Abstract

The implementation of lossless plasmonic modes with very high or very low wave vectors, which are associated with extraordinary large or small nonlocal effective permittivity, could bring a breakthrough in the development of high-performance plasmonic devices. We consider the possibility of obtaining volume plasmon-polariton modes with an extraordinary large or negligibly small longitudinal momentum and nearly zero loss in a 1d lattice consisting of alternating metal and gain semiconductor layers. Solving the dispersion equation, we show that under the condition of the full loss compensation, two traveling plasmonic TM modes can exist in the lattice. One of the modes is capable to provide extraordinary high momentum value, while the other can provide both extraordinary high and low (nearly zero) momentum. On the other hand, only one traveling TE mode can occur, which is capable of providing extraordinary low momentum. The use of such modes opens up new ways to design optical properties and to control light on the nanometer scale.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (1)

J. S. T. Smalley, F. Vallini, S. Montoya, L. Ferrari, S. Shahin, C. T. Riley, B. KantÃl’, E. E. Fullerton, Z. Liu, and Y. Fainman, “Luminescent hyperbolic metasurfaces,” Nature Commun. 7, 13793 (2017).
[Crossref]

2016 (5)

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

V. Popov, A.V. Lavrinenko, and A. Novitsky, “Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation,” Phys. Rev. B 94, 085428 (2016).
[Crossref]

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

R. Liu, C.M. Roberts, Y. Zhong, V.A. Podolskiy, and D. Wasserman, “Epsilon-near-zero photonic wires,” ACS Photon. 3, 1045–1052 (2016).
[Crossref]

A. Marini and F.J. Garcia de Abajo, “Self-organization of frozen light in near-zero-index media with cubic nonlinearity,” Scient. Rep. 6, 20088 (2016).
[Crossref]

2015 (3)

2014 (3)

J.S.T. Smalley, F. Vallini, B. Kante, S. Shahin, and Y. Fainman, “Modal amplification in active waveguides with hyperbolic dispersion at telecommunication frequencies,” Opt. Express 22, 21088–21105 (2014).
[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 90, 013801 (2014).
[Crossref]

Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
[Crossref]

2013 (5)

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Ultra-broadband simultaneous superluminal phase and group velocities in non-Foster epsilon-near-zero matamaterial,” Appl. Phys. Lett. 102, 054108 (2013).
[Crossref]

J. Benedicto, E. Centeno, R. Polles, and A. Moreau, “Ultimate resolution of indefinite metamaterial flat lenses,” Phys. Rev. B 88, 245138 (2013).
[Crossref]

C. Argyropoulos, N.M. Estakhri, F. Monticone, and A. Alu, “Negative refraction, gain and nonlinear effects in hyperbolic metamaterials,” Opt. Express 21, 15037–15047 (2013).
[Crossref] [PubMed]

R.S. Savelev, I.A. Shadrivov, P.A. Belov, N.N. Rosanov, S.V. Fedorov, A.A. Sukhorukov, and Y.S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

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]

2012 (2)

Y. Guo, W. Newman, C.L. Lortes, and Z. Jacob, “Application of hyperbolic metamaterial substrates,” Adv. OptoElectron. 2012, 1–9 (2012).
[Crossref]

Z. Jacob, I.I. Smolyaninov, and E.E. Narimanov, “Broadband Purcell effect: Radiactive decay engineering with metamaterials,” Appl. Phys. Lett. 100, 181105 (2012).
[Crossref]

2011 (5)

V. Intaraprasonk, Z. Yu, and S. Fan, “Image transfer with subwavelength resolution to metal-dielectric interface,” J. Opt. Soc. Am. B 28, 1335–1338 (2011).
[Crossref]

X.B. Kang, W. Tan, and Z.G. Wang, “Validity of effective medium theory for metal-dielectric lamellar gratings,” Opt. Commun. 284, 4237–4242 (2011).
[Crossref]

C. Rizza, A. Di Falco, and A. Ciattoni, “Gain assisted nanocomposite with near zero permittivity modulus at visible frequencies,” Appl. Phys. Lett. 99, 221107 (2011).
[Crossref]

X. Ni, S. Ishii, M.D. Thoreson, V.M. Shalaev, S. Han, S. Lee, and A.V. Kildishev, “Loss-compensated and active hyperbolic metamaterials,” Opt. Express 19, 25242–25254 (2011).
[Crossref]

