Abstract

In this paper, we present a numerical modal study of a simple slab, made of an uniaxial anisotropic material having an “epsilon-near-zero” (ENZ) dielectric function, surrounded by vacuum. We use two Drude models with a different plasma frequency for the direction parallel and perpendicular to the slab surface as toy models to study the effect of uniaxial anisotropy of type I ( > 0, < 0) and type II ( < 0, > 0) on the different electromagnetic modes of the system. In addition to the so-called ENZ mode, studied in detail by Campione et. al [ Phys. Rev. B 91, 121408(R) (2015)], the slab can support quasi-confined (QC) mode in the type I and type II anisotropy frequency ranges. We show that those modes exhibit a strong electric field enhancement, caused by the ENZ character of the dielectric function. In strong contrast with the ENZ mode, QC modes can have a strong electric field enhancement for thick slabs, with a Fabry-Perot-like electromagnetic field distribution spanning over the whole slab thickness. This opens the way for large electric field enhancement in thick slabs with QC ENZ modes. Thick slabs also allow metamaterial designs, giving the possibility to engineer the anisotropy of the effective dielectric function, opening interesting perspectives for the control of field enhancement of the ENZ QC modes and their integration in operating devices, such as detectors, sources, or modulators.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  35. V. M. V. M. Agranovich and D. L. Mills, Surface Polaritons: Electromagnetic Waves at Surfaces and Interfaces (North-Holland Pub. Co., 1982).

2018 (2)

Y. U. Lee, E. Garoni, H. Kita, K. Kamada, B. H. Woo, Y. C. Jun, S. M. Chae, H. J. Kim, K. J. Lee, S. Yoon, E. Choi, F. Mathevet, I. Ozerov, J. C. Ribierre, J. W. Wu, and A. D’Aléo, “Strong nonlinear optical response in the visible spectral range with epsilon-near-zero organic thin films,” Adv. Opt. Mater. 6, 1701400 (2018).
[Crossref]

W. Yang, S. Berthou, X. Lu, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi, K. Watanabe, G. Fève, J.-M. Berroir, G. Zhang, C. Voisin, E. Baudin, and B. Plaçais, “A graphene Zener-Klein transistor cooled by a hyperbolic substrate,” Nat. Nanotechnol. 13, 47–52 (2018).
[Crossref]

2017 (1)

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–158 (2017).
[Crossref]

2016 (5)

M. Lobet, B. Majerus, L. Henrard, and P. Lambin, “Perfect electromagnetic absorption using graphene and epsilon-near-zero metamaterials,” Phys. Rev. B 93, 235424 (2016).
[Crossref]

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7, 11809 (2016).
[Crossref] [PubMed]

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Sci. (New York, N.Y.) 352, 795–797 (2016).
[Crossref]

S. Campione, J. R. Wendt, G. A. Keeler, and T. S. Luk, “Near-infrared strong coupling between metamaterials and epsilon-near-zero modes in degenerately doped semiconductor nanolayers,” ACS Photonics 3, 293–297 (2016).
[Crossref]

S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93, 063846 (2016).
[Crossref]

2015 (6)

S. Campione, I. Brener, and F. Marquier, “Theory of epsilon-near-zero modes in ultrathin films,” Phys. Rev. B 91, 121408 (2015).
[Crossref]

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4, 044011 (2015).
[Crossref]

J. Park, J.-H. Kang, X. Liu, and M. L. Brongersma, “Electrically tunable epsilon-near-zero (ENZ) metafilm absorbers,” Sci. Reports 5, 15754 (2015).
[Crossref]

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]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10, 682–686 (2015).
[Crossref] [PubMed]

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nat. Photonics 9, 674–678 (2015).
[Crossref]

2014 (1)

T. S. Luk, S. Campione, I. Kim, S. Feng, Y. C. Jun, S. Liu, J. B. Wright, I. Brener, P. B. Catrysse, S. Fan, and M. B. Sinclair, “Directional perfect absorption using deep subwavelength low-permittivity films,” Phys. Rev. B 90, 085411 (2014).
[Crossref]

2013 (4)

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonics 7, 907–912 (2013).
[Crossref]

