Abstract

A rigorous full wave analysis of bianisotropic split ring resonator (SRR) metamaterials is presented for different electromagnetic field polarization and propagation directions. An alternative physical explanation is gained by revealing the fact that imaginary wave number leads to the SRR resonance. Metamaterial based parallel plate waveguide and rectangular waveguide are then examined to explore the resonance response to transverse magnetic and transverse electric waves. It is shown that different dispersion properties, such as non-cutoff frequency mode propagation and enhanced bandwidth of single mode operation, become into existence under certain circumstances. In addition, salient dispersion properties are imparted to non-radiative dielectric waveguides and H waveguides by uniaxial bianisotropic SRR metamaterials. Both longitudinal-section magnetic and longitudinal-section electric modes are capable of propagating very slowly due to metamaterial bianisotropic effects. Particularly, the abnormal falling behavior of some higher-order modes, eventually leading to the leakage, may appear when metamaterials are double negative. Fortunately, for other modes, leakage can be reduced due to the magnetoelectric coupling. When the metamaterials are of single negative parameters, leakage elimination can be achieved.

© 2009 Optical Society of America

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and μ," Soviet Phys. Uspekhi. 10, 509-514 (1968).
    [CrossRef]
  2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
    [CrossRef] [PubMed]
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenonmena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  4. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability an permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  5. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  6. R. W. Ziolkowski, "Design, fabrication and testing of double negative metamaterials," IEEE Trans. Antennas Propag. 51, 1516-1529 (2003).
    [CrossRef]
  7. R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and lefthanded metamaterials," Phys. Rev. B 65, 144440 (2002).
    [CrossRef]
  8. D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig "Calculation and measurement of bianisotropy in a split ring resonator," J. Appl. Phys. 100, 024507 (2006).
    [CrossRef]
  9. V. V. Varadan, A. R. Tellakula, "Effective properties of split ring resonator metamaterials using measured scattering parameters: Effect of gap orientation," J. Appl. Phys. 100, 034910 (2006).
    [CrossRef]
  10. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2493-2495 (2004).
    [CrossRef]
  11. P. Gay-Balmaz and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
    [CrossRef]
  12. T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402(1-4), 2004.
    [CrossRef] [PubMed]
  13. T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
    [CrossRef]
  14. P. Markos and C. M. Soukoulis, "Numerical studies of left handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
    [CrossRef]
  15. K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonance for different split ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
    [CrossRef]
  16. R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside- couple split ring resonators for metamaterials design-theory and experiments," IEEE Trans. Microwave Theory Tech. 51, 2572-2581 (2003).
  17. A. Alú 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. Microw. Theory Tech. 52, 199-210 (2004).
    [CrossRef]
  18. 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]
  19. Y. S. Xu, "A study of waveguides field with anisotropic metamaterials," Microwave Opt. Technol. Lett. 41, 426-431 (2004).
    [CrossRef]
  20. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative refractive index waveguides," Phys. Rev. E 67, 057602 (2003).
    [CrossRef]
  21. S. Hrabar, J. Bartolic, and Z. Sipus, "Miniaturization of rectangular waveguide using uniaxial negative permeability metamaterial," IEEE Trans. Antennas Propag. 53, 110-119 (2005).
    [CrossRef]
  22. A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Novel propagation features of double negative H-guides and H-guide couplers," Microwave Opt. Technol. Lett. 47, 185-190 (2005).
    [CrossRef]
  23. P. Yang, D. Lee, and K. Wu, "Nonradiative dielectric waveguide embedded in metamaterial with negative permittivity or permeability," Microwave Opt. Technol. Lett. 45, 207-210 (2005).
    [CrossRef]
  24. P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, and S. Paulotto, "Unimodal surface wave propagation in metamaterial nonradiative dielectric waveguides," Microwave Opt. Technol. Lett. 48, 2557-2560 (2006).
    [CrossRef]
  25. C. Krowne, "Electromagnetic theorems for complex. anisotropic media," IEEE Trans. Antennas Propag. 32, 1224-1230 (1984).
    [CrossRef]
  26. S. A. Tretyakov, "Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (PML)," J. Electromagn. Wave Applic. 12, 821-837 (1998).
    [CrossRef]

2006 (3)

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig "Calculation and measurement of bianisotropy in a split ring resonator," J. Appl. Phys. 100, 024507 (2006).
[CrossRef]

V. V. Varadan, A. R. Tellakula, "Effective properties of split ring resonator metamaterials using measured scattering parameters: Effect of gap orientation," J. Appl. Phys. 100, 034910 (2006).
[CrossRef]