A.A. Orlov, P.M. Voroshilov, P.A. Belov, and Y. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 85, 045424 (2011).
[Crossref]

2010 (2)

A. Ciattoni, C. Rizza, and E. Palange, “Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity,” Phys. Rev. A 81, 043839 (2010).
[Crossref]

J. Zhang, S. Xiao, C. Jeppesen, A. Kristensen, and N.A. Mortensen, “Electromagnetically induced transparency in metamaterials at near-infrared frequency,” Opt. Express 18, 17187–17192 (2010).
[Crossref] [PubMed]

2009 (2)

S.Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A.A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80, 153103 (2009).
[Crossref]

R.J. Pollard, A. Murphy, W.R. Hendren, P.R. Evans, R. Atkinson, G.A. Wurtz, A.V. Zayats, and V.A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett. 102, 127405 (2009).
[Crossref] [PubMed]

2008 (3)

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 462–493 (2008).
[Crossref] [PubMed]

D. de Ceglia, M.A. Vincenti, M.G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J.W. Haus, M.J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77, 033848 (2008).
[Crossref]

2007 (3)

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

B. Sturman, E. Podivilov, and M. Gorkunov, “Eigenmodes for metal-dielectric light-transmitting nanostructures,” Phys. Rev. B 76, 125104 (2007).
[Crossref]

D.A. Genov, M. Ambati, and X. Zhang, “Surface plasmon amplification in planar metal films,” IEEE J. Quant. Electron. 43, 1104–1108 (2007).
[Crossref]

2006 (1)

2005 (1)

S.P. Lepkowski, J.A. Majewski, and G. Jurczak, “Nonlinear elesticity in II-N compounds: Ab initio calculations,” Phys. Rev. B 72, 245201 (2005).
[Crossref]

2004 (1)

1995 (1)

1956 (1)

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

Adegoke, J.

Akozbek, N.

D. de Ceglia, M.A. Vincenti, M.G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J.W. Haus, M.J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77, 033848 (2008).
[Crossref]

Alu, A.

Ambati, M.

D.A. Genov, M. Ambati, and X. Zhang, “Surface plasmon amplification in planar metal films,” IEEE J. Quant. Electron. 43, 1104–1108 (2007).
[Crossref]

Argyropoulos, C.

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, 075418 (2016).
[Crossref]

Atkinson, R.

R.J. Pollard, A. Murphy, W.R. Hendren, P.R. Evans, R. Atkinson, G.A. Wurtz, A.V. Zayats, and V.A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett. 102, 127405 (2009).
[Crossref] [PubMed]

Avrutsky, I.

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

Babicheva, V.E.

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 90, 013801 (2014).
[Crossref]

Bahoura, M.

Belov, P.

Belov, P.A.

R.S. Savelev, I.A. Shadrivov, P.A. Belov, N.N. Rosanov, S.V. Fedorov, A.A. Sukhorukov, and Y.S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

A.A. Orlov, P.M. Voroshilov, P.A. Belov, and Y. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 85, 045424 (2011).
[Crossref]

Benedicto, J.

J. Benedicto, E. Centeno, R. Polles, and A. Moreau, “Ultimate resolution of indefinite metamaterial flat lenses,” Phys. Rev. B 88, 245138 (2013).
[Crossref]

Bettiol, A.A.

S.Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A.A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80, 153103 (2009).
[Crossref]

Bloemer, M.J.

D. de Ceglia, M.A. Vincenti, M.G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J.W. Haus, M.J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77, 033848 (2008).
[Crossref]

Bomberger, C.C.

Bonic, I.

S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Ultra-broadband simultaneous superluminal phase and group velocities in non-Foster epsilon-near-zero matamaterial,” Appl. Phys. Lett. 102, 054108 (2013).
[Crossref]

Bozhevolnyi, S.I.

S. Raza, S.I. Bozhevolnyi, M. Wubs, and N.A. Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys.: Condens. Matter 27, 183204 (2015).

Briggs, D.P.

Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
[Crossref]

Cappeddu, M.G.

D. de Ceglia, M.A. Vincenti, M.G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J.W. Haus, M.J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77, 033848 (2008).
[Crossref]

Centeno, E.

J. Benedicto, E. Centeno, R. Polles, and A. Moreau, “Ultimate resolution of indefinite metamaterial flat lenses,” Phys. Rev. B 88, 245138 (2013).
[Crossref]

Centini, M.