P. Ginzburg, F. J. R. Fortuño, G. A. Wurtz, W. Dickson, A. Murphy, F. Morgan, R. J. Pollard, I. Iorsh, A. Atrashchenko, P. A. Belov, Y. S. Kivshar, A. Nevet, G. Ankonina, M. Orenstein, and A. V. Zayats, “Manipulating polarization of light with ultrathin epsilon-near-zero metamaterials,” Opt. Express 21, 14907 (2013).
[Crossref] [PubMed]

Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, “Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure,” Opt. Express 21, 27371 (2013).
[Crossref] [PubMed]

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13, 5391–5396 (2013).
[Crossref] [PubMed]

2012 (6)

S. Vassant, J.-P. Hugonin, F. Marquier, and J.-J. Greffet, “Berreman mode and epsilon near zero mode,” Opt. Express 20, 23971 (2012).
[Crossref] [PubMed]

S. Vassant, A. Archambault, F. Marquier, F. Pardo, U. Gennser, A. Cavanna, J. L. Pelouard, and J. J. Greffet, “Epsilon-near-zero mode for active optoelectronic devices,” Phys. Rev. Lett. 109, 237401 (2012).
[Crossref]

A. Delteil, A. Vasanelli, Y. Todorov, C. Feuillet Palma, M. Renaudat St-Jean, G. Beaudoin, I. Sagnes, and C. Sirtori, “Charge-induced coherence between intersubband plasmons in a quantum structure,” Phys. Rev. Lett. 109, 246808 (2012).
[Crossref]

Z. Lu, W. Zhao, and K. Shi, “Ultracompact electroabsorption modulators based on tunable epsilon-near-zero-slot waveguides,” IEEE Photonics J. 4, 735–740 (2012).
[Crossref]

S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

C. Argyropoulos, P.-Y. Chen, G. D’Aguanno, N. Engheta, and A. Alù, “Boosting optical nonlinearities in ∊-near-zero plasmonic channels,” Phys. Rev. B 85, 045129 (2012).
[Crossref]

2011 (1)

2009 (2)

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105, 044905 (2009).
[Crossref]

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

2008 (2)

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
[Crossref] [PubMed]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[Crossref] [PubMed]

2007 (1)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

2006 (1)

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ∊-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref]

1999 (1)

S. M. Komirenko, K. W. Kim, M. A. Stroscio, and M. Dutta, “Dispersion of polar optical phonons in wurtzite quantum wells,” Phys. Rev. B 59, 5013–5020 (1999).
[Crossref]

1981 (1)

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
[Crossref]

Agranovich, V. M. V. M.

V. M. V. M. Agranovich and D. L. Mills, Surface Polaritons: Electromagnetic Waves at Surfaces and Interfaces (North-Holland Pub. Co., 1982).

Alam, M. Z.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Sci. (New York, N.Y.) 352, 795–797 (2016).
[Crossref]

S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93, 063846 (2016).
[Crossref]

Albani, M.

Alù, A.

C. Argyropoulos, P.-Y. Chen, G. D’Aguanno, N. Engheta, and A. Alù, “Boosting optical nonlinearities in ∊-near-zero plasmonic channels,” Phys. Rev. B 85, 045129 (2012).
[Crossref]

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105, 044905 (2009).
[Crossref]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[Crossref] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

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]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10, 682–686 (2015).
[Crossref] [PubMed]

Ankonina, G.

Archambault, A.

S. Vassant, A. Archambault, F. Marquier, F. Pardo, U. Gennser, A. Cavanna, J. L. Pelouard, and J. J. Greffet, “Epsilon-near-zero mode for active optoelectronic devices,” Phys. Rev. Lett. 109, 237401 (2012).
[Crossref]

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

Argyropoulos, C.

C. Argyropoulos, P.-Y. Chen, G. D’Aguanno, N. Engheta, and A. Alù, “Boosting optical nonlinearities in ∊-near-zero plasmonic channels,” Phys. Rev. B 85, 045129 (2012).
[Crossref]

Atrashchenko, A.

Bai, Q.

Basov, D. N.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10, 682–686 (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]

Baudin, E.

