Abstract

The optical nonlocality in metal-dielectric multilayer metamaterials is characterized experimentally as a function of the angle of incidence with respect to the TE-polarized incident light. The physical mechanism of the difference between the nonlocal effective permittivity and the effective-medium-theory-based effective permittivity depending on the incident angle is theoretically revealed through the analysis of the band structure, the dispersion relation, and the iso-frequency contours according to the transfer-matrix method. Such effective permittivity difference is also retrieved in the metal-dielectric multilayers based on the measured transmission and reflection spectra.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]

2013 (6)

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[Crossref]

J. Gao, L. Sun, H. Deng, C. J. Mathai, S. Gangopadhyay, and X. Yang, “Experimental realization of epsilon-near-zero metamaterial stacks with metal-dielectric multilayers,” Appl. Phys. Lett. 103, 051111 (2013).
[Crossref]

S. Y. El-Zaizt, “Determination of the complex refractive index of a thick slab material from its spectral reflectance and transmittance at normal incidence,” Optik 124, 157–161 (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]

L. Sun, J. Gao, and X. Yang, “Giant optical nonlocality near the Dirac point in metal-dielectric multilayer meta-materials,” Opt. Express 21, 21542–21555 (2013).
[Crossref] [PubMed]

X. Yang, C. Hu, H. Deng, D. Rosenmann, D. A. Czaplewski, and J. Gao, “Experimental demonstration of near-infrared epsilon-near-zero multilayer metamaterial slabs,” Opt. Express 21, 23631–23639 (2013).
[Crossref] [PubMed]

2012 (2)

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

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

2011 (1)

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

2010 (1)

2009 (2)

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]

M. Silveirinha and N. Engheta, “Transporting an image through a subwavelength hole,” Phys. Rev. Lett. 102, 103902 (2009).
[Crossref] [PubMed]

2008 (3)

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]

R. Pierrea and B. Gralaka, “Appropriate truncation for photonic crystals,” J. Mod. Opt. 55, 1759–1770 (2008).
[Crossref]

2007 (4)

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]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B 76, 245109 (2007).
[Crossref]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
[Crossref] [PubMed]

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

2006 (2)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

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

2005 (1)

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constant of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Alù, A.

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

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[Crossref]

Argyropoulos, C.

C. Argyropoulos, P. Chen, G. D’Aguanno, N. Engheta, and A. Alù, “Boosting optical nonlinearities in ε-near-zero plasmonic channels,” Phys. Rev. B 85, 045129 (2012).
[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. Lett. 90, 191109 (2007).
[Crossref]

Belov, P.

Belov, P. A.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

Caglayan, H.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[Crossref]

Chebykin, A. V.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

Chen, P.

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

Cheng, Q.

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]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constant of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Coenen, T.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[Crossref]

Cui, T. J.

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]

Cummer, S. A.

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]

Czaplewski, D. A.

D’Aguanno, G.

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

Deng, H.

J. Gao, L. Sun, H. Deng, C. J. Mathai, S. Gangopadhyay, and X. Yang, “Experimental realization of epsilon-near-zero metamaterial stacks with metal-dielectric multilayers,” Appl. Phys. Lett. 103, 051111 (2013).
[Crossref]

X. Yang, C. Hu, H. Deng, D. Rosenmann, D. A. Czaplewski, and J. Gao, “Experimental demonstration of near-infrared epsilon-near-zero multilayer metamaterial slabs,” Opt. Express 21, 23631–23639 (2013).
[Crossref] [PubMed]

Edwards, B.

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]

Elser, J.

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

El-Zaizt, S. Y.

S. Y. El-Zaizt, “Determination of the complex refractive index of a thick slab material from its spectral reflectance and transmittance at normal incidence,” Optik 124, 157–161 (2013).
[Crossref]

Engheta, N.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[Crossref]

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

M. Silveirinha and N. Engheta, “Transporting an image through a subwavelength hole,” Phys. Rev. Lett. 102, 103902 (2009).
[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]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B 76, 245109 (2007).
[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]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
[Crossref] [PubMed]

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

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[Crossref]

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]

Feng, S.

Gangopadhyay, S.

J. Gao, L. Sun, H. Deng, C. J. Mathai, S. Gangopadhyay, and X. Yang, “Experimental realization of epsilon-near-zero metamaterial stacks with metal-dielectric multilayers,” Appl. Phys. Lett. 103, 051111 (2013).
[Crossref]

Gao, J.

Gralaka, B.

R. Pierrea and B. Gralaka, “Appropriate truncation for photonic crystals,” J. Mod. Opt. 55, 1759–1770 (2008).
[Crossref]

Hand, T.

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]

Hendren, W. 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]

Hu, C.

Iorsh, I.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constant of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Kivshar, Y.

Kivshar, Y. S.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

Liu, R.

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]

Mathai, C. J.

J. Gao, L. Sun, H. Deng, C. J. Mathai, S. Gangopadhyay, and X. Yang, “Experimental realization of epsilon-near-zero metamaterial stacks with metal-dielectric multilayers,” Appl. Phys. Lett. 103, 051111 (2013).
[Crossref]

Mock, J. J.

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]

Murphy, 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]

Orlov, A.

Orlov, A. A.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Pierrea, R.

R. Pierrea and B. Gralaka, “Appropriate truncation for photonic crystals,” J. Mod. Opt. 55, 1759–1770 (2008).
[Crossref]

Podolskiy, V. 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]

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

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]

Polman, A.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[Crossref]

Rosenmann, D.

Salakhutdinov, I.

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

Salandrino, A.