D. de Ceglia, M.A. Vincenti, M.G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J.W. Haus, M.J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77, 033848 (2008).
[Crossref]

Chiam, S.Y.

S.Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A.A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80, 153103 (2009).
[Crossref]

Ciattoni, A.

C. Rizza, A. Di Falco, and A. Ciattoni, “Gain assisted nanocomposite with near zero permittivity modulus at visible frequencies,” Appl. Phys. Lett. 99, 221107 (2011).
[Crossref]

A. Ciattoni, C. Rizza, and E. Palange, “Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity,” Phys. Rev. A 81, 043839 (2010).
[Crossref]

D’Orazio, A.

D. de Ceglia, M.A. Vincenti, M.G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J.W. Haus, M.J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77, 033848 (2008).
[Crossref]

de Ceglia, D.

D. de Ceglia, M.A. Vincenti, M.G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J.W. Haus, M.J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77, 033848 (2008).
[Crossref]

Di Falco, A.

C. Rizza, A. Di Falco, and A. Ciattoni, “Gain assisted nanocomposite with near zero permittivity modulus at visible frequencies,” Appl. Phys. Lett. 99, 221107 (2011).
[Crossref]

Drachev, V.P.

Elser, J.

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

Estakhri, N.M.

Evans, P.R.

R.J. Pollard, A. Murphy, W.R. Hendren, P.R. Evans, R. Atkinson, G.A. Wurtz, A.V. Zayats, and V.A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett. 102, 127405 (2009).
[Crossref] [PubMed]

Fainman, Y.

J. S. T. Smalley, F. Vallini, S. Montoya, L. Ferrari, S. Shahin, C. T. Riley, B. KantÃl’, E. E. Fullerton, Z. Liu, and Y. Fainman, “Luminescent hyperbolic metasurfaces,” Nature Commun. 7, 13793 (2017).
[Crossref]

J.S.T. Smalley, F. Vallini, S. Shahin, B. Kante, and Y. Fainman, “Gain-enhanced high-k transmission through metal-semiconductor hyperbolic metamaterials,” Opt. Mater. Express 5, 2300–2312 (2015).
[Crossref]

J.S.T. Smalley, F. Vallini, B. Kante, S. Shahin, and Y. Fainman, “Modal amplification in active waveguides with hyperbolic dispersion at telecommunication frequencies,” Opt. Express 22, 21088–21105 (2014).
[Crossref] [PubMed]

M.P. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surface plasmon polaritons on planar metallic waveguides,” Opt. Express 12, 4072–4079 (2004).
[Crossref] [PubMed]

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J.S.T. Smalley, F. Vallini, S. Montoya, L. Ferrari, C.T. Riley, S. Shahin, B. Kante, E. Fullerton, Z. Liu, and Y. Fainman, “Light-emitting hyperbolic metasurfaces at telecom frequencies,” in Advanced Photonics 2016 (IPR, NOMA, SPPCom, SOF), OSA Tech. Digest (OSA, 2016), paper NoM3C.3.
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Y. Guo, W. Newman, C.L. Lortes, and Z. Jacob, “Application of hyperbolic metamaterial substrates,” Adv. OptoElectron. 2012, 1–9 (2012).
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Kildishev, A.V.

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S. Hrabar, I. Krois, I. Bonic, and A. Kiricenko, “Ultra-broadband simultaneous superluminal phase and group velocities in non-Foster epsilon-near-zero matamaterial,” Appl. Phys. Lett. 102, 054108 (2013).
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Kivshar, Y.S.

R.S. Savelev, I.A. Shadrivov, P.A. Belov, N.N. Rosanov, S.V. Fedorov, A.A. Sukhorukov, and Y.S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
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Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
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Krois, I.

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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, 075418 (2016).
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Lederer, F.

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Lepkowski, S.P.