W. Yang, S. Berthou, X. Lu, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi, K. Watanabe, G. Fève, J.-M. Berroir, G. Zhang, C. Voisin, E. Baudin, and B. Plaçais, “A graphene Zener-Klein transistor cooled by a hyperbolic substrate,” Nat. Nanotechnol. 13, 47–52 (2018).
[Crossref]

Beaudoin, G.

A. Delteil, A. Vasanelli, Y. Todorov, C. Feuillet Palma, M. Renaudat St-Jean, G. Beaudoin, I. Sagnes, and C. Sirtori, “Charge-induced coherence between intersubband plasmons in a quantum structure,” Phys. Rev. Lett. 109, 246808 (2012).
[Crossref]

Belov, P. A.

Benz, A.

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4, 044011 (2015).
[Crossref]

Berroir, J.-M.

W. Yang, S. Berthou, X. Lu, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi, K. Watanabe, G. Fève, J.-M. Berroir, G. Zhang, C. Voisin, E. Baudin, and B. Plaçais, “A graphene Zener-Klein transistor cooled by a hyperbolic substrate,” Nat. Nanotechnol. 13, 47–52 (2018).
[Crossref]

Berthou, S.

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S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93, 063846 (2016).
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M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Sci. (New York, N.Y.) 352, 795–797 (2016).
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B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105, 044905 (2009).
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S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
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R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
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S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10, 682–686 (2015).
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S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10, 682–686 (2015).
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Y. U. Lee, E. Garoni, H. Kita, K. Kamada, B. H. Woo, Y. C. Jun, S. M. Chae, H. J. Kim, K. J. Lee, S. Yoon, E. Choi, F. Mathevet, I. Ozerov, J. C. Ribierre, J. W. Wu, and A. D’Aléo, “Strong nonlinear optical response in the visible spectral range with epsilon-near-zero organic thin films,” Adv. Opt. Mater. 6, 1701400 (2018).
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T. S. Luk, S. Campione, I. Kim, S. Feng, Y. C. Jun, S. Liu, J. B. Wright, I. Brener, P. B. Catrysse, S. Fan, and M. B. Sinclair, “Directional perfect absorption using deep subwavelength low-permittivity films,” Phys. Rev. B 90, 085411 (2014).
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Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13, 5391–5396 (2013).
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T. S. Luk, S. Campione, I. Kim, S. Feng, Y. C. Jun, S. Liu, J. B. Wright, I. Brener, P. B. Catrysse, S. Fan, and M. B. Sinclair, “Directional perfect absorption using deep subwavelength low-permittivity films,” Phys. Rev. B 90, 085411 (2014).
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[Crossref] [PubMed]

Voisin, C.

W. Yang, S. Berthou, X. Lu, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi, K. Watanabe, G. Fève, J.-M. Berroir, G. Zhang, C. Voisin, E. Baudin, and B. Plaçais, “A graphene Zener-Klein transistor cooled by a hyperbolic substrate,” Nat. Nanotechnol. 13, 47–52 (2018).
[Crossref]

Wagner, M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10, 682–686 (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]

Watanabe, K.

W. Yang, S. Berthou, X. Lu, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi, K. Watanabe, G. Fève, J.-M. Berroir, G. Zhang, C. Voisin, E. Baudin, and B. Plaçais, “A graphene Zener-Klein transistor cooled by a hyperbolic substrate,” Nat. Nanotechnol. 13, 47–52 (2018).
[Crossref]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10, 682–686 (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]

Wendt, J. R.

S. Campione, J. R. Wendt, G. A. Keeler, and T. S. Luk, “Near-infrared strong coupling between metamaterials and epsilon-near-zero modes in degenerately doped semiconductor nanolayers,” ACS Photonics 3, 293–297 (2016).
[Crossref]

Wilmart, Q.

W. Yang, S. Berthou, X. Lu, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi, K. Watanabe, G. Fève, J.-M. Berroir, G. Zhang, C. Voisin, E. Baudin, and B. Plaçais, “A graphene Zener-Klein transistor cooled by a hyperbolic substrate,” Nat. Nanotechnol. 13, 47–52 (2018).
[Crossref]

Woessner, A.

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nat. Photonics 9, 674–678 (2015).
[Crossref]

Woo, B. H.

