Abstract

The THz and infrared photonic dispersion relations of superlattices composed of polaritonic material and bismuth (Bi) layers are theoretically investigated. The semimetal Bi presents a far-infrared response described by a Drude-like formula with a large high-frequency background dielectric constant. We have considered three different polaritonic materials: NaBr, LiCl and LiH, such that the Bi plasma frequency lies above, in-between and below the characteristic frequencies of the polaritonic materials, respectively. Investigating the photonic band structure of each superlattice, we have found that when the Bi plasma frequency lies below the polaritonic gap, appears a photonic pass band of negative dispersion for TM modes just above the longitudinal-optical phonon frequency, attributed to the frequency dependence of the permittivity for the polaritonic material and the large high-frequency background dielectric constant for Bi, that can be relevant to the metamaterials community.

© 2015 Optical Society of America

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References

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2015 (2)

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

F. Díaz-Monge, A. Paredes-Juárez, D. A. Iakushev, N. M. Makarov, and F. Pérez-Rodríguez, “THz photonic bands of periodic stacks composed of resonant dielectric and nonlocal metal,” Opt. Mater. Express,  5, 361–372 (2015).
[Crossref]

2014 (1)

2013 (5)

A. Orlov, I. Iorsh, P. Belov, and Y. Kivshar, “Complex band structure of nanostructured metal-dielectric metamaterials,” Opt. Express 21, 1593–1598 (2013).
[Crossref] [PubMed]

M. Massaouti, A. A. Basharin, M. Kafesaki, M. F. Acosta, R. I. Merino, V. M. Orera, E. N. Economou, C. M. Soukoulis, and S. Tzortzakis, “Eutectic epsilon-near-zero metamaterial terahertz waveguides,” Opt. Lett. 38, 1140–1142 (2013).
[Crossref] [PubMed]

E. Sánchez-Mora, M. Fernández-Candelario, E. Gómez-Barojas, and F. Pérez-Rodríguez, “Influence of Fe Ions on the Optical Properties of Fe-ZnO Inverse Opals,” J. Supercond. Nov. Magn. 26, 2447–2449 (2013).
[Crossref]

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

A. A. Basharin, C. Mavidis, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Epsilon near zero based phenomena in metamaterials,” Phys. Rev. B 87, 155130 (2013).
[Crossref]

2012 (3)

S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
[Crossref]

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, Ch. Mavidis, J. García de Abajo, E. N. Economou, and C. M. Soukoulis, “Self-organization approach for THz polaritonic metamaterials,” Opt. Express 20, 14663–14682 (2012).
[Crossref] [PubMed]

2011 (2)

B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

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

2010 (3)

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
[Crossref]

J. Manzanares-Martínez, “Analytic expression for the effective plasma frequency in one-dimensional metallic-dielectric photonic crystal,” Progress In Electromagnetics Research M,  13, 189–202 (2010).
[Crossref]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

2009 (3)

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 61903 (2009).
[Crossref]

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
[Crossref]

A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90, 623–627 (2009).
[Crossref]

2007 (6)

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
[Crossref]

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[Crossref] [PubMed]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” App. Phys. Lett. 91, 183518 (2007).
[Crossref]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat Photonics 1, 224–227 (2007).
[Crossref]

S. Guenneau, A. Movchan, G. Pétursson, and S. A. Ramakrishna, “Acoustic metamaterials for sound focusing and confinement,” New J. Phys. 9, 399 (2007).
[Crossref]

2006 (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[Crossref]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[Crossref]

2005 (3)

X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
[Crossref]

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys.: Condens. Matter 17, 3717–3734 (2005).

A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72, 056609 (2005).
[Crossref]

2002 (2)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter 14, 4035–4044 (2002).

2001 (1)

S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001).
[Crossref] [PubMed]

2000 (2)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

1998 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

1987 (2)

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58 (20) 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58 (23) 2486–2489 (1987).
[Crossref] [PubMed]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Uspekhi 10, 509–514 (1968).
[Crossref]

1958 (1)

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109 (5) 1492–1505 (1958).
[Crossref]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Acosta, M. F.

