Abstract

A strategy is proposed to design a certain kind of metamaterial with near-zero electric permittivity over a broad frequency band, i.e., the broadband epsilon-near-zero (ENZ) metamaterials. Based on the Bergman–Milton spectral representation of the effective permittivity, the design is first carried out in the dimensionless spectral space, where the effective permittivity of the ENZ metamaterials is mathematically determined by a series of zeros and poles (singularities), which can be easily arranged as required by the operating band. Then, through a fast inverse algorithm, the mathematical structures of the ENZ metamaterials can be transformed back to their physical structures, which can be put into practical applications. The effective permittivity of the designed ENZ metamaterials is examined, and the distribution of the electric field inside the designed ENZ metamaterials is also explored, in order to reveal the physical reason behind the broadband ENZ phenomenon.

© 2012 Optical Society of America

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References

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  1. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E 70, 046608 (2004).
  2. A. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73, 115111 (2006).
    [CrossRef]
  3. A. Husakou and J. Herrmann, “Steplike transmission of light through a metal-dielectric multilayer structure due to an intensity-dependent sign of the effective dielectric constant,” Phys. Rev. Lett. 99, 127402 (2007).
    [CrossRef]
  4. K. Halterman and S. Feng, “Resonant transmission of electromagnetic fields through subwavelength zero-ϵ slits,” Phys. Rev. A 78, 021805(R) (2008).
    [CrossRef]
  5. A. Alú, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε-near-zero-filled narrow channels,” Phys. Rev. E 78, 016604 (2008).
  6. 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]
  7. Q. Cheng, R. Liu, D. Huang, T. J. Cui, and D. R. Smith, “Circuit verification of tunneling effect in zero permittivity medium,” Appl. Phys. Lett. 91, 234105 (2007).
  8. L. Shen, J. J. Wu, and T. J. Yang, “Anisotropic medium with parabolic dispersion,” Appl. Phys. Lett. 92, 261905 (2008).
  9. S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
    [CrossRef]
  10. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
    [CrossRef]
  11. M. Silveirinha and N. Engheta, “Transporting an image through a subwavelength hole,” Phys. Rev. Lett. 102, 103902 (2009).
  12. N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
    [CrossRef]
  13. A. Alú, 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).
  14. M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B 75, 075119 (2007).
  15. B. Edwards, A. Alú, 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]
  16. 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).
  17. A. Alú and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E 72, 016623 (2005).
    [CrossRef]
  18. L. Sun and K. W. Yu, “Broadband electromagnetic transparency by graded metamaterials: scattering cancellation scheme,” J. Opt. Soc. Am. B 28, 994–1001 (2011).
    [CrossRef]
  19. A. V. Goncharenko and K. R. Chen, “Strategy for designing epsilonnear-zero nanostructured metamaterials over a frequency range,” J. Nanophoton. 4, 041530 (2010).
  20. D. J. Bergman, “The dielectric constant of a composite material—a problem in classical physics,” Phys. Rep. 43, 377–407 (1978).
    [CrossRef]
  21. D. J. Bergman and D. Stroud, “The physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
    [CrossRef]
  22. G. W. Milton, “Bounds on the complex dielectric constant of a composite material,” Appl. Phys. Lett. 37, 300–302 (1980).
    [CrossRef]
  23. G. W. Milton, “Bounds on the complex permittivity of a two-component composite material,” J. Appl. Phys. 52, 5286–5293 (1981).
    [CrossRef]
  24. G. W. Milton, “Bounds on the transport and optical properties of a two-component composite material,” J. Appl. Phys. 52, 5294–5304 (1981).
    [CrossRef]

2011 (1)

2010 (1)

A. V. Goncharenko and K. R. Chen, “Strategy for designing epsilonnear-zero nanostructured metamaterials over a frequency range,” J. Nanophoton. 4, 041530 (2010).

2009 (2)

B. Edwards, A. Alú, 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]

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

2008 (3)

K. Halterman and S. Feng, “Resonant transmission of electromagnetic fields through subwavelength zero-ϵ slits,” Phys. Rev. A 78, 021805(R) (2008).
[CrossRef]

A. Alú, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε-near-zero-filled narrow channels,” Phys. Rev. E 78, 016604 (2008).

L. Shen, J. J. Wu, and T. J. Yang, “Anisotropic medium with parabolic dispersion,” Appl. Phys. Lett. 92, 261905 (2008).

2007 (6)

A. Husakou and J. Herrmann, “Steplike transmission of light through a metal-dielectric multilayer structure due to an intensity-dependent sign of the effective dielectric constant,” Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef]

Q. Cheng, R. Liu, D. Huang, T. J. Cui, and D. R. Smith, “Circuit verification of tunneling effect in zero permittivity medium,” Appl. Phys. Lett. 91, 234105 (2007).