Y. U. Lee, E. Garoni, H. Kita, K. Kamada, B. H. Woo, Y. C. Jun, S. M. Chae, H. J. Kim, K. J. Lee, S. Yoon, E. Choi, F. Mathevet, I. Ozerov, J. C. Ribierre, J. W. Wu, and A. D’Aléo, “Strong nonlinear optical response in the visible spectral range with epsilon-near-zero organic thin films,” Adv. Opt. Mater. 6, 1701400 (2018).
[Crossref]

Wright, J. B.

T. S. Luk, S. Campione, I. Kim, S. Feng, Y. C. Jun, S. Liu, J. B. Wright, I. Brener, P. B. Catrysse, S. Fan, and M. B. Sinclair, “Directional perfect absorption using deep subwavelength low-permittivity films,” Phys. Rev. B 90, 085411 (2014).
[Crossref]

Wu, J. W.

Y. U. Lee, E. Garoni, H. Kita, K. Kamada, B. H. Woo, Y. C. Jun, S. M. Chae, H. J. Kim, K. J. Lee, S. Yoon, E. Choi, F. Mathevet, I. Ozerov, J. C. Ribierre, J. W. Wu, and A. D’Aléo, “Strong nonlinear optical response in the visible spectral range with epsilon-near-zero organic thin films,” Adv. Opt. Mater. 6, 1701400 (2018).
[Crossref]

Wurtz, G. A.

Yang, W.

W. Yang, S. Berthou, X. Lu, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi, K. Watanabe, G. Fève, J.-M. Berroir, G. Zhang, C. Voisin, E. Baudin, and B. Plaçais, “A graphene Zener-Klein transistor cooled by a hyperbolic substrate,” Nat. Nanotechnol. 13, 47–52 (2018).
[Crossref]

Yoon, S.

Y. U. Lee, E. Garoni, H. Kita, K. Kamada, B. H. Woo, Y. C. Jun, S. M. Chae, H. J. Kim, K. J. Lee, S. Yoon, E. Choi, F. Mathevet, I. Ozerov, J. C. Ribierre, J. W. Wu, and A. D’Aléo, “Strong nonlinear optical response in the visible spectral range with epsilon-near-zero organic thin films,” Adv. Opt. Mater. 6, 1701400 (2018).
[Crossref]

Young, M. E.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[Crossref] [PubMed]

Yoxall, E.

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nat. Photonics 9, 674–678 (2015).
[Crossref]

Zayats, A. V.

Zhang, G.

W. Yang, S. Berthou, X. Lu, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi, K. Watanabe, G. Fève, J.-M. Berroir, G. Zhang, C. Voisin, E. Baudin, and B. Plaçais, “A graphene Zener-Klein transistor cooled by a hyperbolic substrate,” Nat. Nanotechnol. 13, 47–52 (2018).
[Crossref]

Zhao, W.

Z. Lu, W. Zhao, and K. Shi, “Ultracompact electroabsorption modulators based on tunable epsilon-near-zero-slot waveguides,” IEEE Photonics J. 4, 735–740 (2012).
[Crossref]

Zhu, S.-E.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10, 682–686 (2015).
[Crossref] [PubMed]

ACS Photonics (1)

S. Campione, J. R. Wendt, G. A. Keeler, and T. S. Luk, “Near-infrared strong coupling between metamaterials and epsilon-near-zero modes in degenerately doped semiconductor nanolayers,” ACS Photonics 3, 293–297 (2016).
[Crossref]

Adv. Opt. Mater. (1)

Y. U. Lee, E. Garoni, H. Kita, K. Kamada, B. H. Woo, Y. C. Jun, S. M. Chae, H. J. Kim, K. J. Lee, S. Yoon, E. Choi, F. Mathevet, I. Ozerov, J. C. Ribierre, J. W. Wu, and A. D’Aléo, “Strong nonlinear optical response in the visible spectral range with epsilon-near-zero organic thin films,” Adv. Opt. Mater. 6, 1701400 (2018).
[Crossref]

IEEE Photonics J. (1)

Z. Lu, W. Zhao, and K. Shi, “Ultracompact electroabsorption modulators based on tunable epsilon-near-zero-slot waveguides,” IEEE Photonics J. 4, 735–740 (2012).
[Crossref]