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, and S. Paulotto, "Unimodal surface wave propagation in metamaterial nonradiative dielectric waveguides," Microwave Opt. Technol. Lett. 48, 2557-2560 (2006).
[CrossRef]

2005 (4)

S. Hrabar, J. Bartolic, and Z. Sipus, "Miniaturization of rectangular waveguide using uniaxial negative permeability metamaterial," IEEE Trans. Antennas Propag. 53, 110-119 (2005).
[CrossRef]

A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Novel propagation features of double negative H-guides and H-guide couplers," Microwave Opt. Technol. Lett. 47, 185-190 (2005).
[CrossRef]

P. Yang, D. Lee, and K. Wu, "Nonradiative dielectric waveguide embedded in metamaterial with negative permittivity or permeability," Microwave Opt. Technol. Lett. 45, 207-210 (2005).
[CrossRef]

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonance for different split ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

2004 (3)

A. Alú 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. Microw. Theory Tech. 52, 199-210 (2004).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2493-2495 (2004).
[CrossRef]

Y. S. Xu, "A study of waveguides field with anisotropic metamaterials," Microwave Opt. Technol. Lett. 41, 426-431 (2004).
[CrossRef]

2003 (4)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative refractive index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

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]

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside- couple split ring resonators for metamaterials design-theory and experiments," IEEE Trans. Microwave Theory Tech. 51, 2572-2581 (2003).

R. W. Ziolkowski, "Design, fabrication and testing of double negative metamaterials," IEEE Trans. Antennas Propag. 51, 1516-1529 (2003).
[CrossRef]

2002 (3)

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and lefthanded metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

P. Markos and C. M. Soukoulis, "Numerical studies of left handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
[CrossRef]

P. Gay-Balmaz and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

2001 (2)

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[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 an permittivity," Phys. Rev. Lett. 84, 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 phenonmena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1998 (1)

S. A. Tretyakov, "Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (PML)," J. Electromagn. Wave Applic. 12, 821-837 (1998).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

1984 (1)

C. Krowne, "Electromagnetic theorems for complex. anisotropic media," IEEE Trans. Antennas Propag. 32, 1224-1230 (1984).
[CrossRef]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and μ," Soviet Phys. Uspekhi. 10, 509-514 (1968).
[CrossRef]

Alú, A.

A. Alú 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. Microw. Theory Tech. 52, 199-210 (2004).
[CrossRef]

Aydin, K.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonance for different split ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

Baccarelli, P.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, and S. Paulotto, "Unimodal surface wave propagation in metamaterial nonradiative dielectric waveguides," Microwave Opt. Technol. Lett. 48, 2557-2560 (2006).
[CrossRef]

Barbosa, A. M.

A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Novel propagation features of double negative H-guides and H-guide couplers," Microwave Opt. Technol. Lett. 47, 185-190 (2005).
[CrossRef]

Bartolic, J.

S. Hrabar, J. Bartolic, and Z. Sipus, "Miniaturization of rectangular waveguide using uniaxial negative permeability metamaterial," IEEE Trans. Antennas Propag. 53, 110-119 (2005).
[CrossRef]

Bulu, I.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonance for different split ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

Burghignoli, P.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, and S. Paulotto, "Unimodal surface wave propagation in metamaterial nonradiative dielectric waveguides," Microwave Opt. Technol. Lett. 48, 2557-2560 (2006).
[CrossRef]

Economou, E. N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2493-2495 (2004).
[CrossRef]

Engheta, N.

A. Alú 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. Microw. Theory Tech. 52, 199-210 (2004).
[CrossRef]

Frezza, F.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, and S. Paulotto, "Unimodal surface wave propagation in metamaterial nonradiative dielectric waveguides," Microwave Opt. Technol. Lett. 48, 2557-2560 (2006).
[CrossRef]

Galli, A.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, and S. Paulotto, "Unimodal surface wave propagation in metamaterial nonradiative dielectric waveguides," Microwave Opt. Technol. Lett. 48, 2557-2560 (2006).
[CrossRef]

Gay-Balmaz, P.

P. Gay-Balmaz and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

Gollub, J.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig "Calculation and measurement of bianisotropy in a split ring resonator," J. Appl. Phys. 100, 024507 (2006).
[CrossRef]

Greegor, R. B.

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[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]

Guven, K.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonance for different split ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

Holden, A. J.

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Hrabar, S.