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

A. Alú, 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).

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B 75, 075119 (2007).

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).

2006 (3)

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. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73, 115111 (2006).
[CrossRef]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
[CrossRef]

2005 (1)

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

2004 (1)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E 70, 046608 (2004).

2002 (1)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

1992 (1)

D. J. Bergman and D. Stroud, “The physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[CrossRef]

1981 (2)

G. W. Milton, “Bounds on the complex permittivity of a two-component composite material,” J. Appl. Phys. 52, 5286–5293 (1981).
[CrossRef]

G. W. Milton, “Bounds on the transport and optical properties of a two-component composite material,” J. Appl. Phys. 52, 5294–5304 (1981).
[CrossRef]

1980 (1)

G. W. Milton, “Bounds on the complex dielectric constant of a composite material,” Appl. Phys. Lett. 37, 300–302 (1980).
[CrossRef]

1978 (1)

D. J. Bergman, “The dielectric constant of a composite material—a problem in classical physics,” Phys. Rep. 43, 377–407 (1978).
[CrossRef]

Alú, A.

B. Edwards, A. Alú, 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. Alú, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε-near-zero-filled narrow channels,” Phys. Rev. E 78, 016604 (2008).

A. Alú, 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).

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

Bergman, D. J.

D. J. Bergman and D. Stroud, “The physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[CrossRef]

D. J. Bergman, “The dielectric constant of a composite material—a problem in classical physics,” Phys. Rep. 43, 377–407 (1978).
[CrossRef]

Chen, K. R.

A. V. Goncharenko and K. R. Chen, “Strategy for designing epsilonnear-zero nanostructured metamaterials over a frequency range,” J. Nanophoton. 4, 041530 (2010).

Cheng, Q.

Q. Cheng, R. Liu, D. Huang, T. J. Cui, and D. R. Smith, “Circuit verification of tunneling effect in zero permittivity medium,” Appl. Phys. Lett. 91, 234105 (2007).

Cui, T. J.

Q. Cheng, R. Liu, D. Huang, T. J. Cui, and D. R. Smith, “Circuit verification of tunneling effect in zero permittivity medium,” Appl. Phys. Lett. 91, 234105 (2007).

Edwards, B.

B. Edwards, A. Alú, 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]

Engheta, N.

B. Edwards, A. Alú, 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]

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

A. Alú, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε-near-zero-filled narrow channels,” Phys. Rev. E 78, 016604 (2008).

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

A. Alú, 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).

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B 75, 075119 (2007).

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).

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
[CrossRef]

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

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Feng, S.

K. Halterman and S. Feng, “Resonant transmission of electromagnetic fields through subwavelength zero-ϵ slits,” Phys. Rev. A 78, 021805(R) (2008).
[CrossRef]

Goncharenko, A. V.

A. V. Goncharenko and K. R. Chen, “Strategy for designing epsilonnear-zero nanostructured metamaterials over a frequency range,” J. Nanophoton. 4, 041530 (2010).

Guerin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Halterman, K.

K. Halterman and S. Feng, “Resonant transmission of electromagnetic fields through subwavelength zero-ϵ slits,” Phys. Rev. A 78, 021805(R) (2008).
[CrossRef]

Herrmann, J.

A. Husakou and J. Herrmann, “Steplike transmission of light through a metal-dielectric multilayer structure due to an intensity-dependent sign of the effective dielectric constant,” Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef]

Huang, D.

Q. Cheng, R. Liu, D. Huang, T. J. Cui, and D. R. Smith, “Circuit verification of tunneling effect in zero permittivity medium,” Appl. Phys. Lett. 91, 234105 (2007).

Husakou, A.

A. Husakou and J. Herrmann, “Steplike transmission of light through a metal-dielectric multilayer structure due to an intensity-dependent sign of the effective dielectric constant,” Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef]

Liu, R.

Q. Cheng, R. Liu, D. Huang, T. J. Cui, and D. R. Smith, “Circuit verification of tunneling effect in zero permittivity medium,” Appl. Phys. Lett. 91, 234105 (2007).

Magath, T.

A. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73, 115111 (2006).
[CrossRef]

Milton, G. W.