S.P. Lepkowski, J.A. Majewski, and G. Jurczak, “Nonlinear elesticity in II-N compounds: Ab initio calculations,” Phys. Rev. B 72, 245201 (2005).
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S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
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R. Liu, C.M. Roberts, Y. Zhong, V.A. Podolskiy, and D. Wasserman, “Epsilon-near-zero photonic wires,” ACS Photon. 3, 1045–1052 (2016).
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J. S. T. Smalley, F. Vallini, S. Montoya, L. Ferrari, S. Shahin, C. T. Riley, B. KantÃl’, E. E. Fullerton, Z. Liu, and Y. Fainman, “Luminescent hyperbolic metasurfaces,” Nature Commun. 7, 13793 (2017).
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J.S.T. Smalley, F. Vallini, S. Montoya, L. Ferrari, C.T. Riley, S. Shahin, B. Kante, E. Fullerton, Z. Liu, and Y. Fainman, “Light-emitting hyperbolic metasurfaces at telecom frequencies,” in Advanced Photonics 2016 (IPR, NOMA, SPPCom, SOF), OSA Tech. Digest (OSA, 2016), paper NoM3C.3.
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Y. Guo, W. Newman, C.L. Lortes, and Z. Jacob, “Application of hyperbolic metamaterial substrates,” Adv. OptoElectron. 2012, 1–9 (2012).
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Majewski, J.A.

S.P. Lepkowski, J.A. Majewski, and G. Jurczak, “Nonlinear elesticity in II-N compounds: Ab initio calculations,” Phys. Rev. B 72, 245201 (2005).
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A. Marini and F.J. Garcia de Abajo, “Self-organization of frozen light in near-zero-index media with cubic nonlinearity,” Scient. Rep. 6, 20088 (2016).
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Monticone, F.

Montoya, S.

J. S. T. Smalley, F. Vallini, S. Montoya, L. Ferrari, S. Shahin, C. T. Riley, B. KantÃl’, E. E. Fullerton, Z. Liu, and Y. Fainman, “Luminescent hyperbolic metasurfaces,” Nature Commun. 7, 13793 (2017).
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J.S.T. Smalley, F. Vallini, S. Montoya, L. Ferrari, C.T. Riley, S. Shahin, B. Kante, E. Fullerton, Z. Liu, and Y. Fainman, “Light-emitting hyperbolic metasurfaces at telecom frequencies,” in Advanced Photonics 2016 (IPR, NOMA, SPPCom, SOF), OSA Tech. Digest (OSA, 2016), paper NoM3C.3.
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J. Benedicto, E. Centeno, R. Polles, and A. Moreau, “Ultimate resolution of indefinite metamaterial flat lenses,” Phys. Rev. B 88, 245138 (2013).
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S. Raza, S.I. Bozhevolnyi, M. Wubs, and N.A. Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys.: Condens. Matter 27, 183204 (2015).

J. Zhang, S. Xiao, C. Jeppesen, A. Kristensen, and N.A. Mortensen, “Electromagnetically induced transparency in metamaterials at near-infrared frequency,” Opt. Express 18, 17187–17192 (2010).
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Narimanov, E.E.

Z. Jacob, I.I. Smolyaninov, and E.E. Narimanov, “Broadband Purcell effect: Radiactive decay engineering with metamaterials,” Appl. Phys. Lett. 100, 181105 (2012).
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Newman, W.

Y. Guo, W. Newman, C.L. Lortes, and Z. Jacob, “Application of hyperbolic metamaterial substrates,” Adv. OptoElectron. 2012, 1–9 (2012).
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Ni, X.

Noginov, M.A.

Novitsky, A.

V. Popov, A.V. Lavrinenko, and A. Novitsky, “Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation,” Phys. Rev. B 94, 085428 (2016).
[Crossref]

Orlov, A.

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 90, 013801 (2014).
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A.A. Orlov, P.M. Voroshilov, P.A. Belov, and Y. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 85, 045424 (2011).
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A. Ciattoni, C. Rizza, and E. Palange, “Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity,” Phys. Rev. A 81, 043839 (2010).
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Podivilov, E.

B. Sturman, E. Podivilov, and M. Gorkunov, “Eigenmodes for metal-dielectric light-transmitting nanostructures,” Phys. Rev. B 76, 125104 (2007).
[Crossref]

Podolskiy, V.A.

R. Liu, C.M. Roberts, Y. Zhong, V.A. Podolskiy, and D. Wasserman, “Epsilon-near-zero photonic wires,” ACS Photon. 3, 1045–1052 (2016).
[Crossref]

R.J. Pollard, A. Murphy, W.R. Hendren, P.R. Evans, R. Atkinson, G.A. Wurtz, A.V. Zayats, and V.A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett. 102, 127405 (2009).
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Pollard, R.J.

