Abstract

Layered hyperbolic metamaterials are able to support bulk modes with wavevectors much larger than light in free space. These modes are the foundation of many proposed metamaterial devices. In this paper, we present experimental data measuring the dispersion relationship of these modes in infrared semiconductor hyperbolic metamaterials. The metamaterial optical properties are modeled by taking into account the functional form of the carrier density in the sample due to conduction band bending and the non-parabolicity of the effective mass. In two different samples, we observe multiple volume plasmon polariton modes, and the mode dispersion is traced out by using grating couplers with multiple periodicities. We close by discussing ways to improve these materials.

© 2017 Optical Society of America

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2016 (2)

A. A. Krokhin, J. Arriaga, L. N. Gumen, and V. P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93(7), 075418 (2016).
[Crossref]

D. Wei, C. Harris, C. C. Bomberger, J. Zhang, J. Zide, and S. Law, “Single-material semiconductor hyperbolic metamaterials,” Opt. Express 24(8), 8735–8745 (2016).
[Crossref] [PubMed]

2015 (8)

D. Blazek, M. Cada, and J. Pistora, “Surface plasmon polaritons at linearly graded semiconductor interfaces,” Opt. Express 23(5), 6264–6276 (2015).
[Crossref] [PubMed]

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91(19), 195147 (2015).
[Crossref]

T. Taliercio, V. N. Guilengui, L. Cerutti, J. B. Rodriguez, F. Barho, M. J. Rodrigo, F. Gonzalez-Posada, E. Tournié, M. Niehle, and A. Trampert, “Fano-like resonances sustained by Si doped InAsSb plasmonic resonators integrated in GaSb matrix,” Opt. Express 23(23), 29423–29433 (2015).
[Crossref] [PubMed]

N. Vasilantonakis, M. E. Nasir, W. Dickson, G. A. Wurtz, and A. V. Zayats, “Bulk plasmon-polaritons in hyperbolic nanorod metamaterial waveguides,” Laser Photonics Rev. 9(3), 345–353 (2015).
[Crossref] [PubMed]

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
[Crossref] [PubMed]

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

K. V. Sreekanth, K. H. Krishna, A. De Luca, and G. Strangi, “Large spontaneous emission rate enhancement in grating coupled hyperbolic metamaterials,” Sci. Rep. 4(1), 6340 (2015).
[Crossref] [PubMed]

2014 (6)

P. Shekhar and Z. Jacob, “Strong coupling in hyperbolic metamaterials,” Phys. Rev. B 90(4), 045313 (2014).
[Crossref]

S. V. Zhukovsky, A. A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. E. Sipe, “Photonic-band-gap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials,” Phys. Rev. A – At. Mol. Opt. Phys. 90, 1–11 (2014).

S. V. Zhukovsky, A. Andryieuski, J. E. Sipe, and A. V. Lavrinenko, “From surface to volume plasmons in hyperbolic metamaterials: General existence conditions for bulk high-k waves in metal-dielectric and graphene-dielectric multilayers,” Phys. Rev. B 90(15), 155429 (2014).
[Crossref]

K. V. Sreekanth, A. De Luca, and G. Strangi, “Excitation of volume plasmon polaritons in metal-dielectric metamaterials using 1D and 2D diffraction gratings,” J. Opt. 16(10), 105103 (2014).
[Crossref]

S. Law, R. Liu, and D. Wasserman, “Doped semiconductors with band-edge plasma frequencies,” J. Vac. Sci. Technol. B 32(5), 52601 (2014).
[Crossref]

P. Shekhar, J. Atkinson, and Z. Jacob, “Hyperbolic metamaterials: fundamentals and applications,” Nano Converg 1(1), 14 (2014).
[Crossref] [PubMed]

2013 (3)

S. V. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21(12), 14982–14987 (2013).
[Crossref] [PubMed]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Rev. 7(2), 265–271 (2013).
[Crossref]

2012 (6)

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[Crossref]

