikov, E. Ozbay, and S. Nojima, “Asymmetric transmission of terahertz waves using polar dielectrics,” Opt. Express 22(3), 3075–3088 (2014).
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L. Zinkiewicz, J. Haberko, and P. Wasylczyk, “Highly asymmetric near infrared light transmission in an all-dielectric grating-on-mirror photonic structure,” Opt. Express 23(4), 4206–4211 (2015).
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F. T. Gundogdu, A. E. Serebryannikov, A. O. Cakmak, and E. Ozbay, “Asymmetric transmission in prisms using structures and materials with isotropic-type dispersion,” Opt. Express 23(19), 24120–24132 (2015).
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B. Orazbayev, M. Beruete, and I. Khromova, “Tunable beam steering enabled by graphene metamaterials,” Opt. Express 24(8), 8848–8861 (2016).
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J. Wu, L. Jiang, J. Guo, X. Dai, Y. Xiang, and S. Wen, “Tunable perfect absorption at infrared frequencies by a graphene-hBN hyper crystal,” Opt. Express 24(15), 17103–17114 (2016).
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Opt. Lett. (2)

Photon. Nanostr. Fundam. Appl. (1)

M. Kafesaki, A. A. Basharin, E. N. Economou, and C. M. Soukoulis, “THz metamaterials made of phonon-polariton materials,” Photon. Nanostr. Fundam. Appl. 12(4), 376–386 (2014).
[Crossref]

Phys. Rev. A (2)

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[Crossref]

A. E. Serebryannikov, K. B. Alici, T. Magath, A. O. Cakmak, and E. Ozbay, “Asymmetric Fabry-Perot-type transmission in photonic-crystal gratings with one-sided corrugations at a two-way coupling,” Phys. Rev. A 86(5), 053835 (2012).
[Crossref]

Phys. Rev. Appl (2)

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Plasmonics (1)

H. Hajian, I. D. Rukhlenko, P. T. Leung, H. Caglayan, and E. Ozbay, “Guided plasmon modes of a graphene-coated Kerr slab,” Plasmonics 11(3), 735–741 (2016).
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Figures (7)

Fig. 1
Fig. 1 (a) Geometry of a single period of the studied structure; (b) Schematic showing connection between deflection and asymmetric transmission; r−1, t−1, and r0 denote reflection and transmission of the order m = −1 and reflection of the order m = 0, respectively; fw and bw stand for forward and backward illumination cases; (c) Permittivity of LiF, εLiF, Re(εLiF) -solid blue line, Im(εLiF) -dashed green line; (d) Permittivity of grapheme-dielectric metamaterial, Re ( ε ( x x ) g m )-solid red lines and Im ( ε ( x x ) g m )-dashed black lines; numbers near curves give values of µ in eV.
Fig. 2
Fig. 2 (a) Schematic of the layered graphene-dielectric metamaterial. Six layers of graphene and six dielectric layers are shown here; (b) Permittivity of LiF, εLiF, and graphene-dielectric metamaterial, ε ( x x ) g m in the studied frequency range: Re(εLiF)-solid blue line, Im(εLiF) -dashed green line; Re ( ε ( x x ) g m )-dash-dotted red lines and Im ( ε ( x x ) g m )-dotted black lines; numbers at the red lines mean µ in eV; rectangular rose bars at the plot top approximately indicate location of the range of 0 < Re ( ε ( x x ) g m ) < 0.5 at µ = 0.162 eV and µ = 0.3 eV; rectangular blue bar at the plot bottom approximately indicates location of the range of 0 < Re(εLiF) < 0.5.
Fig. 3
Fig. 3 (a) First-order forward-case transmittance, t 1 , at θ = 60°; (b) first-order backward-case transmittance, t 1 , at θ = 60°; (c) first-order forward-case transmittance, t 1 , at θ = 82°; (d) first-order backward-case transmittance, t 1 , at θ = 82°; solid black line -µ = 0.01 eV, dashed red line -µ = 0.162 eV; dotted violet line -µ = 0.23 eV; dash-dotted green line -µ = 0.3 eV; solid light-blue line -µ = 0.7 eV; thin solid dark-blue lines -zero-order transmittance, t 0 = t 0 = t 0 (nonzero mainly at f > 24 THz); graphene metamaterial is located below the LiF slab; inset in plot (d) shows fragment of plot (c); fw and bw stand for forward and backward cases; asterisks and number signs indicate spectral location of some of the regimes of tunable asymmetric transmission and tunable deflection, respectively. Numbers near some of the curves indicate µ in eV (in the same color as the curves).
Fig. 4
Fig. 4 First-order forward-case transmittance, t 1 , at θ = 60°; (b) first-order backard-case transmittance, t 1 , at θ = 60°; (c) first-order forward-case transmittance, t 1 , at θ = 82°; (d) first-order backward-case transmittance, t 1 , at θ = 82°; solid black line -µ = 0.01 eV, dashed red line -µ = 0.162 eV; dotted violet line -µ = 0.23 eV; dash-dotted green line -µ = 0.3 eV; solid light-blue line -µ = 0.7 eV; thin solid dark-blue lines -zero-order transmittance, t 0 = t 0 = t 0 (nonzero mainly at f > 24 THz); slab of graphene-dielectric metamaterial is located between the Si grating and the LiF slab, as shown in Fig. 1(a); insets in plots (b), (d) are fragments of plots (a), (c), respectively; fw, bw, and asterisks and number signs have the same meaning as in Fig. 3. Numbers near some of the curves indicate µ in eV (in the same color as the curves).
Fig. 5
Fig. 5 Electric field distribution within one period of the structure, in which the slab of metamaterial is located between the Si grating and the LiF slab, at f = 24.57 THz and θ = 60°, (a) µ = 0.01 eV and (b) µ = 0.7 eV at forward-case illumination, and (c) µ = 0.01 eV and (d) µ = 0.7 eV at backward-case illumination. Solid lines show location of the structural components.
Fig. 6
Fig. 6 (a) First-order forward-case transmittance, t 1 , and (b) first-order backward-case transmittance, t 1 at θ = 60° in the vicinity of 25 THz; solid black line -µ = 0.01 eV, dashed red line -µ = 0.162 eV; dotted violet line -µ = 0.23 eV; dash-dotted green line µ = 0.3 eV; solid light-blue line -µ = 0.7 eV; fw, bw, number signs, and numbers near some of the curves have the same meaning as in Figs. 3 and 4.
Fig. 7
Fig. 7 Same as Fig. 6 but in the vicinity of 17 THz; asterisk sign has the same meaning as in Figs. 3 and 4.

Equations (7)

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ϕ 1 = arcsin ( sin θ 2 π / k L ) ,
ε L i F = ε + ( ε 0 ε ) ω T 2 / ( ω T 2 ω 2 + i Γ ω ) ,
σ i n t r a = e 2 4 i 2 π { 16 k B T Ω ln ( 2 cosh ( μ 2 k B T ) ) } ,
σ i n t r a = e 2 4 1 2 + e 2 4 1 π arctan ( Ω 2 μ 2 k B T ) e 2 4 i 2 π ln ( Ω + 2 μ ) 2 ( Ω 2 μ ) 2 + ( 2 k B T ) 2 ,
ε ( x x ) g m = ε ( z z ) g m = ε d i σ / ( ω ε 0 d ) ,
ε ( y y ) g m = ε d ,
y = ( t S i / 2 ) [ 1 + cos ( 2 π x / L ) ] ,

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