Abstract

In this paper, the dispersive behavior around the plasma frequency in a magnetically uniaxial metamaterial is experimentally investigated. We show by theoretical analysis, parameter retrieval and experiment that when material loss is considered, while the plasma frequency is defined by the frequency where the real part of permeability approaches zero, ultra fast phase velocity actually appears at a slightly lower frequency, due to the change of the dispersion diagram. Both parameter retrieval and experimental data show that within a narrow frequency band to the left of the plasma frequency, the inherent loss keeps finite and is much less than that in the corresponding resonant region. In a real metamaterial sample, an ultra fast phase velocity of 24,440 times the speed of light in free space is measured, and negative phase propagation due to the only negative permeability is observed. The existence of such ultra fast phase velocity with finite loss perfectly explains how the highly directivity antennas based on near-zero refractive index metamaterial work, and can be further used in other applications such as in-phase wave divider and coherent wave sources.

© 2010 OSA

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References

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  1. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
  2. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
    [CrossRef]
  3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
    [CrossRef] [PubMed]
  4. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
    [CrossRef] [PubMed]
  5. F. Zhang, S. Potet, and J. Caobonell, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE Trans. Microw. Theory Tech. 56(11), 2566–2573 (2008).
    [CrossRef]
  6. A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of epsilon -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 016604 (2008).
    [CrossRef] [PubMed]
  7. 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(3), 033903 (2008).
    [CrossRef] [PubMed]
  8. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
    [CrossRef] [PubMed]
  9. T. Jiang, Y. Luo, Z. Wang, L. Peng, J. Huangfu, W. Cui, W. Ma, H. Chen, and L. Ran, “Rainbow-like radiation from an omni-directional source placed in a uniaxial metamaterial slab,” Opt. Express 17(9), 7068–7073 (2009).
    [CrossRef] [PubMed]
  10. M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
    [CrossRef] [PubMed]
  11. M. Bozzi, L. Perregrini, D. Deslandes, K. Wu, and G. Conciaurol, “A compact, wideband, phase-equalized waveguide divider/combiner for power amplification,” Microwave Conference, 33rd European (2003).
  12. G. A. Zheng, “Abrupt change of reflectivity from the strongly anisotropic metamaterial,” Opt. Commun. 281(8), 1941–1944 (2008).
    [CrossRef]
  13. S. Qiao, G. A. Zheng, H. Zhang, and L. X. Ran, “Transition behavior of k-surface: from hyperbola to ellipse,” Prog. Electromagn. Res. 81, 267–277 (2008).
    [CrossRef]
  14. S. Qiao, G. A. Zheng, W. Ren, and L. X. Ran, “Possible abnormal group velocity in the normal dispersive anisotropic media,” J. Electromagn. Waves Appl. 22(10), 1309–1317 (2008).
    [CrossRef]
  15. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
    [CrossRef]
  16. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
    [CrossRef]
  17. X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
    [CrossRef] [PubMed]

2009 (1)

2008 (6)

F. Zhang, S. Potet, and J. Caobonell, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE Trans. Microw. Theory Tech. 56(11), 2566–2573 (2008).
[CrossRef]

A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of epsilon -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 016604 (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(3), 033903 (2008).
[CrossRef] [PubMed]

G. A. Zheng, “Abrupt change of reflectivity from the strongly anisotropic metamaterial,” Opt. Commun. 281(8), 1941–1944 (2008).
[CrossRef]

S. Qiao, G. A. Zheng, H. Zhang, and L. X. Ran, “Transition behavior of k-surface: from hyperbola to ellipse,” Prog. Electromagn. Res. 81, 267–277 (2008).
[CrossRef]

S. Qiao, G. A. Zheng, W. Ren, and L. X. Ran, “Possible abnormal group velocity in the normal dispersive anisotropic media,” J. Electromagn. Waves Appl. 22(10), 1309–1317 (2008).
[CrossRef]

2006 (1)

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006).
[CrossRef] [PubMed]

2004 (2)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[CrossRef] [PubMed]

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

2002 (2)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[CrossRef] [PubMed]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Alù, A.

A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of epsilon -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 016604 (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(3), 033903 (2008).
[CrossRef] [PubMed]

Caobonell, J.

F. Zhang, S. Potet, and J. Caobonell, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE Trans. Microw. Theory Tech. 56(11), 2566–2573 (2008).
[CrossRef]

Chen, H.

Chen, X. D.

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Cui, W.

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(3), 033903 (2008).
[CrossRef] [PubMed]

Engheta, N.

A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of epsilon -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 016604 (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(3), 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(15), 157403 (2006).
[CrossRef] [PubMed]

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[CrossRef] [PubMed]

Grzegorczyk, T. M.

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Guérin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Huangfu, J.

Jiang, T.

Kong, J. A.

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Luo, Y.

Ma, W.

Markoš, P.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Pacheco, J.

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Peng, L.

Potet, S.

F. Zhang, S. Potet, and J. Caobonell, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE Trans. Microw. Theory Tech. 56(11), 2566–2573 (2008).
[CrossRef]

Qiao, S.