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]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Sihvola, A. H.

A. H. Sihvola, Electromagnetic mixing formulas and applications (IET, 1999).
[Crossref]

Silveirinha, M.

M. Silveirinha and N. Engheta, “Transporting an image through a subwavelength hole,” Phys. Rev. Lett. 102, 103902 (2009).
[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]

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

Silveirinha, M. G.

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]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B 76, 245109 (2007).
[Crossref]

Simovski, C. R.

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

Smith, D. R.

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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

Sun, L.

J. Gao, L. Sun, H. Deng, C. J. Mathai, S. Gangopadhyay, and X. Yang, “Experimental realization of epsilon-near-zero metamaterial stacks with metal-dielectric multilayers,” Appl. Phys. Lett. 103, 051111 (2013).
[Crossref]

L. Sun, J. Gao, and X. Yang, “Giant optical nonlocality near the Dirac point in metal-dielectric multilayer meta-materials,” Opt. Express 21, 21542–21555 (2013).
[Crossref] [PubMed]

Vesseur, E. J. R.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[Crossref]

Voroshilov, P. M.

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

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]

Yang, X.

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]

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).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

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

J. Gao, L. Sun, H. Deng, C. J. Mathai, S. Gangopadhyay, and X. Yang, “Experimental realization of epsilon-near-zero metamaterial stacks with metal-dielectric multilayers,” Appl. Phys. Lett. 103, 051111 (2013).
[Crossref]

J. Mod. Opt. (1)

R. Pierrea and B. Gralaka, “Appropriate truncation for photonic crystals,” J. Mod. Opt. 55, 1759–1770 (2008).
[Crossref]

Opt. Express (4)

Optik (1)

S. Y. El-Zaizt, “Determination of the complex refractive index of a thick slab material from its spectral reflectance and transmittance at normal incidence,” Optik 124, 157–161 (2013).
[Crossref]

Phys. Rev. B (6)

A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
[Crossref]

A. V. Chebykin, A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, “Nonlocal effective parameters of multilayered metal-dielectric metamaterials,” Phys. Rev. B 86, 115420 (2012).
[Crossref]

P. B. Johnson and R. W. Christy, “Optical constant of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

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

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B 76, 245109 (2007).
[Crossref]

Phys. Rev. E (1)

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
[Crossref]

Phys. Rev. Lett. (6)

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]

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

M. Silveirinha and N. Engheta, “Transporting an image through a subwavelength hole,” Phys. Rev. Lett. 102, 103902 (2009).
[Crossref] [PubMed]

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett. 110, 013902 (2013).
[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]

Science (2)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
[Crossref] [PubMed]

Other (1)

A. H. Sihvola, Electromagnetic mixing formulas and applications (IET, 1999).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of the Au-Al2O3 multilayer stack on a quartz substrate. (b) The SEM picture of the cross section of the fabricated 4-pair Au-Al2O3 multilayer stack.
Fig. 2
Fig. 2 (a) The real part and (b) the imaginary part of the band structure of the Au-Al2O3 multilayer stack. (c) The dispersion relation of the Au-Al2O3 multilayer stack. (d) The transmission, (e) reflection, and (f) absorption spectra of the Au-Al2O3 multilayer stack.
Fig. 3
Fig. 3 (a) The transmission, (b) reflection, and (c) absorption spectra of the Au-Al2O3 multilayer stack in experiments (black curves) and in theory (red curves) at different angles of incidence from 10° to 80°.
Fig. 4
Fig. 4 (a) The difference between the nonlocal ENZ wavelength and the EMT-based ENZ wavelength as a function of the angle of incidence. (b) The real part of the effective permittivity difference at the nonlocal ENZ wavelength of θ = 0° according to Eq. (5) with respect to different angles of incidence. (c) The real part of the measured effective permittivity difference (black triangles) compared to the theoretical prediction (red circles) at different angles of incidence. The IFCs at different wavelengths where Re ( ε eff nonloc ) = sin 2 θ and Re(kz/kp) = Im(kz/k0) at the incident angles of (d) θ = 0° and (e) θ = 50°.

Equations (8)

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( k z 2 + k x 2 ) / ε eff = k 0 2 ,
ε eff EMT = ( ε 1 d 1 + ε 2 d 2 ) / ( d 1 + d 2 ) .
cos ( k z ( d 1 + d 2 ) ) = cos ( k 1 d 1 ) cos ( k 2 d 2 ) ( k 1 / k 2 + k 2 / k 2 ) / 2 sin ( k 1 d 1 ) sin ( k 2 d 2 ) ,
ε eff nonloc = arccos 2 ( cos ( k 1 d 1 ) cos ( k 2 d 2 ) ( k 1 / k 2 + k 2 / k 2 ) / 2 sin ( k 1 d 1 ) sin ( k 2 d 2 ) ) k 0 2 ( d 1 + d 2 ) 2 + sin 2 θ .
Δ ε eff = ε eff nonloc ε eff EMT .
n = ( 1 + R as ) / ( 1 R as ) + ( 4 R as / ( ( 1 R as ) 2 κ 2 ) 1 / 2 ,
κ = λ / ( 4 π d ) ln ( ( T 2 ( 1 R ) 2 + ( ( T 2 ( 1 R 2 ) ) 2 + 4 T 2 ) 1 / 2 ) / ( 2 T ) ) ,
R as = R / ( 1 + ( T 2 ( 1 R ) 2 + ( ( T 2 ( 1 R 2 ) ) 2 + 4 T 2 ) 1 / 2 ) / 2 ) .

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