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
[Crossref]

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).
[Crossref] [PubMed]

S. Law, D. C. Adams, A. M. Taylor, and D. Wasserman, “Mid-infrared designer metals,” Opt. Express 20(11), 12155–12165 (2012).
[Crossref] [PubMed]

V. N. Guilengui, L. Cerutti, J. B. Rodriguez, E. Tournie, and T. Taliercio, “Localized surface plasmon resonances in highly doped semiconductors nanostructures,” Appl. Phys. Lett. 101(16), 161113 (2012).
[Crossref]

2011 (2)

M. Shahzad, G. Medhi, R. E. Peale, W. R. Buchwald, J. W. Cleary, R. Soref, G. D. Boreman, and O. Edwards, “Infrared surface plasmons on heavily doped silicon,” J. Appl. Phys. 110(12), 123105 (2011).
[Crossref]

J. C. Ginn, R. L. Jarecki, E. A. Shaner, and P. S. Davids, “Infrared plasmons on heavily-doped silicon,” J. Appl. Phys. 110(4), 043110 (2011).
[Crossref]

2009 (4)

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79(3), 035401 (2009).
[Crossref]

A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009).
[Crossref] [PubMed]

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1(3), 484 (2009).
[Crossref]

2008 (2)

2007 (1)

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

2006 (1)

J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046618 (2006).
[Crossref] [PubMed]

1961 (1)

M. Cardona, “Electron Effective Masses of InAs and GaAs as a Function of Temperature and Doping,” Phys. Rev. 121(3), 752–758 (1961).
[Crossref]

1957 (1)

W. G. Spitzer and H. Y. Fan, “Determination of Optical Constants and Carrier Effective Mass of Semiconductors,” Phys. Rev. 106(5), 882–890 (1957).
[Crossref]

Adams, D. C.

Alekseyev, L.

A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

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

Andersen, T.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
[Crossref] [PubMed]

Andryieuski, A.

S. V. Zhukovsky, A. Andryieuski, J. E. Sipe, and A. V. Lavrinenko, “From surface to volume plasmons in hyperbolic metamaterials: General existence conditions for bulk high-k waves in metal-dielectric and graphene-dielectric multilayers,” Phys. Rev. B 90(15), 155429 (2014).
[Crossref]

Arriaga, J.

A. A. Krokhin, J. Arriaga, L. N. Gumen, and V. P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93(7), 075418 (2016).
[Crossref]

Atkinson, J.

P. Shekhar, J. Atkinson, and Z. Jacob, “Hyperbolic metamaterials: fundamentals and applications,” Nano Converg 1(1), 14 (2014).
[Crossref] [PubMed]

Babicheva, V. E.

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

S. V. Zhukovsky, A. A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. E. Sipe, “Photonic-band-gap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials,” Phys. Rev. A – At. Mol. Opt. Phys. 90, 1–11 (2014).

Barho, F.

Basov, D. N.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
[Crossref] [PubMed]

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Berini, P.

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1(3), 484 (2009).
[Crossref]

Blazek, D.

Boltasseva, A.

Bomberger, C. C.

Boreman, G. D.

M. Shahzad, G. Medhi, R. E. Peale, W. R. Buchwald, J. W. Cleary, R. Soref, G. D. Boreman, and O. Edwards, “Infrared surface plasmons on heavily doped silicon,” J. Appl. Phys. 110(12), 123105 (2011).
[Crossref]

Bozhevolnyi, S. I.

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79(3), 035401 (2009).
[Crossref]

T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi 245(1), 9–19 (2008).
[Crossref]

Braun, P. X.

A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

Buchwald, W. R.

M. Shahzad, G. Medhi, R. E. Peale, W. R. Buchwald, J. W. Cleary, R. Soref, G. D. Boreman, and O. Edwards, “Infrared surface plasmons on heavily doped silicon,” J. Appl. Phys. 110(12), 123105 (2011).
[Crossref]

Cada, M.