R.J. Pollard, A. Murphy, W.R. Hendren, P.R. Evans, R. Atkinson, G.A. Wurtz, A.V. Zayats, and V.A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett. 102, 127405 (2009).
[Crossref] [PubMed]

Polles, R.

J. Benedicto, E. Centeno, R. Polles, and A. Moreau, “Ultimate resolution of indefinite metamaterial flat lenses,” Phys. Rev. B 88, 245138 (2013).
[Crossref]

Pommet, D. A.

Popov, V.

V. Popov, A.V. Lavrinenko, and A. Novitsky, “Operator approach to effective medium theory to overcome a breakdown of Maxwell Garnett approximation,” Phys. Rev. B 94, 085428 (2016).
[Crossref]

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S. Raza, S.I. Bozhevolnyi, M. Wubs, and N.A. Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys.: Condens. Matter 27, 183204 (2015).

Riley, C. T.

J. S. T. Smalley, F. Vallini, S. Montoya, L. Ferrari, S. Shahin, C. T. Riley, B. KantÃl’, E. E. Fullerton, Z. Liu, and Y. Fainman, “Luminescent hyperbolic metasurfaces,” Nature Commun. 7, 13793 (2017).
[Crossref]

Riley, C.T.

J.S.T. Smalley, F. Vallini, S. Montoya, L. Ferrari, C.T. Riley, S. Shahin, B. Kante, E. Fullerton, Z. Liu, and Y. Fainman, “Light-emitting hyperbolic metasurfaces at telecom frequencies,” in Advanced Photonics 2016 (IPR, NOMA, SPPCom, SOF), OSA Tech. Digest (OSA, 2016), paper NoM3C.3.
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A. Ciattoni, C. Rizza, and E. Palange, “Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity,” Phys. Rev. A 81, 043839 (2010).
[Crossref]

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R. Liu, C.M. Roberts, Y. Zhong, V.A. Podolskiy, and D. Wasserman, “Epsilon-near-zero photonic wires,” ACS Photon. 3, 1045–1052 (2016).
[Crossref]

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S.Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A.A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80, 153103 (2009).
[Crossref]

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R.S. Savelev, I.A. Shadrivov, P.A. Belov, N.N. Rosanov, S.V. Fedorov, A.A. Sukhorukov, and Y.S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
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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. Rev. 90, 191109 (2007).

Savelev, R.S.

R.S. Savelev, I.A. Shadrivov, P.A. Belov, N.N. Rosanov, S.V. Fedorov, A.A. Sukhorukov, and Y.S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Scalora, M.

D. de Ceglia, M.A. Vincenti, M.G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J.W. Haus, M.J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77, 033848 (2008).
[Crossref]

Shadrivov, I.A.

R.S. Savelev, I.A. Shadrivov, P.A. Belov, N.N. Rosanov, S.V. Fedorov, A.A. Sukhorukov, and Y.S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Shahin, S.

J. S. T. Smalley, F. Vallini, S. Montoya, L. Ferrari, S. Shahin, C. T. Riley, B. KantÃl’, E. E. Fullerton, Z. Liu, and Y. Fainman, “Luminescent hyperbolic metasurfaces,” Nature Commun. 7, 13793 (2017).
[Crossref]

J.S.T. Smalley, F. Vallini, S. Shahin, B. Kante, and Y. Fainman, “Gain-enhanced high-k transmission through metal-semiconductor hyperbolic metamaterials,” Opt. Mater. Express 5, 2300–2312 (2015).
[Crossref]

J.S.T. Smalley, F. Vallini, B. Kante, S. Shahin, and Y. Fainman, “Modal amplification in active waveguides with hyperbolic dispersion at telecommunication frequencies,” Opt. Express 22, 21088–21105 (2014).
[Crossref] [PubMed]

J.S.T. Smalley, F. Vallini, S. Montoya, L. Ferrari, C.T. Riley, S. Shahin, B. Kante, E. Fullerton, Z. Liu, and Y. Fainman, “Light-emitting hyperbolic metasurfaces at telecom frequencies,” in Advanced Photonics 2016 (IPR, NOMA, SPPCom, SOF), OSA Tech. Digest (OSA, 2016), paper NoM3C.3.
[Crossref]

Shalaev, V.M.

Singh, R.

S.Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A.A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80, 153103 (2009).
[Crossref]

Sipe, J.E.