G. W. Milton, “Bounds on the complex permittivity of a two-component composite material,” J. Appl. Phys. 52, 5286–5293 (1981).
[CrossRef]

G. W. Milton, “Bounds on the transport and optical properties of a two-component composite material,” J. Appl. Phys. 52, 5294–5304 (1981).
[CrossRef]

G. W. Milton, “Bounds on the complex dielectric constant of a composite material,” Appl. Phys. Lett. 37, 300–302 (1980).
[CrossRef]

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Salandrino, A.

A. Alú, 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).

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Schuenemann, K.

A. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73, 115111 (2006).
[CrossRef]

Serebryannikov, A. E.

A. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73, 115111 (2006).
[CrossRef]

Shen, L.

L. Shen, J. J. Wu, and T. J. Yang, “Anisotropic medium with parabolic dispersion,” Appl. Phys. Lett. 92, 261905 (2008).

Silveirinha, M.

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

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B 75, 075119 (2007).

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.

B. Edwards, A. Alú, 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. Alú, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε-near-zero-filled narrow channels,” Phys. Rev. E 78, 016604 (2008).

A. Alú, 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).

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).

Smith, D. R.

Q. Cheng, R. Liu, D. Huang, T. J. Cui, and D. R. Smith, “Circuit verification of tunneling effect in zero permittivity medium,” Appl. Phys. Lett. 91, 234105 (2007).

Stroud, D.

D. J. Bergman and D. Stroud, “The physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[CrossRef]

Sun, L.

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Vasylchenko, O. Y.

A. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73, 115111 (2006).
[CrossRef]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Wu, J. J.

L. Shen, J. J. Wu, and T. J. Yang, “Anisotropic medium with parabolic dispersion,” Appl. Phys. Lett. 92, 261905 (2008).

Yang, T. J.

L. Shen, J. J. Wu, and T. J. Yang, “Anisotropic medium with parabolic dispersion,” Appl. Phys. Lett. 92, 261905 (2008).

Yu, K. W.

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E 70, 046608 (2004).

Appl. Phys. Lett. (3)

Q. Cheng, R. Liu, D. Huang, T. J. Cui, and D. R. Smith, “Circuit verification of tunneling effect in zero permittivity medium,” Appl. Phys. Lett. 91, 234105 (2007).

L. Shen, J. J. Wu, and T. J. Yang, “Anisotropic medium with parabolic dispersion,” Appl. Phys. Lett. 92, 261905 (2008).

G. W. Milton, “Bounds on the complex dielectric constant of a composite material,” Appl. Phys. Lett. 37, 300–302 (1980).
[CrossRef]

J. Appl. Phys. (3)

G. W. Milton, “Bounds on the complex permittivity of a two-component composite material,” J. Appl. Phys. 52, 5286–5293 (1981).
[CrossRef]

G. W. Milton, “Bounds on the transport and optical properties of a two-component composite material,” J. Appl. Phys. 52, 5294–5304 (1981).
[CrossRef]

B. Edwards, A. Alú, 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]

J. Nanophoton. (1)

A. V. Goncharenko and K. R. Chen, “Strategy for designing epsilonnear-zero nanostructured metamaterials over a frequency range,” J. Nanophoton. 4, 041530 (2010).

J. Opt. Soc. Am. B (1)

Phys. Rep. (1)

D. J. Bergman, “The dielectric constant of a composite material—a problem in classical physics,” Phys. Rep. 43, 377–407 (1978).
[CrossRef]

Phys. Rev. A (1)

K. Halterman and S. Feng, “Resonant transmission of electromagnetic fields through subwavelength zero-ϵ slits,” Phys. Rev. A 78, 021805(R) (2008).
[CrossRef]

Phys. Rev. B (5)

A. E. Serebryannikov, T. Magath, K. Schuenemann, and O. Y. Vasylchenko, “Scattering of s-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials,” Phys. Rev. B 73, 115111 (2006).
[CrossRef]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
[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).

A. Alú, 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).

M. Silveirinha and N. Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B 75, 075119 (2007).

Phys. Rev. E (3)

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

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E 70, 046608 (2004).

A. Alú, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε-near-zero-filled narrow channels,” Phys. Rev. E 78, 016604 (2008).

