Abstract

The efficient analysis of practical metamaterial slabs, formed by networks of diverse split-ring resonators, is presented in this paper, concerning their competence to guide surface waves. Dispersion curves of the supported modes are consistently derived through closed-form expressions with average constitutive parameters of the slab’s medium, estimated in terms of finite difference time domain (FDTD) simulations of the metamaterial’s unit cell. Then, the resonant frequencies in the first Brillouin zone are computed via a rigorous FDTD model of the structure’s unit cell and results are elaborately collated with their theoretical counterparts. The comparison reveals the lack of the analytical method to provide relatively correct outcomes for high Bloch numbers due to the nonlocal phenomena which become dominant near the Brillouin zone edge.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial designtheory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
    [CrossRef]
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    [CrossRef]
  6. C. Caloz, A. Sanada, and T. Itoh, "A novel composite right-/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth," IEEE Trans. Microwave Theory Tech. 52, 980-992 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, and T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn. 43, 1329-1332 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
    [CrossRef]
  26. I. Shadrivov, R. Ziolkowski, A. Zharov, and Y. Kivshar, "Excitation of guided waves in layered structures with negative refraction," Opt. Express 13, 481-492 (2005).
    [CrossRef] [PubMed]
  27. J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic resonance plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402-1-195402-7 (2005).
    [CrossRef]
  28. B. I. Popa and S. A. Cummer, "Direct measurment of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617-1-016617-5 (2006).
    [CrossRef]
  29. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104-1-195104-5 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008

F. Bilotti, A. Alu, and L. Vegni, "Design of miniaturized metamaterial patch Antennas with μ-negative loading," IEEE Trans. Antennas Propag. 56, 1640-1647 (2008).
[CrossRef]

A. Erentok and R. Ziolkowski, "Metamaterial-inspired efficient electrically small antennas," IEEE Trans. Antennas Propag. 56, 691-707 (2008).
[CrossRef]

M. Antoniades and G. Eleftheriades, "A CPS leaky-wave antenna with reduced beam squinting using NRI-TL metamaterials," IEEE Trans. Antennas Propag. 56, 708-721 (2008).
[CrossRef]

G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, "Influence of losses on the superresolution performances of an impedance-matched negative-index material," J. Opt. Soc. Am. B 25, 236-246 (2008).
[CrossRef]

M. Silveirinha, P. A. Belov, and C. R. Simovski, "Ultimate limit of resolution of subwavelength imaging devices formed by metallic rods," Opt. Lett. 33, 1726-1728 (2008).
[CrossRef] [PubMed]

2007

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description of electromagnetic behaviors in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606-1-026606-8 (2007).
[CrossRef]

C. R. Simovski and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Phys. Rev. B 75, 195111-1-195111-10 (2007).
[CrossRef]

C. R. Simovski, "Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices," Metamaterials 1, 62-80 (2007).
[CrossRef]

N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, and T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn. 43, 1329-1332 (2007).
[CrossRef]

P. Ikonen and S. Tretyakov, "Determination of generalized permeability function and field energy density in artificial magnetics using the equivalent-circuit method," IEEE Trans. Microwave Theory Tech. 55, 92-99 (2007).
[CrossRef]

2006

2005

I. Shadrivov, R. Ziolkowski, A. Zharov, and Y. Kivshar, "Excitation of guided waves in layered structures with negative refraction," Opt. Express 13, 481-492 (2005).
[CrossRef] [PubMed]

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic resonance plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402-1-195402-7 (2005).
[CrossRef]

K. Aydin, I. Bulu, and E. Ozbay, "Focusing of electromagnetic waves by a left-handed metamaterial flat lens," Opt. Express 13, 8753-8759 (2005).
[CrossRef] [PubMed]

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Fundamental modal properties of surface waves on metamaterial grounded slabs," IEEE Trans. Microwave Theory Tech. 53, 1431-1442 (2005).
[CrossRef]

2004

C. Caloz, A. Sanada, and T. Itoh, "A novel composite right-/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth," IEEE Trans. Microwave Theory Tech. 52, 980-992 (2004).
[CrossRef]