S. Hrabar, J. Bartolic, and Z. Sipus, "Miniaturization of rectangular waveguide using uniaxial negative permeability metamaterial," IEEE Trans. Antennas Propag. 53, 110-119 (2005).
[CrossRef]

Kafesaki, M.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonance for different split ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2493-2495 (2004).
[CrossRef]

Katsarakis, N.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2493-2495 (2004).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative refractive index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

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]

Koschny, T.

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2493-2495 (2004).
[CrossRef]

Krowne, C.

C. Krowne, "Electromagnetic theorems for complex. anisotropic media," IEEE Trans. Antennas Propag. 32, 1224-1230 (1984).
[CrossRef]

Lampariello, P.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, and S. Paulotto, "Unimodal surface wave propagation in metamaterial nonradiative dielectric waveguides," Microwave Opt. Technol. Lett. 48, 2557-2560 (2006).
[CrossRef]

Lee, D.

P. Yang, D. Lee, and K. Wu, "Nonradiative dielectric waveguide embedded in metamaterial with negative permittivity or permeability," Microwave Opt. Technol. Lett. 45, 207-210 (2005).
[CrossRef]

Markos, P.

P. Markos and C. M. Soukoulis, "Numerical studies of left handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
[CrossRef]

Marqués, R.

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside- couple split ring resonators for metamaterials design-theory and experiments," IEEE Trans. Microwave Theory Tech. 51, 2572-2581 (2003).

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and lefthanded metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Martel, J.

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside- couple split ring resonators for metamaterials design-theory and experiments," IEEE Trans. Microwave Theory Tech. 51, 2572-2581 (2003).

Martin, O. J. F.

P. Gay-Balmaz and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

Medina, F.

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside- couple split ring resonators for metamaterials design-theory and experiments," IEEE Trans. Microwave Theory Tech. 51, 2572-2581 (2003).

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and lefthanded metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Mesa, F.

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside- couple split ring resonators for metamaterials design-theory and experiments," IEEE Trans. Microwave Theory Tech. 51, 2572-2581 (2003).

Mock, J. J.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig "Calculation and measurement of bianisotropy in a split ring resonator," J. Appl. Phys. 100, 024507 (2006).
[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 an permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Ozbay, E.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonance for different split ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

Padilla, W. J.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig "Calculation and measurement of bianisotropy in a split ring resonator," J. Appl. Phys. 100, 024507 (2006).
[CrossRef]

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

Paiva, C. R.

A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Novel propagation features of double negative H-guides and H-guide couplers," Microwave Opt. Technol. Lett. 47, 185-190 (2005).
[CrossRef]

Parazzoli, C. G.

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

Paulotto, S.

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, and S. Paulotto, "Unimodal surface wave propagation in metamaterial nonradiative dielectric waveguides," Microwave Opt. Technol. Lett. 48, 2557-2560 (2006).
[CrossRef]

Pendry, J. B.

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Rafii-El-Idrissi, R.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and lefthanded metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Robbins, D. J.

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

Schuhmann, R.

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

Schultz, S.

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

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

Schurig, D.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig "Calculation and measurement of bianisotropy in a split ring resonator," J. Appl. Phys. 100, 024507 (2006).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative refractive index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sipus, Z.

S. Hrabar, J. Bartolic, and Z. Sipus, "Miniaturization of rectangular waveguide using uniaxial negative permeability metamaterial," IEEE Trans. Antennas Propag. 53, 110-119 (2005).
[CrossRef]

Smith, D. R.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig "Calculation and measurement of bianisotropy in a split ring resonator," J. Appl. Phys. 100, 024507 (2006).
[CrossRef]

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

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

Soukoulis, C. M.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonance for different split ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2493-2495 (2004).
[CrossRef]

P. Markos and C. M. Soukoulis, "Numerical studies of left handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
[CrossRef]

Stewart, W. J.

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative refractive index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

Tellakula, A. R.

V. V. Varadan, A. R. Tellakula, "Effective properties of split ring resonator metamaterials using measured scattering parameters: Effect of gap orientation," J. Appl. Phys. 100, 034910 (2006).
[CrossRef]

Topa, A. L.

A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Novel propagation features of double negative H-guides and H-guide couplers," Microwave Opt. Technol. Lett. 47, 185-190 (2005).
[CrossRef]

Tretyakov, S. A.

S. A. Tretyakov, "Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (PML)," J. Electromagn. Wave Applic. 12, 821-837 (1998).
[CrossRef]

Varadan, V. V.