Phys. Rev. Lett. (4)

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. Husakou and J. Herrmann, “Steplike transmission of light through a metal-dielectric multilayer structure due to an intensity-dependent sign of the effective dielectric constant,” Phys. Rev. Lett. 99, 127402 (2007).
[CrossRef]

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

S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Science (1)

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

Solid State Phys. (1)

D. J. Bergman and D. Stroud, “The physical properties of macroscopically inhomogeneous media,” Solid State Phys. 46, 147–269 (1992).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

The ENZ structure is a flat metal–dielectric multilayer stack. Every layer contains two components: metallic inclusions in a dielectric host. The permittivity of the metallic inclusions is denoted as ε 1 ( ω ) , and the permittivity of the dielectric host is denoted as ε 2 . The volume fraction of the metallic inclusions in the i th layer is f i , and the thickness of the i th layer is d i . Note that the thickness of each layer is normalized by a summation rule i = 1 N d i = 1 .

Fig. 2.
Fig. 2.

Effective permittivity of the ENZ structure designed by the zeroth-order approach. The green dots indicate the zero frequencies, and the back crosses indicate the pole frequencies. To make a clear demonstration, only the first and the last zero frequencies are indicated in (b). In the lossless condition, the effective permittivity is displayed by blue solid curves. When loss is under consideration, the real part of the effective permittivity is displayed by red solid curve, while the imaginary part of the effective permittivity is displayed by red dashed curve. The operating frequency band is set to be ω [ 0.3 , 0.7 ] , indicated by arrows. The loss of the metallic inclusions is set to be γ = 0.05 . Panel (a) gives the results of a ten-layer structure. Panel (b) gives the results of a 15-layer structure.

Fig. 3.
Fig. 3.

Legends are the same as those in Fig. 2. The (a) ten-layer and (b) 15-layer cases are studied. Because of further restriction on the real part of the effective permittivity, it is clear that the results of the first-order approach are better than that of the zeroth-order.

Fig. 4.
Fig. 4.

Distribution of the electric field inside the first-order designed ten-layer ENZ structure. The amplitudes of the electric field are denoted by different colors, and the brighter colors indicate higher amplitudes. The boundaries of the operating frequency band are denoted by two dashed lines. Because of the continuity of the electric displacement, when a finite extra field is applied on the ENZ structure, the electric displacement in the whole space should also be finite. Therefore, the electric field should be very large inside the ENZ structure over the operating frequency band, caused by the near-zero effective permittivity. That is clearly indicated in the figure.

Equations (23)

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

ε 1 ( ω ) = 1 1 ω ( ω + i γ ) .
ε 2 = 1 .
i = 1 N d i = 1 .
ε e ( i ) ( s ) = ε 2 ( 1 f i / s ) .
s = ε 2 / ( ε 2 ε 1 ) .
ε e ( s ) = [ i = 1 N d i ε 2 ( 1 f i / s ) ] 1 .
ε e ( s ) = ε 2 i = 1 N s z i s s i .
0 s 1 < z 1 < s 2 < z 2 < s N < z N 1 .
ε e ( ω ) = i = 1 N [ ( ω 2 z i ) ( ω 2 s i ) + i ω γ ( z i s i ) ( ω 2 s i ) 2 + ω 2 γ 2 ] .
ε e ( ω ) = i = 1 N ω 2 z i ω 2 s i ,
ω i = ω a + ( i 1 ) Δ ω ( i = 1 , 2 , , N ) .
ω i = { 0 ( i = 1 ) ( ω a + Δ ω / 2 ) + ( i 2 ) Δ ω ( i = 2 , 3 , , N ) .
1 ε e 1 = i = 1 N f i d i s f i = i = 1 N f i d i ω 2 f i + i ω γ .
i = 1 N ω 2 s i ω 2 z i 1 = i = 1 N f i d i ω 2 f i .
ε e ( s ) = ε 2 [ 1 i = 1 N F i s s i ] .
ε e ( ω ) = [ 1 i = 1 N F i ( ω 2 s i ) ( ω 2 s i ) 2 + ω 2 γ 2 ] + i i = 1 N F i ω γ ( ω 2 s i ) 2 + ω 2 γ 2 .
[ 1 i = 1 N F i ( ω 2 s i ) ( ω 2 s i ) 2 + ω 2 γ 2 ] ω = ω i = 0 ,
1 i = 1 N F i s s i = ε e ( s ) = [ i = 1 N d i ( 1 f i / s ) ] 1 .
P ( s i , F i ; s ) i = 1 N ( s s i ) = ε e ( s ) = i = 1 N ( s f i ) Q ( f i , d i ; s ) .
P ( s i , F i ; s ) i = 1 N ( s s i ) = 0 ,
i = 1 N ( s s i ) = A N s N + A N 1 s N 1 + + A 0 ,
Q ( f i , d i ; s ) = B N s N + B N 1 s N 1 + + B 0 ,
A N = B N , A N 1 = B N 1 , , A 0 = B 0 .

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