A. Alu and N. Engheta, "Guided modes in a waveguide filled with a pair of single-negative (SNG), doublenegative (DNG), and/or double-positive (DPS) layers," IEEE Trans. Microwave Theory Tech. 52, 199-210 (2004).
[CrossRef]

2003

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial designtheory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

A. Grbic and G. V. Eleftheriades, "Periodic analysis of a 2-D negative refractive index transmission line structure," IEEE Trans. Antennas Propag. 51, 2604-2611 (2003).
[CrossRef]

R. W. Ziolkowski, "Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs," Opt. Express 11, 662-681 (2003).
[CrossRef] [PubMed]

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

2002

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104-1-195104-5 (2002).
[CrossRef]

2001

R. Ruppin, "Surface polaritons of a left-handed material slab," J. Phys.: Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

2000

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

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, 4184-4187 (2000).
[CrossRef] [PubMed]

1999

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Antoniades, M.

M. Antoniades and G. Eleftheriades, "A CPS leaky-wave antenna with reduced beam squinting using NRI-TL metamaterials," IEEE Trans. Antennas Propag. 56, 708-721 (2008).
[CrossRef]

Antonopoulos, C. S.

N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, and T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn. 43, 1329-1332 (2007).
[CrossRef]

Aydin, K.

Baccarelli, P.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Fundamental modal properties of surface waves on metamaterial grounded slabs," IEEE Trans. Microwave Theory Tech. 53, 1431-1442 (2005).
[CrossRef]

Belov, P. A.

Bilotti, F.

F. Bilotti, A. Alu, and L. Vegni, "Design of miniaturized metamaterial patch Antennas with μ-negative loading," IEEE Trans. Antennas Propag. 56, 1640-1647 (2008).
[CrossRef]

Bloemer, M. J.

Bulu, I.

Burghignoli, P.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Fundamental modal properties of surface waves on metamaterial grounded slabs," IEEE Trans. Microwave Theory Tech. 53, 1431-1442 (2005).
[CrossRef]

Caloz, C.

C. Caloz, A. Sanada, and T. Itoh, "A novel composite right-/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth," IEEE Trans. Microwave Theory Tech. 52, 980-992 (2004).
[CrossRef]

Cui, T. J.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description of electromagnetic behaviors in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606-1-026606-8 (2007).
[CrossRef]

Cummer, S. A.

B. I. Popa and S. A. Cummer, "Direct measurment of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617-1-016617-5 (2006).
[CrossRef]

D’Aguanno, G.

Eleftheriades, G.

M. Antoniades and G. Eleftheriades, "A CPS leaky-wave antenna with reduced beam squinting using NRI-TL metamaterials," IEEE Trans. Antennas Propag. 56, 708-721 (2008).
[CrossRef]

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, "Periodic analysis of a 2-D negative refractive index transmission line structure," IEEE Trans. Antennas Propag. 51, 2604-2611 (2003).
[CrossRef]

Erentok, A.

A. Erentok and R. Ziolkowski, "Metamaterial-inspired efficient electrically small antennas," IEEE Trans. Antennas Propag. 56, 691-707 (2008).
[CrossRef]

Frezza, F.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Fundamental modal properties of surface waves on metamaterial grounded slabs," IEEE Trans. Microwave Theory Tech. 53, 1431-1442 (2005).
[CrossRef]

Galli, A.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Fundamental modal properties of surface waves on metamaterial grounded slabs," IEEE Trans. Microwave Theory Tech. 53, 1431-1442 (2005).
[CrossRef]

Gollub, J. N.

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic resonance plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402-1-195402-7 (2005).
[CrossRef]

Grbic, A.

A. Grbic and G. V. Eleftheriades, "Periodic analysis of a 2-D negative refractive index transmission line structure," IEEE Trans. Antennas Propag. 51, 2604-2611 (2003).
[CrossRef]

Grzegorczyk, T. M.