J. Appl. Phys. (1)

B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. 105, 044905 (2009).
[Crossref]

Nano Lett. (1)

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13, 5391–5396 (2013).
[Crossref] [PubMed]

Nat. Commun. (2)

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]

P. N. Dyachenko, S. Molesky, A. Y. Petrov, M. Störmer, T. Krekeler, S. Lang, M. Ritter, Z. Jacob, and M. Eich, “Controlling thermal emission with refractory epsilon-near-zero metamaterials via topological transitions,” Nat. Commun. 7, 11809 (2016).
[Crossref] [PubMed]

Nat. Nanotechnol. (2)

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10, 682–686 (2015).
[Crossref] [PubMed]

W. Yang, S. Berthou, X. Lu, Q. Wilmart, A. Denis, M. Rosticher, T. Taniguchi, K. Watanabe, G. Fève, J.-M. Berroir, G. Zhang, C. Voisin, E. Baudin, and B. Plaçais, “A graphene Zener-Klein transistor cooled by a hyperbolic substrate,” Nat. Nanotechnol. 13, 47–52 (2018).
[Crossref]

Nat. Photonics (3)

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nat. Photonics 9, 674–678 (2015).
[Crossref]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11, 149–158 (2017).
[Crossref]

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonics 7, 907–912 (2013).
[Crossref]

Opt. Express (3)

Opt. Mater. Express (1)

Phys. Rev. A (1)

S. A. Schulz, A. A. Tahir, M. Z. Alam, J. Upham, I. De Leon, and R. W. Boyd, “Optical response of dipole antennas on an epsilon-near-zero substrate,” Phys. Rev. A 93, 063846 (2016).
[Crossref]

Phys. Rev. Appl. (1)

S. Campione, S. Liu, A. Benz, J. F. Klem, M. B. Sinclair, and I. Brener, “Epsilon-near-zero modes for tailored light-matter interaction,” Phys. Rev. Appl. 4, 044011 (2015).
[Crossref]

Phys. Rev. B (8)

M. Lobet, B. Majerus, L. Henrard, and P. Lambin, “Perfect electromagnetic absorption using graphene and epsilon-near-zero metamaterials,” Phys. Rev. B 93, 235424 (2016).
[Crossref]

A. Archambault, T. V. Teperik, F. Marquier, and J. J. Greffet, “Surface plasmon Fourier optics,” Phys. Rev. B 79, 195414 (2009).
[Crossref]

S. Campione, I. Brener, and F. Marquier, “Theory of epsilon-near-zero modes in ultrathin films,” Phys. Rev. B 91, 121408 (2015).
[Crossref]

S. M. Komirenko, K. W. Kim, M. A. Stroscio, and M. Dutta, “Dispersion of polar optical phonons in wurtzite quantum wells,” Phys. Rev. B 59, 5013–5020 (1999).
[Crossref]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

C. Argyropoulos, P.-Y. Chen, G. D’Aguanno, N. Engheta, and A. Alù, “Boosting optical nonlinearities in ∊-near-zero plasmonic channels,” Phys. Rev. B 85, 045129 (2012).
[Crossref]

S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

T. S. Luk, S. Campione, I. Kim, S. Feng, Y. C. Jun, S. Liu, J. B. Wright, I. Brener, P. B. Catrysse, S. Fan, and M. B. Sinclair, “Directional perfect absorption using deep subwavelength low-permittivity films,” Phys. Rev. B 90, 085411 (2014).
[Crossref]

Phys. Rev. Lett. (6)

S. Vassant, A. Archambault, F. Marquier, F. Pardo, U. Gennser, A. Cavanna, J. L. Pelouard, and J. J. Greffet, “Epsilon-near-zero mode for active optoelectronic devices,” Phys. Rev. Lett. 109, 237401 (2012).
[Crossref]

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ∊-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref]

R. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. 100, 023903 (2008).
[Crossref] [PubMed]

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[Crossref] [PubMed]

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927–1930 (1981).
[Crossref]

A. Delteil, A. Vasanelli, Y. Todorov, C. Feuillet Palma, M. Renaudat St-Jean, G. Beaudoin, I. Sagnes, and C. Sirtori, “Charge-induced coherence between intersubband plasmons in a quantum structure,” Phys. Rev. Lett. 109, 246808 (2012).
[Crossref]