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 90, 013801 (2014).
[Crossref]

Small, C.E.

Smalley, J. S. T.

J. S. T. Smalley, F. Vallini, S. Montoya, L. Ferrari, S. Shahin, C. T. Riley, B. KantÃl’, E. E. Fullerton, Z. Liu, and Y. Fainman, “Luminescent hyperbolic metasurfaces,” Nature Commun. 7, 13793 (2017).
[Crossref]

Smalley, J.S.T.

Smolyaninov, I.I.

Z. Jacob, I.I. Smolyaninov, and E.E. Narimanov, “Broadband Purcell effect: Radiactive decay engineering with metamaterials,” Appl. Phys. Lett. 100, 181105 (2012).
[Crossref]

Sturman, B.

B. Sturman, E. Podivilov, and M. Gorkunov, “Eigenmodes for metal-dielectric light-transmitting nanostructures,” Phys. Rev. B 76, 125104 (2007).
[Crossref]

Sukhorukov, A.A.

R.S. Savelev, I.A. Shadrivov, P.A. Belov, N.N. Rosanov, S.V. Fedorov, A.A. Sukhorukov, and Y.S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Tan, W.

X.B. Kang, W. Tan, and Z.G. Wang, “Validity of effective medium theory for metal-dielectric lamellar gratings,” Opt. Commun. 284, 4237–4242 (2011).
[Crossref]

Tetz, K.

Thoreson, M.D.

Valentine, J.

Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
[Crossref]

Vallini, F.

J. S. T. Smalley, F. Vallini, S. Montoya, L. Ferrari, S. Shahin, C. T. Riley, B. KantÃl’, E. E. Fullerton, Z. Liu, and Y. Fainman, “Luminescent hyperbolic metasurfaces,” Nature Commun. 7, 13793 (2017).
[Crossref]

J.S.T. Smalley, F. Vallini, S. Shahin, B. Kante, and Y. Fainman, “Gain-enhanced high-k transmission through metal-semiconductor hyperbolic metamaterials,” Opt. Mater. Express 5, 2300–2312 (2015).
[Crossref]

J.S.T. Smalley, F. Vallini, B. Kante, S. Shahin, and Y. Fainman, “Modal amplification in active waveguides with hyperbolic dispersion at telecommunication frequencies,” Opt. Express 22, 21088–21105 (2014).
[Crossref] [PubMed]

J.S.T. Smalley, F. Vallini, S. Montoya, L. Ferrari, C.T. Riley, S. Shahin, B. Kante, E. Fullerton, Z. Liu, and Y. Fainman, “Light-emitting hyperbolic metasurfaces at telecom frequencies,” in Advanced Photonics 2016 (IPR, NOMA, SPPCom, SOF), OSA Tech. Digest (OSA, 2016), paper NoM3C.3.
[Crossref]

Vincenti, M.A.

D. de Ceglia, M.A. Vincenti, M.G. Cappeddu, M. Centini, N. Akozbek, A. D’Orazio, J.W. Haus, M.J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77, 033848 (2008).
[Crossref]

Voroshilov, P.M.

A.A. Orlov, P.M. Voroshilov, P.A. Belov, and Y. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 85, 045424 (2011).
[Crossref]

Wang, Y.

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
[Crossref] [PubMed]

Wang, Z.G.

X.B. Kang, W. Tan, and Z.G. Wang, “Validity of effective medium theory for metal-dielectric lamellar gratings,” Opt. Commun. 284, 4237–4242 (2011).
[Crossref]

Wasserman, D.

R. Liu, C.M. Roberts, Y. Zhong, V.A. Podolskiy, and D. Wasserman, “Epsilon-near-zero photonic wires,” ACS Photon. 3, 1045–1052 (2016).
[Crossref]

Wei, D.

Wubs, M.

S. Raza, S.I. Bozhevolnyi, M. Wubs, and N.A. Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys.: Condens. Matter 27, 183204 (2015).

Wurtz, G.A.

R.J. Pollard, A. Murphy, W.R. Hendren, P.R. Evans, R. Atkinson, G.A. Wurtz, A.V. Zayats, and V.A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett. 102, 127405 (2009).
[Crossref] [PubMed]

Xiao, S.

Yang, Y.

Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
[Crossref]

Yu, Z.

Zayats, A.V.