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

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. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Huang, D.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description of electromagnetic behaviors in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606-1-026606-8 (2007).
[CrossRef]

Ikonen, P.

P. Ikonen and S. Tretyakov, "Determination of generalized permeability function and field energy density in artificial magnetics using the equivalent-circuit method," IEEE Trans. Microwave Theory Tech. 55, 92-99 (2007).
[CrossRef]

Itoh, T.

C. Caloz, A. Sanada, and T. Itoh, "A novel composite right-/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth," IEEE Trans. Microwave Theory Tech. 52, 980-992 (2004).
[CrossRef]

Kantartzis, N. V.

N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, and T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn. 43, 1329-1332 (2007).
[CrossRef]

Kivshar, Y.

Kong, J. A.

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

Lampariello, P.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Fundamental modal properties of surface waves on metamaterial grounded slabs," IEEE Trans. Microwave Theory Tech. 53, 1431-1442 (2005).
[CrossRef]

Liu, R.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description of electromagnetic behaviors in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606-1-026606-8 (2007).
[CrossRef]

Lovat, G.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Fundamental modal properties of surface waves on metamaterial grounded slabs," IEEE Trans. Microwave Theory Tech. 53, 1431-1442 (2005).
[CrossRef]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104-1-195104-5 (2002).
[CrossRef]

Marques, R.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial designtheory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Martel, J.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial designtheory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Mattiucci, N.

Medina, F.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial designtheory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Mesa, F.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial designtheory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Mock, J. J.

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic resonance plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402-1-195402-7 (2005).
[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, 4184-4187 (2000).
[CrossRef] [PubMed]

Ozbay, E.

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, 4184-4187 (2000).
[CrossRef] [PubMed]

Paulotto, S.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Fundamental modal properties of surface waves on metamaterial grounded slabs," IEEE Trans. Microwave Theory Tech. 53, 1431-1442 (2005).
[CrossRef]

Pendry, J. B.

D. R. Smith and J. B. Pendry, "Homogenization of metamaterials by field averaging," J. Opt. Soc. Am. B 23, 391-403 (2006).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Perram, T.

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic resonance plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402-1-195402-7 (2005).
[CrossRef]

Popa, B. I.

B. I. Popa and S. A. Cummer, "Direct measurment of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617-1-016617-5 (2006).
[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. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Ruppin, R.

R. Ruppin, "Surface polaritons of a left-handed material slab," J. Phys.: Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

Sanada, A.

C. Caloz, A. Sanada, and T. Itoh, "A novel composite right-/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth," IEEE Trans. Microwave Theory Tech. 52, 980-992 (2004).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104-1-195104-5 (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, 4184-4187 (2000).
[CrossRef] [PubMed]

Shadrivov, I.

Silveirinha, M.

Simovski, C. R.

M. Silveirinha, P. A. Belov, and C. R. Simovski, "Ultimate limit of resolution of subwavelength imaging devices formed by metallic rods," Opt. Lett. 33, 1726-1728 (2008).
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C. R. Simovski, "Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices," Metamaterials 1, 62-80 (2007).
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R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description of electromagnetic behaviors in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606-1-026606-8 (2007).
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D. R. Smith and J. B. Pendry, "Homogenization of metamaterials by field averaging," J. Opt. Soc. Am. B 23, 391-403 (2006).
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J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic resonance plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402-1-195402-7 (2005).
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D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104-1-195104-5 (2002).
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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, 4184-4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104-1-195104-5 (2002).
[CrossRef]

Sounas, D. L.

N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, and T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn. 43, 1329-1332 (2007).
[CrossRef]

Tretyakov, S.

P. Ikonen and S. Tretyakov, "Determination of generalized permeability function and field energy density in artificial magnetics using the equivalent-circuit method," IEEE Trans. Microwave Theory Tech. 55, 92-99 (2007).
[CrossRef]

Tretyakov, S. A.

C. R. Simovski and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Phys. Rev. B 75, 195111-1-195111-10 (2007).
[CrossRef]

Tsiboukis, T. D.

