Abstract

A metamaterial, arranged by stacking layers of planar constituents suitably shaped to be responsive to arbitrarily linearly polarized incident waves is here shown to exhibit 2D-isotropic effective negative refractive index (NRI). The general concept underlying this metamaterial design consists of closely pairing two metallic particles to accomplish, as a result of their tight coupling, both symmetric and antisymmetric resonance modes, whose proper superposition can lead to an effective negative refraction response. The proposed structure is composed by layers of periodically arranged pairs of face coupled loaded tripoles printed on the opposite sides of a single dielectric substrate. Through a comprehensive characterization of the transmission properties of such metamaterial, together with the analysis of its dispersion diagram, conclusive evidence that the medium exhibits effective NRI properties as well as good impedance matching to free space is provided. We also describe some guidelines to design the proposed metamaterial with a prescribed operational frequency bandwidth, dependently on the structure parameters.

© 2009 OSA

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  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]
  2. 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]
  3. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
    [CrossRef]
  4. J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006).
    [CrossRef] [PubMed]
  5. J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, “Experimental demonstration of negative index of refraction,” Appl. Phys. Lett. 88, 221,103/1–3 (2006).
  6. G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
    [CrossRef]
  7. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes in metal nanowires and left-handed materials,” J. Nonlinear Opt. Phys. 11(1), 65–74 (2002).
    [CrossRef]
  8. V. Podolskiy, A. Sarychev, and V. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11(7), 735–745 (2003).
    [CrossRef] [PubMed]
  9. G. Shvets and Y. A. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A, Pure Appl. Opt. 8(4), S122–S130 (2006).
    [CrossRef]
  10. V. Lomakin, Y. Fainman, Y. Urzhumov, and G. Shvets, “Doubly negative metamaterials in the near infrared and visible regimes based on thin film nanocomposites,” Opt. Express 14(23), 11164–11177 (2006).
    [CrossRef] [PubMed]
  11. A. Vallecchi, and F. Capolino, “Metamaterials based on pairs of tightly-coupled scatterers,” in Theory and Phenomena of Metamaterials, chap. 19 (CRC Press, Boca Raton, FL, 2009).
  12. J. C. Vardaxoglou, Frequency Selective Surfaces: Analysis and Design (Research Studies Press, NewYork, 1997).
  13. B. A. Munk, Frequency selective surfaces: Theory and Design (Wiley, New York, 2000).
  14. Th. Koschny, L. Zhang and C. M. Soukoulis, “Isotropic three-dimensional left-handed metamaterials,” Phys. Rev. B 71, 121103/1–4 (2005).
  15. C. R. Simovski and H. Sailing, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting omega particles,” Phys. Lett. A 311(2-3), 254–263 (2003).
    [CrossRef]
  16. N. Wongkasemand, A. Akyurtlu, and K. A. Marx, “Group theory based design of isotropic negative refractive index metamaterials,” Progress in Electromagnetics Research 63, 295–310 (2006).
    [CrossRef]
  17. A. Grbica, G. V. Eleftheriades, “An isotropic three-dimensional negative-refractive-index transmission-line metamaterial,” J. Appl. Phys. 98, 043106/1–5 (2005).
  18. M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmission-line matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55(12), 2930–2941 (2007).
    [CrossRef]
  19. C. Imhof and R. Zengerle, “Pairs of metallic crosses as a left-handed metamaterial with improved polarization properties,” Opt. Express 14(18), 8257–8262 (2006).
    [CrossRef] [PubMed]
  20. L. Markley and G. V. Eleftheriades, “A negative-refractive-index metamaterial for incident plane waves of arbitrary polarization,” IEEE Antennas Wirel. Propag. Lett. 6(11), 28–32 (2007).
    [CrossRef]
  21. M. Kafesaki, I. Tsiapa, N. Katsarakis, T. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variations,” Phys. Rev. B 75, 235114/1–9 (2007).
  22. A. Vallecchi, F. Capolino, and A. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microwave Wireless Comp. Lett. 19(5), 269–271 (2009).
    [CrossRef]
  23. K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peaks in metamaterials,” Opt. Lett. 29(22), 2623–2625 (2004).
    [CrossRef] [PubMed]
  24. X. 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 70, 016608/1–7 (2004).
  25. C. R. Simovski, “Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials (Amst.) 1(2), 62–80 (2007).
    [CrossRef]
  26. C. R. Simovski, S.A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B 75, 195111/1–9 (2007).
  27. C. R. Simovski, “On the extraction of local material parameters of meta-materials from experimental or simulated data,” in Theory and Phenomena of Metamaterials, Chap. 11 (CRC Press, Boca Raton, FL, 2009).
  28. D. Seetharamdoo, R Sauleau, K Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys . 98, 063505/1–4 (2005).
    [CrossRef]