R.J. Pollard, A. Murphy, W.R. Hendren, P.R. Evans, R. Atkinson, G.A. Wurtz, A.V. Zayats, and V.A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett. 102, 127405 (2009).
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Zhang, J.

Zhang, S.

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
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Zhang, W.

S.Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A.A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80, 153103 (2009).
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Zhang, X.

S. Zhang, D.A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 047401 (2008).
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D.A. Genov, M. Ambati, and X. Zhang, “Surface plasmon amplification in planar metal films,” IEEE J. Quant. Electron. 43, 1104–1108 (2007).
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R. Liu, C.M. Roberts, Y. Zhong, V.A. Podolskiy, and D. Wasserman, “Epsilon-near-zero photonic wires,” ACS Photon. 3, 1045–1052 (2016).
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Zhu, G.

Zhukovsky, S.V.

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 90, 013801 (2014).
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Zide, J.

ACS Photon. (1)

R. Liu, C.M. Roberts, Y. Zhong, V.A. Podolskiy, and D. Wasserman, “Epsilon-near-zero photonic wires,” ACS Photon. 3, 1045–1052 (2016).
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Y. Guo, W. Newman, C.L. Lortes, and Z. Jacob, “Application of hyperbolic metamaterial substrates,” Adv. OptoElectron. 2012, 1–9 (2012).
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Z. Jacob, I.I. Smolyaninov, and E.E. Narimanov, “Broadband Purcell effect: Radiactive decay engineering with metamaterials,” Appl. Phys. Lett. 100, 181105 (2012).
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C. Rizza, A. Di Falco, and A. Ciattoni, “Gain assisted nanocomposite with near zero permittivity modulus at visible frequencies,” Appl. Phys. Lett. 99, 221107 (2011).
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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. Rev. 90, 191109 (2007).

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J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 462–493 (2008).
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D.A. Genov, M. Ambati, and X. Zhang, “Surface plasmon amplification in planar metal films,” IEEE J. Quant. Electron. 43, 1104–1108 (2007).
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S. Raza, S.I. Bozhevolnyi, M. Wubs, and N.A. Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys.: Condens. Matter 27, 183204 (2015).

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Y. Yang, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nature Commun. 5, 5753 (2014).
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J. S. T. Smalley, F. Vallini, S. Montoya, L. Ferrari, S. Shahin, C. T. Riley, B. KantÃl’, E. E. Fullerton, Z. Liu, and Y. Fainman, “Luminescent hyperbolic metasurfaces,” Nature Commun. 7, 13793 (2017).
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Opt. Commun. (1)

X.B. Kang, W. Tan, and Z.G. Wang, “Validity of effective medium theory for metal-dielectric lamellar gratings,” Opt. Commun. 284, 4237–4242 (2011).
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Opt. Express (8)

A. Orlov, I. Iorsh, P. Belov, and Y. Kivshar, “Complex band structure of nanostructured metal-dielectric metamaterials,” Opt. Express 21, 1593–1598 (2013).
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J. Zhang, S. Xiao, C. Jeppesen, A. Kristensen, and N.A. Mortensen, “Electromagnetically induced transparency in metamaterials at near-infrared frequency,” Opt. Express 18, 17187–17192 (2010).
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C. Argyropoulos, N.M. Estakhri, F. Monticone, and A. Alu, “Negative refraction, gain and nonlinear effects in hyperbolic metamaterials,” Opt. Express 21, 15037–15047 (2013).
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X. Ni, S. Ishii, M.D. Thoreson, V.M. Shalaev, S. Han, S. Lee, and A.V. Kildishev, “Loss-compensated and active hyperbolic metamaterials,” Opt. Express 19, 25242–25254 (2011).
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J.S.T. Smalley, F. Vallini, B. Kante, S. Shahin, and Y. Fainman, “Modal amplification in active waveguides with hyperbolic dispersion at telecommunication frequencies,” Opt. Express 22, 21088–21105 (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 90, 013801 (2014).
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J. Benedicto, E. Centeno, R. Polles, and A. Moreau, “Ultimate resolution of indefinite metamaterial flat lenses,” Phys. Rev. B 88, 245138 (2013).
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S.Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A.A. Bettiol, “Analogue of electromagnetically induced transparency in a terahertz metamaterial,” Phys. Rev. B 80, 153103 (2009).
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R.J. Pollard, A. Murphy, W.R. Hendren, P.R. Evans, R. Atkinson, G.A. Wurtz, A.V. Zayats, and V.A. Podolskiy, “Optical nonlocalities and additional waves in epsilon-near-zero metamaterials,” Phys. Rev. Lett. 102, 127405 (2009).
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J.S.T. Smalley, F. Vallini, S. Montoya, L. Ferrari, C.T. Riley, S. Shahin, B. Kante, E. Fullerton, Z. Liu, and Y. Fainman, “Light-emitting hyperbolic metasurfaces at telecom frequencies,” in Advanced Photonics 2016 (IPR, NOMA, SPPCom, SOF), OSA Tech. Digest (OSA, 2016), paper NoM3C.3.
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Figures (7)