N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, and T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn. 43, 1329-1332 (2007).
[CrossRef]

Vier, D. C.

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic resonance plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402-1-195402-7 (2005).
[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, 4184-4187 (2000).
[CrossRef] [PubMed]

Wu, B. I.

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

Zhang, Y.

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
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Zhao, B.

R. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, "Description of electromagnetic behaviors in artificial metamaterials based on effective medium theory," Phys. Rev. E 76, 026606-1-026606-8 (2007).
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A. Erentok and R. Ziolkowski, "Metamaterial-inspired efficient electrically small antennas," IEEE Trans. Antennas Propag. 56, 691-707 (2008).
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F. Bilotti, A. Alu, and L. Vegni, "Design of miniaturized metamaterial patch Antennas with μ-negative loading," IEEE Trans. Antennas Propag. 56, 1640-1647 (2008).
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A. Erentok and R. Ziolkowski, "Metamaterial-inspired efficient electrically small antennas," IEEE Trans. Antennas Propag. 56, 691-707 (2008).
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M. Antoniades and G. Eleftheriades, "A CPS leaky-wave antenna with reduced beam squinting using NRI-TL metamaterials," IEEE Trans. Antennas Propag. 56, 708-721 (2008).
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IEEE Trans. Magn.

N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, and T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn. 43, 1329-1332 (2007).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

P. Ikonen and S. Tretyakov, "Determination of generalized permeability function and field energy density in artificial magnetics using the equivalent-circuit method," IEEE Trans. Microwave Theory Tech. 55, 92-99 (2007).
[CrossRef]

C. Caloz, A. Sanada, and T. Itoh, "A novel composite right-/left-handed coupled-line directional coupler with arbitrary coupling level and broad bandwidth," IEEE Trans. Microwave Theory Tech. 52, 980-992 (2004).
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A. Alu and N. Engheta, "Guided modes in a waveguide filled with a pair of single-negative (SNG), doublenegative (DNG), and/or double-positive (DPS) layers," IEEE Trans. Microwave Theory Tech. 52, 199-210 (2004).
[CrossRef]

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, G. Lovat, and S. Paulotto, "Fundamental modal properties of surface waves on metamaterial grounded slabs," IEEE Trans. Microwave Theory Tech. 53, 1431-1442 (2005).
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J. Appl. Phys.

B. I. Wu, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, "Guided modes with imaginary transverse wave number in a slab waveguide with negative permittivity and permeability," J. Appl. Phys. 93, 9386-9388 (2003).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys.: Condens. Matter

R. Ruppin, "Surface polaritons of a left-handed material slab," J. Phys.: Condens. Matter 13, 1811-1819 (2001).
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Metamaterials

C. R. Simovski, "Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices," Metamaterials 1, 62-80 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104-1-195104-5 (2002).
[CrossRef]

C. R. Simovski and S. A. Tretyakov, "Local constitutive parameters of metamaterials from an effective-medium perspective," Phys. Rev. B 75, 195111-1-195111-10 (2007).
[CrossRef]

J. N. Gollub, D. R. Smith, D. C. Vier, T. Perram, and J. J. Mock, "Experimental characterization of magnetic resonance plasmons on metamaterials with negative permeability," Phys. Rev. B 71, 195402-1-195402-7 (2005).
[CrossRef]

Phys. Rev. E

B. I. Popa and S. A. Cummer, "Direct measurment of evanescent wave enhancement inside passive metamaterials," Phys. Rev. E 73, 016617-1-016617-5 (2006).
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J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
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[CrossRef] [PubMed]

Other

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Left handed materials composed of only S-shaped resonators," Phys. Rev. E 70, 057605-1-057605-4 (2004).
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F. Mesa, M. J. Freire, R. Marques, and J. D. Baena, "Three-dimensional superresolution in metamaterial slab lenses: Experiment and theory," Phys. Rev. B 72, 235117-1-235117-6 (2005).
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B. Edwards, A. Alu, M. 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, 033903-1-033903-4 (2008).
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X. Chen, T.M. Grzegorczyk, B. I. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70,016608-1-016608-7 (2004).
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P. A. Belov and Y. Hao, "Subwavelength imaging at optical frequencies using atransmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Phys. Rev. B 73, 113110-1-113110-4 (2006).
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D. L. Sounas, N. V. Kantartzis, and T. D. Tsiboukis, "Temporal characteristics of resonant surface polaritons in superlensing planar double-negative slabs: Development of analytical schemes and numerical models," Phys. Rev. E 76, 046606-1-046606-12 (2007).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

An infinite planar DNG slab with effective constitutive parameters ε̿(ω) and μ̿(ω).