Cardona, M.

M. Cardona, “Electron Effective Masses of InAs and GaAs as a Function of Temperature and Doping,” Phys. Rev. 121(3), 752–758 (1961).
[Crossref]

Cerutti, L.

Cheng, L.

A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

Cleary, J. W.

M. Shahzad, G. Medhi, R. E. Peale, W. R. Buchwald, J. W. Cleary, R. Soref, G. D. Boreman, and O. Edwards, “Infrared surface plasmons on heavily doped silicon,” J. Appl. Phys. 110(12), 123105 (2011).
[Crossref]

Cortes, C. L.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[Crossref]

Dai, S.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
[Crossref] [PubMed]

Davids, P. S.

J. C. Ginn, R. L. Jarecki, E. A. Shaner, and P. S. Davids, “Infrared plasmons on heavily-doped silicon,” J. Appl. Phys. 110(4), 043110 (2011).
[Crossref]

De Luca, A.

K. V. Sreekanth, K. H. Krishna, A. De Luca, and G. Strangi, “Large spontaneous emission rate enhancement in grating coupled hyperbolic metamaterials,” Sci. Rep. 4(1), 6340 (2015).
[Crossref] [PubMed]

K. V. Sreekanth, A. De Luca, and G. Strangi, “Excitation of volume plasmon polaritons in metal-dielectric metamaterials using 1D and 2D diffraction gratings,” J. Opt. 16(10), 105103 (2014).
[Crossref]

Dickson, W.

N. Vasilantonakis, M. E. Nasir, W. Dickson, G. A. Wurtz, and A. V. Zayats, “Bulk plasmon-polaritons in hyperbolic nanorod metamaterial waveguides,” Laser Photonics Rev. 9(3), 345–353 (2015).
[Crossref] [PubMed]

Drachev, V. P.

A. A. Krokhin, J. Arriaga, L. N. Gumen, and V. P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93(7), 075418 (2016).
[Crossref]

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Rev. 7(2), 265–271 (2013).
[Crossref]

Edwards, O.

M. Shahzad, G. Medhi, R. E. Peale, W. R. Buchwald, J. W. Cleary, R. Soref, G. D. Boreman, and O. Edwards, “Infrared surface plasmons on heavily doped silicon,” J. Appl. Phys. 110(12), 123105 (2011).
[Crossref]

Fan, H. Y.

W. G. Spitzer and H. Y. Fan, “Determination of Optical Constants and Carrier Effective Mass of Semiconductors,” Phys. Rev. 106(5), 882–890 (1957).
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S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
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S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
[Crossref] [PubMed]

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A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

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

Gao, J.

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91(19), 195147 (2015).
[Crossref]

Ginn, J. C.

J. C. Ginn, R. L. Jarecki, E. A. Shaner, and P. S. Davids, “Infrared plasmons on heavily-doped silicon,” J. Appl. Phys. 110(4), 043110 (2011).
[Crossref]

Gmachl, C.

A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
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A. J. Hoffman, V. A. Podolskiy, D. L. Sivco, and C. Gmachl, “Sub-diffraction negative and positive index modes in mid-infrared waveguides,” Opt. Express 16(21), 16404–16409 (2008).
[Crossref] [PubMed]

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

Gonzalez-Posada, F.

Guilengui, V. N.

Gumen, L. N.

A. A. Krokhin, J. Arriaga, L. N. Gumen, and V. P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93(7), 075418 (2016).
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Guo, Y.

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
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Harris, C.

Hoffman, A. J.

A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
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A. J. Hoffman, V. A. Podolskiy, D. L. Sivco, and C. Gmachl, “Sub-diffraction negative and positive index modes in mid-infrared waveguides,” Opt. Express 16(21), 16404–16409 (2008).
[Crossref] [PubMed]

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

Howard, S. S.

A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
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A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
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Ishii, S.

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Rev. 7(2), 265–271 (2013).
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Jacob, Z.