Fig. 1
Fig. 1 The unit cell of the structure under consideration.
Fig. 2
Fig. 2 The function |F(f, ϵeff)| (logarithmic scale) at Im(ϵ2)=−0.2 and d = 100 nm for the TM polarization.
Fig. 3
Fig. 3 The function |F(f, ϵeff)| (logarithmic scale) at Im(ϵ2)=−0.2 and d = 100 nm for the TE polarization.
Fig. 4
Fig. 4 The dependence of ϵ e f f ( A ) (green curves) and corresponding ϵ 2 ( 0 ) (blue curves) vs f at different values of d for the even TM mode.
Fig. 5
Fig. 5 The dependence of ϵ e f f ( B ) (green curves) and corresponding ϵ 2 ( 0 ) (blue curves) vs f at different values of d for the odd TM mode.
Fig. 6
Fig. 6 The dependence of ϵ e f f ( A ) (green curves) and corresponding Im ϵ 2 ( 0 ) (blue curves) vs Reϵ2 for the even TM mode at d = 90 nm.
Fig. 7
Fig. 7 The dependence Im ϵ 2 ( 0 ) ( k 0 d ) (blue curves) and corresponding f(k0d) (green curves) at which ϵeff = 0 for different values of Reϵ2.

Equations (16)

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ϵ e f f ( k ) ϵ e f f ( k ) = k 2 / k 0 2 ,
F = cos ( k 1 d 1 ) cos ( k 2 d 2 ) γ sin ( k 1 d 1 ) sin ( k 2 d 2 ) 1 = 0 ,
k 1 ϵ 1 tan k 1 d 1 2 + k 2 ϵ 2 tan k 2 d 2 2 = 0 ,
k 1 ϵ 1 tan k 2 d 2 2 + k 2 ϵ 2 tan k 1 d 1 2 = 0 ,
k 1 tan k 1 d 1 2 + k 2 tan k 2 d 2 2 = 0 ,
k 1 tan k 2 d 2 2 + k 2 tan k 1 d 1 2 = 0 ,
ϵ e f f ( k 0 d 1 , k 0 d 2 , ϵ 1 , ϵ 2 ) = r s 2 ϵ e f f ( r s k 0 d 1 , r s k 0 d 2 , ϵ 1 , ϵ 2 / r ) .
ϵ e f f = [ ( 1 f ) / ϵ 1 + f / ϵ 2 ] 1 .
ϵ 1 tan ( k 0 d 1 ϵ 1 / 2 ) + ϵ 2 tan ( k 0 d 2 ϵ 2 ) = 0 ,
sin z = 2 tan z / 2 1 + tan 2 z / 2 and cos z = 1 tan 2 z / 2 1 + tan 2 z / 2 ,
tan z 1 ( tan z 1 + k 2 ϵ 1 k 1 ϵ 2 ) + tan z 2 ( tan z 2 + k 1 ϵ 2 k 2 ϵ 1 ) = 0 ,
tan 2 z 2 i tan z 2 ( ϵ 1 ϵ 2 + ϵ 2 ϵ 1 ) 1 0 ,
tan 2 z 1 + i tan z 1 ( ϵ 1 ϵ 2 + ϵ 2 ϵ 1 ) 1 0 ,
f 2 k 0 d Re arctan [ ( b 2 + 4 b ) / 2 ] ϵ 2 ϵ e f f
f 1 + 2 k 0 d Re arctan [ ( b 2 + 4 + b ) / 2 ] ϵ 1 ϵ e f f
b = i ( ϵ 1 ϵ 2 + ϵ 2 ϵ 1 ) .

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