Anderson, P. W.

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109 (5) 1492–1505 (1958).
[Crossref]

Argyros, A.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Avrutsky, I.

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Basharin, A. A.

Beere, H. E.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Belov, P.

Beltram, F.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Berry, E.

S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001).
[Crossref] [PubMed]

Bickauskaite, G.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Bityurin, N.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

Brongersma, M. L.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[Crossref] [PubMed]

Brun, M.

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 61903 (2009).
[Crossref]

Busso, M.

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B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
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A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90, 623–627 (2009).
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J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
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R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
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F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
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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, 035128 (2011).
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A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
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V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
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S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
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J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
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Tosti, G.

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
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Vamvakaki, M.

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G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

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V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
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X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
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X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
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J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
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AIP Conf. Proc. (1)

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
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App. Phys. Lett. (1)

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” App. Phys. Lett. 91, 183518 (2007).
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Appl. Phys. Lett. (3)

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X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
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J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

EAS Publications Series (1)

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
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J. Appl. Phys. (2)

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
[Crossref]

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
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J. Nanophoton. (1)

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

J. Phys.: Condens. Matter (3)

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys.: Condens. Matter 17, 3717–3734 (2005).

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter 14, 4035–4044 (2002).

J. Supercond. Nov. Magn. (1)

E. Sánchez-Mora, M. Fernández-Candelario, E. Gómez-Barojas, and F. Pérez-Rodríguez, “Influence of Fe Ions on the Optical Properties of Fe-ZnO Inverse Opals,” J. Supercond. Nov. Magn. 26, 2447–2449 (2013).
[Crossref]

JETP Letters (1)

A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90, 623–627 (2009).
[Crossref]

Nat Photonics (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat Photonics 1, 224–227 (2007).
[Crossref]

Nat. Commun. (1)

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Nature (1)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Nature Photonics (1)

S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
[Crossref]

New J. Phys. (1)

S. Guenneau, A. Movchan, G. Pétursson, and S. A. Ramakrishna, “Acoustic metamaterials for sound focusing and confinement,” New J. Phys. 9, 399 (2007).
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Opt. Express (3)

Opt. Lett. (1)

Opt. Mater. Express (1)

P. Soc. Photo-Opt. Ins. (1)

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Phys. Med. Biol. (1)

S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001).
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Phys. Rev. (1)

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109 (5) 1492–1505 (1958).
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Phys. Rev. B (3)

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84, 035128 (2011).
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Figures (8)

Fig. 1
Fig. 1 Scheme of a superlattice with two alternating non-magnetic polaritonic-material/bismuth layers. The system represents a uniaxial crystal with the c-axis parallel to the z direction.
Fig. 2
Fig. 2 Frequency dependence of the real (solid line, 1) and imaginary (dashed line, 2) parts of the parameter ε b ( ω ) ω d a / c calculated for a superlattice composed of alternating Bi and polaritonic layers.
Fig. 3
Fig. 3 Left panels: Curves of frequency ω versus η1 (10) [η2 (11)] for TE [TM] modes in a NaBr/Bi superlattice at θ = 45°. Right panels: s– and p–polarization reflectivity and transmissivity spectra for a stack of 50 NaBr/Bi bilayers in air.
Fig. 4
Fig. 4 Left panels: Curves of frequency ω versus η1 (10) [η2 (11)] for TE [TM] modes in a LiCl/Bi superlattice at θ = 45°. Right panels: s– and p–polarization reflectivity and transmissivity spectra for a stack of 50 LiCl/Bi bilayers in air.
Fig. 5
Fig. 5 Left panels: Curves of frequency ω versus η1 (10) [η2 (11)] for TE [TM] modes in a LiH/Bi superlattice at θ = 45°. Right panels: s– and p–polarization reflectivity and transmissivity spectra for a stack of 50 LiH/Bi bilayers in air.
Fig. 6
Fig. 6 Curves of ω versus the real (left column) and imaginary (right column) parts of the Bloch wave number kz for a LiH/Bi superlattice at θ = 45°, for both polarizations. The indices j and j′ correspond to the Fabry-Perot resonances in the polaritonic material and m in the Bi medium.
Fig. 7
Fig. 7 Bulk dispersion curves for the phonon-polariton (photon) modes in LiH, blue lines (Bi, red lines). The A and C solid lines (B and D dashed curves) correspond to the real (imaginary) parts of the wave vectors k z a and k z b for the electromagnetic modes in the LiH and Bi layers of the superlattice, as in Fig. 6. The indices j and j′ correspond to the Fabry-Perot resonances in the polaritonic material and m in the Bi medium.
Fig. 8
Fig. 8 s– and p–polarization reflectivity and transmissivity spectra at θ = 45° for a stack of 50 LiH/Bi bilayers in air. The thicknesses of the LiH and Bi layers are the same as those of the superlattice in Figs. 6 and 7.