V. V. Varadan, A. R. Tellakula, "Effective properties of split ring resonator metamaterials using measured scattering parameters: Effect of gap orientation," J. Appl. Phys. 100, 034910 (2006).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and μ," Soviet Phys. Uspekhi. 10, 509-514 (1968).
[CrossRef]

Vetter, A. M.

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

Vier, D. C.

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

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

Weiland, T.

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

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]

Wu, K.

P. Yang, D. Lee, and K. Wu, "Nonradiative dielectric waveguide embedded in metamaterial with negative permittivity or permeability," Microwave Opt. Technol. Lett. 45, 207-210 (2005).
[CrossRef]

Xu, Y. S.

Y. S. Xu, "A study of waveguides field with anisotropic metamaterials," Microwave Opt. Technol. Lett. 41, 426-431 (2004).
[CrossRef]

Yang, P.

P. Yang, D. Lee, and K. Wu, "Nonradiative dielectric waveguide embedded in metamaterial with negative permittivity or permeability," Microwave Opt. Technol. Lett. 45, 207-210 (2005).
[CrossRef]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

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).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, "Design, fabrication and testing of double negative metamaterials," IEEE Trans. Antennas Propag. 51, 1516-1529 (2003).
[CrossRef]

Appl. Phys. Lett. (1)

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2493-2495 (2004).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

R. W. Ziolkowski, "Design, fabrication and testing of double negative metamaterials," IEEE Trans. Antennas Propag. 51, 1516-1529 (2003).
[CrossRef]

S. Hrabar, J. Bartolic, and Z. Sipus, "Miniaturization of rectangular waveguide using uniaxial negative permeability metamaterial," IEEE Trans. Antennas Propag. 53, 110-119 (2005).
[CrossRef]

C. Krowne, "Electromagnetic theorems for complex. anisotropic media," IEEE Trans. Antennas Propag. 32, 1224-1230 (1984).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

A. Alú 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. Microw. Theory Tech. 52, 199-210 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

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

R. Marqués, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside- couple split ring resonators for metamaterials design-theory and experiments," IEEE Trans. Microwave Theory Tech. 51, 2572-2581 (2003).

J. Appl. Phys. (5)

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig "Calculation and measurement of bianisotropy in a split ring resonator," J. Appl. Phys. 100, 024507 (2006).
[CrossRef]

V. V. Varadan, A. R. Tellakula, "Effective properties of split ring resonator metamaterials using measured scattering parameters: Effect of gap orientation," J. Appl. Phys. 100, 034910 (2006).
[CrossRef]

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]

P. Gay-Balmaz and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

T. Weiland, R. Schuhmann, R. B. Greegor, C. G. Parazzoli, A. M. Vetter, D. R. Smith, D. C. Vier, S. Schultz, "Ab initio numerical simulation of left handed metamaterials: comparison of calculation and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

J. Electromagn. Wave Applic. (1)

S. A. Tretyakov, "Uniaxial omega medium as a physically realizable alternative for the perfectly matched layer (PML)," J. Electromagn. Wave Applic. 12, 821-837 (1998).
[CrossRef]

Microwave Opt. Technol. Lett. (4)

A. L. Topa, C. R. Paiva, and A. M. Barbosa, "Novel propagation features of double negative H-guides and H-guide couplers," Microwave Opt. Technol. Lett. 47, 185-190 (2005).
[CrossRef]

P. Yang, D. Lee, and K. Wu, "Nonradiative dielectric waveguide embedded in metamaterial with negative permittivity or permeability," Microwave Opt. Technol. Lett. 45, 207-210 (2005).
[CrossRef]

P. Baccarelli, P. Burghignoli, F. Frezza, A. Galli, P. Lampariello, and S. Paulotto, "Unimodal surface wave propagation in metamaterial nonradiative dielectric waveguides," Microwave Opt. Technol. Lett. 48, 2557-2560 (2006).
[CrossRef]

Y. S. Xu, "A study of waveguides field with anisotropic metamaterials," Microwave Opt. Technol. Lett. 41, 426-431 (2004).
[CrossRef]

New J. Phys. (1)

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, "Investigation of magnetic resonance for different split ring resonator parameters and designs," New J. Phys. 7, 168 (2005).
[CrossRef]

Phys. Rev. B (1)

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and lefthanded metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Phys. Rev. E (2)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, "Guided modes in negative refractive index waveguides," Phys. Rev. E 67, 057602 (2003).
[CrossRef]

P. Markos and C. M. Soukoulis, "Numerical studies of left handed materials and arrays of split ring resonators," Phys. Rev. E 65, 036622 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Soviet Phys. Uspekhi. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and μ," Soviet Phys. Uspekhi. 10, 509-514 (1968).
[CrossRef]

Other (1)

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402(1-4), 2004.
[CrossRef] [PubMed]

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Figures (13)

Fig. 1.
Fig. 1.