S. Qiao, G. A. Zheng, H. Zhang, and L. X. Ran, “Transition behavior of k-surface: from hyperbola to ellipse,” Prog. Electromagn. Res. 81, 267–277 (2008).
[CrossRef]

S. Qiao, G. A. Zheng, W. Ren, and L. X. Ran, “Possible abnormal group velocity in the normal dispersive anisotropic media,” J. Electromagn. Waves Appl. 22(10), 1309–1317 (2008).
[CrossRef]

Ran, L.

Ran, L. X.

S. Qiao, G. A. Zheng, W. Ren, and L. X. Ran, “Possible abnormal group velocity in the normal dispersive anisotropic media,” J. Electromagn. Waves Appl. 22(10), 1309–1317 (2008).
[CrossRef]

S. Qiao, G. A. Zheng, H. Zhang, and L. X. Ran, “Transition behavior of k-surface: from hyperbola to ellipse,” Prog. Electromagn. Res. 81, 267–277 (2008).
[CrossRef]

Ren, W.

S. Qiao, G. A. Zheng, W. Ren, and L. X. Ran, “Possible abnormal group velocity in the normal dispersive anisotropic media,” J. Electromagn. Waves Appl. 22(10), 1309–1317 (2008).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[CrossRef] [PubMed]

Schultz, S.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Silveirinha, M.

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(3), 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(15), 157403 (2006).
[CrossRef] [PubMed]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of epsilon -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 016604 (2008).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[CrossRef] [PubMed]

Wang, Z.

Wu, B.-I.

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

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(3), 033903 (2008).
[CrossRef] [PubMed]

Zhang, F.

F. Zhang, S. Potet, and J. Caobonell, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE Trans. Microw. Theory Tech. 56(11), 2566–2573 (2008).
[CrossRef]

Zhang, H.

S. Qiao, G. A. Zheng, H. Zhang, and L. X. Ran, “Transition behavior of k-surface: from hyperbola to ellipse,” Prog. Electromagn. Res. 81, 267–277 (2008).
[CrossRef]

Zheng, G. A.

S. Qiao, G. A. Zheng, W. Ren, and L. X. Ran, “Possible abnormal group velocity in the normal dispersive anisotropic media,” J. Electromagn. Waves Appl. 22(10), 1309–1317 (2008).
[CrossRef]

S. Qiao, G. A. Zheng, H. Zhang, and L. X. Ran, “Transition behavior of k-surface: from hyperbola to ellipse,” Prog. Electromagn. Res. 81, 267–277 (2008).
[CrossRef]

G. A. Zheng, “Abrupt change of reflectivity from the strongly anisotropic metamaterial,” Opt. Commun. 281(8), 1941–1944 (2008).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[CrossRef] [PubMed]

IEEE Trans. Microw. Theory Tech. (2)

F. Zhang, S. Potet, and J. Caobonell, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE Trans. Microw. Theory Tech. 56(11), 2566–2573 (2008).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. Electromagn. Waves Appl. (1)

S. Qiao, G. A. Zheng, W. Ren, and L. X. Ran, “Possible abnormal group velocity in the normal dispersive anisotropic media,” J. Electromagn. Waves Appl. 22(10), 1309–1317 (2008).
[CrossRef]

Opt. Commun. (1)

G. A. Zheng, “Abrupt change of reflectivity from the strongly anisotropic metamaterial,” Opt. Commun. 281(8), 1941–1944 (2008).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (3)

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of epsilon -near-zero-filled narrow channels,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 016604 (2008).
[CrossRef] [PubMed]

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[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(3), 033903 (2008).
[CrossRef] [PubMed]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[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(15), 157403 (2006).
[CrossRef] [PubMed]

Prog. Electromagn. Res. (1)

S. Qiao, G. A. Zheng, H. Zhang, and L. X. Ran, “Transition behavior of k-surface: from hyperbola to ellipse,” Prog. Electromagn. Res. 81, 267–277 (2008).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Other (2)

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

M. Bozzi, L. Perregrini, D. Deslandes, K. Wu, and G. Conciaurol, “A compact, wideband, phase-equalized waveguide divider/combiner for power amplification,” Microwave Conference, 33rd European (2003).

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Figures (4)

Fig. 1
Fig. 1

Dispersion diagram of k x in a plasma medium with (a) γ e = 0 , ε r = 1 and (b) γ e = 0.002 ω p , ε r = 1 + 0.05 i , where k z = 0 .

Fig. 2
Fig. 2

(a) Photograph and the geometry of the SRRs consisting of the metamaterial sample. (b)The real and imaginary parts of μ r z retrieved from simulation data.

Fig. 3
Fig. 3

(a) Experimental setup. Eight horizontal parallel lines represent eight PCBs shown in Fig. 2(a). (b), (c) The measured phase and amplitude of the electric field at points a, b and c, separately.

Fig. 4
Fig. 4

Calculated PV curves based on the measured data (dashed red line) and the retrieved data in Fig. 2(b) (solid black line).

Equations (2)

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μ ¯ ¯ = diag( μ r x , μ r y , μ r z ) μ 0 .
k x 2 / μ r z + k z 2 = ε r k 0 2 = ε r ( ω / c ) 2 .

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