Sci. (New York, N.Y.) (1)

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Sci. (New York, N.Y.) 352, 795–797 (2016).
[Crossref]

Sci. Reports (1)

J. Park, J.-H. Kang, X. Liu, and M. L. Brongersma, “Electrically tunable epsilon-near-zero (ENZ) metafilm absorbers,” Sci. Reports 5, 15754 (2015).
[Crossref]

Other (1)

V. M. V. M. Agranovich and D. L. Mills, Surface Polaritons: Electromagnetic Waves at Surfaces and Interfaces (North-Holland Pub. Co., 1982).

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Figures (16)

Fig. 1
Fig. 1 Geometry of the system.
Fig. 2
Fig. 2 ENZ frequency range and enhancement associated with a Drude model describing the dielectric properties of a slab in the direction perpendicular to the interfaces (s). Left: real and imaginary part for a dielectric function described by a Drude model describing with ωp=10000 cm−1, γ=100 cm−1. Right: corresponding KENZ factor, representing the enhancement of the electric field intensity. In both figures, the green shaded area corresponds to the ENZ range defined as KENZ > 20.
Fig. 3
Fig. 3 Dielectric function (left) and dispersion relations (right) for a slab with type I anisotropy (ωp = 0.6ωp). The green shaded area represent the ENZ range (see text). The hatched area represent the frequency range where QC modes exist. In the dispersion relations, solid lines indicate symmetric modes and dashed lines anti-symmetric modes. ωp = 10000cm−1, γ = γ = 100 cm−1, d = 5 nm.
Fig. 4
Fig. 4 Dielectric function (left) and dispersion relations (right) for a slab with type II anisotropy (ωp = 1.4ωp). The green shaded area represent the ENZ range (see text). The hatched shaded area represent the frequency range where QC modes exist. In the dispersion relations, solid lines indicate symmetric modes and dashed lines anti-symmetric modes. ωp = 10000cm−1, γ = γ = 100 cm−1, d = 5 nm.
Fig. 5
Fig. 5 Magnetic and electric field spatial distribution at kx = 5×107m−1) for symmetric (top row) and the anti-symmetric modes (bottom row). The gray shaded area represent the slab. The modes are normalized so that |H|=1 at the slab surfaces. ωp = 10000 cm−1, ωp = 1.4ωp, γ = γ = 100 cm−1, d = 5 nm.
Fig. 6
Fig. 6 Dispersion relations for a slab of 100nm thickness. Solid lines indicate symmetric modes and dashed lines anti-symmetric modes. The green shaded area correspond to the ENZ range, and the hatched area correspond to the QC mode range. The LR mode is not ENZ anymore. ωp = 10000cm−1, ωp = 1.05ωp, γ = γ = 100 cm−1, d = 100 nm.
Fig. 7
Fig. 7 Magnetic and electric field spatial distribution at kx = 5 × 107m−1 for symmetric mode (top row) and the anti-symmetric QC 1 mode (bottom row). The gray shaded area represent the slab. ωp = 10000 cm−1, ωp = 1.05ωp, γ = γ = 100 cm−1, d = 100 nm.
Fig. 8
Fig. 8 Coupling scheme to QC modes. a) Purcell factor for a dipole point-like source placed at 10nm above a 200nm anisotropic slab in vacuum for a dipole orientation along x and z direction (ωp = 10000cm−1, ωp = 1.4ωp, γ = γ = 100 cm−1). b) Absorption as a function of wavenumber and wavevector, in Kretschmann configuration using a Silicon prism with a 200 nm slab of anisotropic material on top of the prism, with same parameters as in a). c) Absolute value of the electric field (|Ez|) along the z direction as a function of z and frequency, in the Kretschmann configuration for an incident angle of θi= 50 degree (dashed red line in b). The incident field has a unity amplitude.
Fig. 9
Fig. 9 Dispersion relations for a slab of 2nm thickness. Solid lines indicate symmetric modes and dashed lines anti-symmetric modes. The green shaded area correspond to the ENZ range. ωp = 10000cm−1, γ = γ = 100 cm−1, d = 2 nm.
Fig. 10
Fig. 10 Dispersion relations for a slab of 2nm thickness. Solid lines indicate symmetric modes and dashed lines anti-symmetric modes. The green shaded area correspond to the ENZ range. ωp = 10000cm−1, γ = γ = 100 cm−1, d = 2 nm.
Fig. 11
Fig. 11 Electromagnetic field distribution for the LR symmetric mode (top row) and SR asymmetric modes (bottom row) for different levels of type II anisotropy. ωp = 10000cm−1, γ = γ = 100 cm−1, d = 2 nm.
Fig. 12
Fig. 12 Color plot of the dispersion relation for symmetric (left) and anti-symmetric (right) modes The plotted quantity is 1/|log(δ)| where δ is the left term of Eq. (5). Losses are divided by 10 for clarity of the plot. ωp = 10000cm−1, ωp = 1.4ωp, γ = γ = 10 cm−1, d = 5 nm.
Fig. 13
Fig. 13 Color plot of the dispersion relation for symmetric (left) and anti-symmetric (right) modes The plotted quantity is 1/|log(δ)| where δ is the left term of Eq. (5). Losses are divided by 10 for clarity of the plot. ωp = 10000cm−1, ωp = 1.1ωpγ = γ = 10 cm−1, d = 100 nm.
Fig. 14
Fig. 14 Electric field spatial distribution (right: |Ez|, left: |Ex|) along the z direction as a function of wavenumber, in Kretschmann configuration, with a silicon prism, at an incident angle of 50 degree. The slab is 200 nm thick, with ωp = 10000cm−1, ωp = 1.4ωpγ = γ = 10 cm−1, d = 200 nm.
Fig. 15
Fig. 15 Left: absorption as a function of wavenumber and wavevector, for 200 nm slab of anisotropic material in vacuum. (ωp = 10000cm−1, ωp = 1.4ωp, γ = γ = 200 cm−1). Middle: Absolute value of the electric field (|Ez|) along the z direction as a function of space and frequency, in the Kretschmann configuration for an incident angle of θi= 50 degree. Right: Corresponding |Ex| field distribution.
Fig. 16
Fig. 16 Quality factor of the modes for a slab with type II anisotropy (ωp = 1.4ωp), corresponding to the dispersion relation of Fig. 4. Solid lines indicate symmetric modes and dashed lines anti-symmetric modes. ωp = 10000cm−1, γ = γ = 100 cm−1, d = 5 nm.