The SRR unit

Fig. 2.
Fig. 2.

Six orientations of SRR relative to different electromagnetic field polarization and propagation direction of the incident TEM field

Fig. 3.
Fig. 3.

Geometry of parallel plate waveguide and rectangular waveguide filled with SRR metamaterials

Fig. 4.
Fig. 4.

Metamaterial waveguide with different SRR orientations

Fig.  5.
Fig. 5.

The none cutoff frequency TM modes in parallel plate waveguide with SRR metamaterials εyy = -3, εzz = 1, μxx = -1, κ=1, l = 8 mm

Fig. 6.
Fig. 6.

Configuration of nonradiative dielectric waveguide and H waveguide with SRR metamaterials

Fig. 7.
Fig. 7.

Spatial orientation of SRRs in the host isotropic medium

Fig. 8.
Fig. 8.

Relationship of |βz | and magnetoelectric coupling κ in nonradiative dielectric waveguide with SRR metamaterials (a) ε 1 = 1, ε 2 = 3, μ 2 = 2.5, f = 35 GHz, s = 0.4λ 0, q = 0.6λ 0 (b) ε 1 = 1, ε 2 = -3, μ 2 = -2.5, f = 35 GHz, s = 0.4λ0, q = 0.6λ 0

Fig. 9.
Fig. 9.

Variation of the |βz | with frequency f for the dominant LSM01 (conventional NRD waveguide with εr =4, μr =1, s = 4 mm, q = 5 mm; double negative metamaterial NRD waveguide with ε 1 = 1, ε 2 = -4 , μ 2 = -1, κ = 5 and 10, s = 4 mm, q = 5 mm)

Fig. 10.
Fig. 10.

Energy flow of LSM01 mode varied with longitudinal wave number in the nonradiative dielectric with SRR metamaterials

Fig. 11.
Fig. 11.

Abnormal falling behavior of LSM higher modes in the proposed nonradiative dielectric waveguide/H waveguide with double negative parameters (ε 1 = 1, ε 2 = -3, μ 2 = -1, κ = 1, s = 5 mm, q = 5 mm) and TM1 mode in air filled parallel plate guide

Fig. 12.
Fig. 12.

Variation of the |βz | versus frequency f for LSM modes in the proposed nonradiative dielectric waveguide/H waveguide ((a) for double positive metamaterials with ε 1 = 1, ε 2 = 2, μ 2 = 2.5, κ = 0.1, 1.2, and 1.4, s = 5 mm, q = 5 mm (b) for double negative metamaterials with ε 1 =1, ε 2 = -3, μ 2 =-1.5, κ = 2.3, 2.5, and 3, s = 5 mm, q = 5 mm) and TM1 mode in air filled parallel plate guide

Fig. 13.
Fig. 13.

Variation of the |βz | versus frequency f for LSM modes in proposed nonradiative dielectric waveguide/H waveguide with single negative metamaterials ε 1=1, ε 2 =-3.5, μ 2 =1.5, κ = 0, 1, and 3, s = 5 mm, q = 5 mm and TM1 mode in air filled parallel plate guide

Tables (1)

Tables Icon

Table 1. Wave numbers for the SRR metamaterials shown in Fig. 2(c) ~ Fig. 2(f).

Equations (49)