Tables (1)

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Table 1 Parameters of the polaritonic materials

Equations (24)

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ε a = ε a , ( ω 2 ω LO 2 + i ω ν a ) / ( ω 2 ω TO 2 + i ω ν a ) ,
ε b = ε b , [ 1 ω P 2 / ( ω 2 + i ν b ω ) ] ,
cos ( k z Λ ) = cos ( k z a d a ) cos ( k z b d b ) α sin ( k z a d a ) sin ( k z b d b ) ,
α = { 1 2 [ ( k z a / k z b ) + ( k z b / k z a ) ] , for TE modes , 1 2 [ ( ε b k z a / ε a k z b ) + ( ε a k z b / ε b k z a ) ] , for TM modes .
ε x = ε y = ( ε a d a + ε b d b ) / Λ and ε z 1 = Λ 1 [ ( d a / ε a ) + ( d b / ε b ) ] .
k z a d a 1 , k z b d b 1 ,
ε x = ε y = ε b ( 1 [ 1 ( ω Λ / 2 c ) ε b tan [ ( ω Λ / 2 c ) ε b ] Λ ε b d a ( ε a ε b ) ] 1 ) ,
| ε b | ω Λ c d a Λ 1 ,
k z = { ( ε y ω 2 / c 2 ) k x 2 , for TE modes , ε x [ ( ω 2 / c 2 ) ( k x 2 / ε z ) ] , for TM modes .
k z = ω c η 1 , η 1 = ε y sin 2 θ ; for TE modes ,
k z = ω c η 2 , η 2 = ε x [ 1 ( sin 2 θ / ε z ) ] ; for TM modes .
ε x = ε y = ε ¯ ( 1 ω P 2 , eff ω ( ω + i ν b ) ) ,
ω P , eff = d b Λ ε b , ε ¯ ω P ,
ε ¯ = ( ε a , d a + ε b , d b ) / Λ .
ε x = ε y ε b , d b Λ ( 1 ω P , eff 2 ω ( ω + i ν b ) ) ,
ε x = ε y ε ˜ ( 1 ω P , eff 2 ω ( ω + i ν b ) ) ,
ω P , eff = d b Λ ε b , ε ˜ ω P ω P ,
ε ˜ = ( ε a ( 0 ) d a + ε b , d b ) / Λ .
ε x = ε y ε a . ω LO 2 ω TO 2 ω 2 ω TO 2 d a Λ + ε b , d b Λ .
ω 1 2 = ω TO 2 + ε a , d a ( ε b , d b Λ sin 2 θ ) ( ω LO 2 ω TO 2 ) ,
ω 2 2 = ω TO 2 + ε a , d a ε b , d b ( ω LO 2 ω TO 2 ) ,
[ k z a ] d a = j π , j = 1 , 2 , 3 , ,
[ k z b ] d b = π
ω * = ω LO ( 1 ω TO 2 sin 2 θ / ω LO 2 ε a , 1 sin 2 θ / ε a , ) 1 / 2 .

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