P. Shekhar, J. Atkinson, and Z. Jacob, “Hyperbolic metamaterials: fundamentals and applications,” Nano Converg 1(1), 14 (2014).
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P. Shekhar and Z. Jacob, “Strong coupling in hyperbolic metamaterials,” Phys. Rev. B 90(4), 045313 (2014).
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C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[Crossref]

Jarecki, R. L.

J. C. Ginn, R. L. Jarecki, E. A. Shaner, and P. S. Davids, “Infrared plasmons on heavily-doped silicon,” J. Appl. Phys. 110(4), 043110 (2011).
[Crossref]

Jarillo-Herrero, P.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
[Crossref] [PubMed]

Jung, J.

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79(3), 035401 (2009).
[Crossref]

Keilmann, F.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
[Crossref] [PubMed]

Kidwai, O.

S. V. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21(12), 14982–14987 (2013).
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O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
[Crossref]

Kildishev, A. V.

V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015).
[Crossref] [PubMed]

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Rev. 7(2), 265–271 (2013).
[Crossref]

Kivshar, Y.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Krishna, K. H.

K. V. Sreekanth, K. H. Krishna, A. De Luca, and G. Strangi, “Large spontaneous emission rate enhancement in grating coupled hyperbolic metamaterials,” Sci. Rep. 4(1), 6340 (2015).
[Crossref] [PubMed]

Krokhin, A. A.

A. A. Krokhin, J. Arriaga, L. N. Gumen, and V. P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93(7), 075418 (2016).
[Crossref]

Lavrinenko, A. V.

S. V. Zhukovsky, A. Andryieuski, J. E. Sipe, and A. V. Lavrinenko, “From surface to volume plasmons in hyperbolic metamaterials: General existence conditions for bulk high-k waves in metal-dielectric and graphene-dielectric multilayers,” Phys. Rev. B 90(15), 155429 (2014).
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S. V. Zhukovsky, A. A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. E. Sipe, “Photonic-band-gap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials,” Phys. Rev. A – At. Mol. Opt. Phys. 90, 1–11 (2014).

Law, S.

Lepage, D.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

Li, Z.

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91(19), 195147 (2015).
[Crossref]

Liu, M. K.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
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S. Law, R. Liu, and D. Wasserman, “Doped semiconductors with band-edge plasma frequencies,” J. Vac. Sci. Technol. B 32(5), 52601 (2014).
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L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
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D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).
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D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3, 1205 (2012).
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L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91(19), 195147 (2015).
[Crossref]

Ma, Q.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
[Crossref] [PubMed]

Mcleod, A. S.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
[Crossref] [PubMed]

Medhi, G.

M. Shahzad, G. Medhi, R. E. Peale, W. R. Buchwald, J. W. Cleary, R. Soref, G. D. Boreman, and O. Edwards, “Infrared surface plasmons on heavily doped silicon,” J. Appl. Phys. 110(12), 123105 (2011).
[Crossref]

Molesky, S.

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

Narimanov, E.

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Rev. 7(2), 265–271 (2013).
[Crossref]

Narimanov, E. E.

A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

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

Nasir, M. E.

N. Vasilantonakis, M. E. Nasir, W. Dickson, G. A. Wurtz, and A. V. Zayats, “Bulk plasmon-polaritons in hyperbolic nanorod metamaterial waveguides,” Laser Photonics Rev. 9(3), 345–353 (2015).
[Crossref] [PubMed]

Newman, W.

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[Crossref]

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
[Crossref]

Niehle, M.

Orlov, A. A.

S. V. Zhukovsky, A. A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. E. Sipe, “Photonic-band-gap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials,” Phys. Rev. A – At. Mol. Opt. Phys. 90, 1–11 (2014).

Peale, R. E.

M. Shahzad, G. Medhi, R. E. Peale, W. R. Buchwald, J. W. Cleary, R. Soref, G. D. Boreman, and O. Edwards, “Infrared surface plasmons on heavily doped silicon,” J. Appl. Phys. 110(12), 123105 (2011).
[Crossref]

Pistora, J.