Fig. 2.
Fig. 2.

Geometry of (a) an edge-coupled SRR, (b) a broadside SRR, and (c) an S-ring.

Fig. 3.
Fig. 3.

Numerically extracted average constitutive parameters ε̅ xx and μ̅ yy of (a) the broadside SRR with w = 3 mm, s = 0.25 mm, g = 0.5 mm, h = 0.5 mm, px = py = 5 mm, L = 5 mm and (b) the S-ring with w = 0.5 mm, s = 0.25 mm, h = 0.5 mm, ℓ1 = ℓ2 = 3 mm, px = 5.5 mm, py = 2.5 mm, L = 4 mm.

Fig. 4.
Fig. 4.

Analytically derived dispersion diagram for a planar DNG slab with a width of d = 15 mm, composed of broadside SRRs on constant y-planes. The geometrical parameters of the SRRs are: w = 3 mm, s = 0.25 mm, g = 0.5 mm, h = 0.5 mm, px = py = 5 mm, and L = 5 mm. Magnetic resonance f m0 and magnetic plasma fmp frequency specify the range of the resulting band, while shaded regions correspond to the different k z cases. Blue lines describe the variation of symmetrical modes and red lines that of antisymmetrical ones.

Fig. 5.
Fig. 5.

Analytically derived dispersion diagram for a planar DNG slab with a width of d = 15 mm, composed of S-rings on constant y-planes. The geometrical parameters of the S-rings are: w = 0.5 mm, s = 0.25 mm, h = 0.5 mm, ℓ1 = ℓ2 = 3 mm, px = 5.5 mm, py = 2.5 mm, and L = 4 mm. Electric f e0 and magnetic f m0 resonance frequencies indicate the range of the resulting bandgap. Blue lines describe the variation of symmetrical modes and red lines that of antisymmetrical ones.

Fig. 6.
Fig. 6.

Analytically (solid lines) and numerically (dots) derived dispersion curves for a planar DNG slab with a width of d = 15 mm, composed of broadside SRRs on constant y-planes. The geometrical parameters of the SRRs are: w = 3 mm, s = 0.25 mm, g = 0.5 mm, h = 0.5 mm, px = py = 5 mm, and L = 5 mm.

Fig. 7.
Fig. 7.

Numerically derived dispersion diagram for a planar DNG slab with a width of d = 15 mm, composed of S-rings on constant y-planes. The geometrical parameters of the S-rings are: w = 0.5 mm, s = 0.25 mm, h = 0.5 mm, ℓ1 = ℓ2 = 3 mm, px = 5.5 mm, py = 2.5 mm, and L = 4 mm.

Fig. 8.
Fig. 8.

Analytically (solid lines) and numerically (dots) derived dispersion curves for a thin DNG slab with a width of d = 5 mm, composed of one broadside SRR in the z-direction. The parameters of the SRR are: w = 3 mm, s = 0.25 mm, g = 0.5 mm, and h = 0.5 mm.

Tables (1)

Tables Icon

Table 1. Mode frequencies for the S-ring arrangement of Fig. 5 and qy = 0.45π/py .

Equations (6)

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

azμyy=±kztan±1(kzd2),
azεyy=±kztan±1(kzd2).
εxx=1ωp2ω2,
μyy=1ω2ω2ωm02,
ε̅=εeffsin(θ/2)θ/2[cos(θ/2)]Sb,
μ̅=μeffsin(θ/2)θ/2[cos(θ/2)]−Sb,

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