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

D = ε 0 ( ε ¯ · E + Z 0 κ ¯ · H )
B = μ 0 ( 1 Z 0 κ ¯ T · E + μ ¯ · H )
ε xx = 1 , ε yy = a + b ω 2 ( ω 0 2 ω 2 ) , ε zz = a
μ xx = 1 + c ω 2 ( ω 0 2 ω 2 ) , μ yy = 1 , μ zz = 1
κ yx = = id ω 0 ω ( ω 0 2 ω 2 )
i ' × h = ε ¯ · E + κ ¯ · h
i ' × E = κ ¯ T · E + μ ¯ · h
' = x ' x ̂ + y ' y ̂ z ̂
( + β ) h x = ε yy E y
( β ) E y = μ xx h x
β 2 = μ xx ε yy κ 2
β h y = ε xx E x
β E x = μ yy h y
β 2 = ε xx μ yy = 1
S 11 = Γ ( 1 T 2 ) 1 Γ 2 T 2 , S 21 = T ( 1 Γ 2 ) 1 Γ 2 T 2
( ε xx β 2 ε xx μ yy x ' 2 + ε yy β 2 μ xx ε yy + κ 2 y ' 2 ε zz ) E z
= ( β β 2 ε xx μ yy + β β 2 μ xx ε yy + κ 2 ) x ' y ' 2 h z
( μ xx β 2 μ xx ε yy + κ 2 x ' 2 + μ yy β 2 ε xx μ yy y ' 2 μ zz ) h z
= ( β β 2 ε xx μ yy + β β 2 μ xx ε yy + κ 2 ) x ' y ' 2 E z
[ y ' 2 + ε zz ε yy ( μ xx ε yy κ 2 β 2 ) ] E z = 0
k z 2 = β 2 k 0 2 = ( μ xx ε yy κ 2 ) k 0 2 ε yy ε zz k c 2
( x ' 2 β 2 μ xx ε yy + κ 2 μ xx μ zz ) h z = 0
k z 2 = β 2 k 0 2 = ( μ xx ε yy κ 2 ) k 0 2 μ xx μ zz k c 2
f c = nc 2 l ( n 1 )
ε ¯ = [ ε 1 0 0 0 ε 2 0 0 0 ε 2 ] , μ ¯ = [ μ 1 0 0 0 μ 2 0 0 0 μ 2 ] , κ ¯ = i [ 0 0 0 0 0 κ 0 κ 0 ]
ε 1 a , ε 2 1 + ς a ( ω 0 2 ω 2 ) + b ω 2 ( ω 0 2 ω 2 )
μ 1 1 , μ 2 ξ + ( ω 0 2 ω 2 ) + c ω 2 ( ω 0 2 ω 2 )
κ d ω 0 ω ( ω 0 2 ω 2 )
x ' 2 h y + ε 2 ε 1 y ' 2 h y = ( ε 2 μ 2 κ 2 ε 2 ε 1 k ' z 2 ) h y
h z = i 1 k ' z y ' h y
E x = 1 k ' z ε 1 ( y ' 2 h y k ' z 2 h y )
E y = 1 k ' z ε 2 ( y ' x ' h y κ y ' h y )
E z = i 1 ε 2 ( x ' h y κ h y )
h y = f ( x ' ) g ( y ' ) exp ( j k ' z z ' )
x ' 2 f ( x ' ) + k ' x 2 f ( x ' ) = 0
y ' 2 g ( y ' ) + k ' y 2 g ( y ' ) = 0
k ' x 1 2 + ε 2 ε 1 ( k ' y 2 + k ' z 2 ) = ε 2 μ 2 κ 2
k ' x 0 2 + k ' y 2 + k ' z 2 = 1
g ( y ' ) = G sin ( k ' y y ' ) ( n = 1,2,3 , )
f ( x ' ) = { F 1 exp [ k ' x 0 ( x ' + q ' ) ] x ' < q ' F 2 [ cos ( k ' x 1 x ' ) + R sin ( k ' x 1 x ' ) ] q ' < x < q ' F 3 exp [ k ' x 0 ( x ' q ' ) ] q ' < x '
[ k ' x 1 cot ( k ' x 1 q ' ) + k ' x 0 ε 2 ] [ k ' x 1 tan ( k ' x 1 q ' ) k ' x 0 ε 2 ] + κ 2 = 0
[ k ' x 1 cot ( k ' x 1 q ' ) + k ' x 0 μ 2 ] [ k ' x 1 tan ( k ' x 1 q ' ) k ' x 0 μ 2 ] + κ 2 = 0
k ' x 1 2 + μ 2 μ 1 ( k ' y 2 + k ' z 2 ) = ε 2 μ 2 κ 2
κ max = ε 2 μ 2 ε 2 ε 1 k ' y 2 k ' x 1 2
κ min = ε 2 μ 2 + ε 2 ε 1 k ' y 2 k ' x 1 2
P 01 = 1 2 Re x ' = l ' l ' y ' = 0 s ' E × h * · z ̂ dy ' dx '
= ± 1 2 Re x ' = l ' l ' y ' = 0 s ' E x h y * dy ' dx '
= ± F 2 2 G 2 s ' l ' 2 ε 1 [ 1 β z ( λ 0 2 s ) + β z ]
k ' z 2 = ε 1 ε 2 ( ε 2 μ 2 κ 2 k ' x 1 2 ) k ' y 2

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