Poddubny, A.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
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S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009).
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A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

A. J. Hoffman, V. A. Podolskiy, D. L. Sivco, and C. Gmachl, “Sub-diffraction negative and positive index modes in mid-infrared waveguides,” Opt. Express 16(21), 16404–16409 (2008).
[Crossref] [PubMed]

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

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A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

Shahzad, M.

M. Shahzad, G. Medhi, R. E. Peale, W. R. Buchwald, J. W. Cleary, R. Soref, G. D. Boreman, and O. Edwards, “Infrared surface plasmons on heavily doped silicon,” J. Appl. Phys. 110(12), 123105 (2011).
[Crossref]

Shalaev, V. M.

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Rev. 7(2), 265–271 (2013).
[Crossref]

Shalaginov, M. Y.

Shaner, E. A.

J. C. Ginn, R. L. Jarecki, E. A. Shaner, and P. S. Davids, “Infrared plasmons on heavily-doped silicon,” J. Appl. Phys. 110(4), 043110 (2011).
[Crossref]

Shekhar, P.

P. Shekhar and Z. Jacob, “Strong coupling in hyperbolic metamaterials,” Phys. Rev. B 90(4), 045313 (2014).
[Crossref]

P. Shekhar, J. Atkinson, and Z. Jacob, “Hyperbolic metamaterials: fundamentals and applications,” Nano Converg 1(1), 14 (2014).
[Crossref] [PubMed]

Sipe, J. E.

S. V. Zhukovsky, A. Andryieuski, J. E. Sipe, and A. V. Lavrinenko, “From surface to volume plasmons in hyperbolic metamaterials: General existence conditions for bulk high-k waves in metal-dielectric and graphene-dielectric multilayers,” Phys. Rev. B 90(15), 155429 (2014).
[Crossref]

S. V. Zhukovsky, A. A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. E. Sipe, “Photonic-band-gap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials,” Phys. Rev. A – At. Mol. Opt. Phys. 90, 1–11 (2014).

S. V. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21(12), 14982–14987 (2013).
[Crossref] [PubMed]

O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
[Crossref]

Sivco, D. L.

A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

A. J. Hoffman, V. A. Podolskiy, D. L. Sivco, and C. Gmachl, “Sub-diffraction negative and positive index modes in mid-infrared waveguides,” Opt. Express 16(21), 16404–16409 (2008).
[Crossref] [PubMed]

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

Søndergaard, T.

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79(3), 035401 (2009).
[Crossref]

T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi 245(1), 9–19 (2008).
[Crossref]

Soref, R.

M. Shahzad, G. Medhi, R. E. Peale, W. R. Buchwald, J. W. Cleary, R. Soref, G. D. Boreman, and O. Edwards, “Infrared surface plasmons on heavily doped silicon,” J. Appl. Phys. 110(12), 123105 (2011).
[Crossref]

Spitzer, W. G.

W. G. Spitzer and H. Y. Fan, “Determination of Optical Constants and Carrier Effective Mass of Semiconductors,” Phys. Rev. 106(5), 882–890 (1957).
[Crossref]

Sreekanth, K. V.

K. V. Sreekanth, K. H. Krishna, A. De Luca, and G. Strangi, “Large spontaneous emission rate enhancement in grating coupled hyperbolic metamaterials,” Sci. Rep. 4(1), 6340 (2015).
[Crossref] [PubMed]

K. V. Sreekanth, A. De Luca, and G. Strangi, “Excitation of volume plasmon polaritons in metal-dielectric metamaterials using 1D and 2D diffraction gratings,” J. Opt. 16(10), 105103 (2014).
[Crossref]

Sridhar, A.