Equations (27)

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( ω ) = ( s ( ω ) 0 0 0 s ( ω ) 0 0 0 s ( ω ) ) .
s ( ω ) = 1 ω p 2 ω 2 + i ω γ ,
s ( ω ) = 1 ω p 2 ω 2 + i ω γ .
| E z s | 2 = | 1 s | 2 | E z v | 2 = K ENZ | E z v | 2 .
( k v s + k s ) ± ( k v s k s ) exp ( i k s d ) = 0 ,
k v 2 = ω 2 c 2 k 2 ,
k s 2 = s ω 2 c 2 s k 2 s ,
D = 0 ,
B = 0 ,
× E = B t ,
× H = D t .
E = ( E x 0 E z ) ,
H = ( 0 H y 0 ) .
H y 1 = A e i k v z e i ( k v x ω t ) ,
H y 3 = A e i k v ( z d ) e i ( k v x ω t ) .
H y 2 = ( B e i k s ( z d ) + C e i k s z ) e i ( k s x ω t ) .
E x = 1 i ω 0 H y z .
E x 1 = k v ω 0 v A e i k v z ,
E x 2 = k s ω 0 s ( B e i k s ( z d ) C e i k s z ) ,
E x 3 = k v ω 0 v A e i k v ( z d ) ,
B e i k s d = C k s s k v v k s s + k v v .
B e i k s d = C k s s k v v k s s + k v v .
( k v v + k s s ) 2 = ( k s s + k v v ) 2 exp ( 2 i k s d ) ,
k 2 = ω 2 c 2 ( 1 ) 1 .
ω asympt = ω p 2 ω p 2 ω p 2 + ω p 2 ,
ω p = 1 1 a 2 ω p .
log ( 1 | DR | ) ,

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