A. J. Hoffman, A. Sridhar, P. X. Braun, L. Alekseyev, S. S. Howard, K. J. Franz, L. Cheng, F. Sen Choa, D. L. Sivco, V. A. Podolskiy, E. E. Narimanov, and C. Gmachl, “Midinfrared semiconductor optical metamaterials,” J. Appl. Phys. 105(12), 122411 (2009).
[Crossref]

Strangi, G.

K. V. Sreekanth, K. H. Krishna, A. De Luca, and G. Strangi, “Large spontaneous emission rate enhancement in grating coupled hyperbolic metamaterials,” Sci. Rep. 4(1), 6340 (2015).
[Crossref] [PubMed]

K. V. Sreekanth, A. De Luca, and G. Strangi, “Excitation of volume plasmon polaritons in metal-dielectric metamaterials using 1D and 2D diffraction gratings,” J. Opt. 16(10), 105103 (2014).
[Crossref]

Sun, L.

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91(19), 195147 (2015).
[Crossref]

Taliercio, T.

Taniguchi, T.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
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Taylor, A. M.

Thiemens, M.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
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Tournie, E.

V. N. Guilengui, L. Cerutti, J. B. Rodriguez, E. Tournie, and T. Taliercio, “Localized surface plasmon resonances in highly doped semiconductors nanostructures,” Appl. Phys. Lett. 101(16), 161113 (2012).
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Trampert, A.

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N. Vasilantonakis, M. E. Nasir, W. Dickson, G. A. Wurtz, and A. V. Zayats, “Bulk plasmon-polaritons in hyperbolic nanorod metamaterial waveguides,” Laser Photonics Rev. 9(3), 345–353 (2015).
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Wagner, M.

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S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
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Wei, D.

Wu, C.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
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Wurtz, G. A.

N. Vasilantonakis, M. E. Nasir, W. Dickson, G. A. Wurtz, and A. V. Zayats, “Bulk plasmon-polaritons in hyperbolic nanorod metamaterial waveguides,” Laser Photonics Rev. 9(3), 345–353 (2015).
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Yang, X.

L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91(19), 195147 (2015).
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Zayats, A. V.

N. Vasilantonakis, M. E. Nasir, W. Dickson, G. A. Wurtz, and A. V. Zayats, “Bulk plasmon-polaritons in hyperbolic nanorod metamaterial waveguides,” Laser Photonics Rev. 9(3), 345–353 (2015).
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Zhang, J.

Zhang, X.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
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S. V. Zhukovsky, A. Andryieuski, J. E. Sipe, and A. V. Lavrinenko, “From surface to volume plasmons in hyperbolic metamaterials: General existence conditions for bulk high-k waves in metal-dielectric and graphene-dielectric multilayers,” Phys. Rev. B 90(15), 155429 (2014).
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S. V. Zhukovsky, A. A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. E. Sipe, “Photonic-band-gap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials,” Phys. Rev. A – At. Mol. Opt. Phys. 90, 1–11 (2014).

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K. V. Sreekanth, A. De Luca, and G. Strangi, “Excitation of volume plasmon polaritons in metal-dielectric metamaterials using 1D and 2D diffraction gratings,” J. Opt. 16(10), 105103 (2014).
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C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. 14(6), 063001 (2012).
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S. Law, R. Liu, and D. Wasserman, “Doped semiconductors with band-edge plasma frequencies,” J. Vac. Sci. Technol. B 32(5), 52601 (2014).
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S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Rev. 7(2), 265–271 (2013).
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N. Vasilantonakis, M. E. Nasir, W. Dickson, G. A. Wurtz, and A. V. Zayats, “Bulk plasmon-polaritons in hyperbolic nanorod metamaterial waveguides,” Laser Photonics Rev. 9(3), 345–353 (2015).
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S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nat. Commun. 6, 6963 (2015).
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A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
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A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
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O. Kidwai, S. V. Zhukovsky, and J. E. Sipe, “Effective-medium approach to planar multilayer hyperbolic metamaterials: Strengths and limitations,” Phys. Rev. A 85(5), 053842 (2012).
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Phys. Rev. A – At. Mol. Opt. Phys. (1)

S. V. Zhukovsky, A. A. Orlov, V. E. Babicheva, A. V. Lavrinenko, and J. E. Sipe, “Photonic-band-gap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials,” Phys. Rev. A – At. Mol. Opt. Phys. 90, 1–11 (2014).

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J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79(3), 035401 (2009).
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L. Sun, Z. Li, T. S. Luk, X. Yang, and J. Gao, “Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials,” Phys. Rev. B 91(19), 195147 (2015).
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S. V. Zhukovsky, A. Andryieuski, J. E. Sipe, and A. V. Lavrinenko, “From surface to volume plasmons in hyperbolic metamaterials: General existence conditions for bulk high-k waves in metal-dielectric and graphene-dielectric multilayers,” Phys. Rev. B 90(15), 155429 (2014).
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A. A. Krokhin, J. Arriaga, L. N. Gumen, and V. P. Drachev, “High-frequency homogenization for layered hyperbolic metamaterials,” Phys. Rev. B 93(7), 075418 (2016).
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P. Shekhar and Z. Jacob, “Strong coupling in hyperbolic metamaterials,” Phys. Rev. B 90(4), 045313 (2014).
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K. V. Sreekanth, K. H. Krishna, A. De Luca, and G. Strangi, “Large spontaneous emission rate enhancement in grating coupled hyperbolic metamaterials,” Sci. Rep. 4(1), 6340 (2015).
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[Crossref]

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Figures (6)

Fig. 1
Fig. 1

(a) Conduction band profile (black) and carrier density (red) in the Si:InAs/InAs superlattice from Sample 1 as calculated using a self-consistent Poisson solver. In region a, the material is modeled as a Drude metal with a constant carrier density, while in region c, the material is modeled as undoped InAs with a constant permittivity of 12.3. In the shaded region b, the carrier density depends on depth as described below. (b) Experimental (symbols) and empirical model (black line) for plasma frequency as a function of carrier density in doped InAs. Data from [29].

Fig. 2
Fig. 2

Reflection spectra for Sample 1 without a grating (blue and yellow) and with a grating (black and red) for both TM (black and blue) and TE (red and yellow) polarized light. For both polarizations without the grating and for TE-polarized light with the grating, no VPP modes are observed. Only for TM-polarized light with the grating are long-wavelength VPP modes visible.

Fig. 3
Fig. 3

(a) Experimental and (b) simulated TM-polarized reflection from Sample 3 for four different period gratings, as indicated in the legend. VPP modes are clearly visible and marked with arrows in (a). In (b), the out-of-plane magnetic field profile is shown for two VPP modes. The shorter wavelength resonance has no nodes, while the longer wavelength resonance has one node, as expected for VPPs.

Fig. 4
Fig. 4

(a) Experimental and (b) simulated TM-polarized reflection from Sample 1 for five different period gratings, as indicated in the legend. Two VPP modes are visible, though they are not well-separated.

Fig. 5
Fig. 5

Dispersion relations for VPP modes for experimental (filled symbols) and simulated (open symbols) data for Sample 1 (a) and Sample 3 (b). Lines are a guide to the eye.

Fig. 6
Fig. 6

Comparison of models for TM-polarized reflection for Sample 1 with a 2μm period grating. Experimental data is shown in black, modeled reflection assuming a sharp interface with low scattering (Γ = 2x1013 rad/s) is shown in red, a sharp interface with high scattering (Γ = 4x1013 rad/s) is shown in yellow, and the graded interface is shown in green.

Equations (4)

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

ε || ( ω )= ε m (ω)+η ε d 1+η ε (ω)= 1+η 1 ε m (ω) + η ε d
k x k o =sinθ+ λ Λ
n(z)= n max ( 0.5226+ 1.5170 1+exp( z225.5435 38.8166 ) )
ω p (n)=4.5433× 10 13 +8.44× 10 9 × n 0.23363

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