2009

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

A. Vallecchi, F. Capolino, and A. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microwave Wireless Comp. Lett. 19(5), 269–271 (2009).
[CrossRef]

2007

C. R. Simovski, “Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials (Amst.) 1(2), 62–80 (2007).
[CrossRef]

M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmission-line matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55(12), 2930–2941 (2007).
[CrossRef]

L. Markley and G. V. Eleftheriades, “A negative-refractive-index metamaterial for incident plane waves of arbitrary polarization,” IEEE Antennas Wirel. Propag. Lett. 6(11), 28–32 (2007).
[CrossRef]

2006

2005

D. Seetharamdoo, R Sauleau, K Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys . 98, 063505/1–4 (2005).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[CrossRef]

2004

2003

V. Podolskiy, A. Sarychev, and V. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11(7), 735–745 (2003).
[CrossRef] [PubMed]

C. R. Simovski and H. Sailing, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting omega particles,” Phys. Lett. A 311(2-3), 254–263 (2003).
[CrossRef]

2002

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes in metal nanowires and left-handed materials,” J. Nonlinear Opt. Phys. 11(1), 65–74 (2002).
[CrossRef]

2000

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

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]

Akyurtlu, A.

N. Wongkasemand, A. Akyurtlu, and K. A. Marx, “Group theory based design of isotropic negative refractive index metamaterials,” Progress in Electromagnetics Research 63, 295–310 (2006).
[CrossRef]

Aydin, K.

Cai, W.

Caloz, C.

M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmission-line matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55(12), 2930–2941 (2007).
[CrossRef]

Capolino, F.

A. Vallecchi, F. Capolino, and A. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microwave Wireless Comp. Lett. 19(5), 269–271 (2009).
[CrossRef]

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

Chettiar, U. K.

Donzelli, G.

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

Drachev, V. P.

Economon, E. N.

Eleftheriades, G. V.

L. Markley and G. V. Eleftheriades, “A negative-refractive-index metamaterial for incident plane waves of arbitrary polarization,” IEEE Antennas Wirel. Propag. Lett. 6(11), 28–32 (2007).
[CrossRef]

Fainman, Y.

Guven, K.

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]

Imhof, C.

Kafesaki, M.

Kildishev, A. V.

Koschny, T.

Lomakin, V.

Mahdjoubi, K

D. Seetharamdoo, R Sauleau, K Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys . 98, 063505/1–4 (2005).
[CrossRef]

Markley, L.

L. Markley and G. V. Eleftheriades, “A negative-refractive-index metamaterial for incident plane waves of arbitrary polarization,” IEEE Antennas Wirel. Propag. Lett. 6(11), 28–32 (2007).
[CrossRef]

Marx, K. A.

N. Wongkasemand, A. Akyurtlu, and K. A. Marx, “Group theory based design of isotropic negative refractive index metamaterials,” Progress in Electromagnetics Research 63, 295–310 (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 and permittivity,” Phys. Rev. Lett. 84(18), 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(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]

Podolskiy, V.

Podolskiy, V. A.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes in metal nanowires and left-handed materials,” J. Nonlinear Opt. Phys. 11(1), 65–74 (2002).
[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]

Russer, P.

M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmission-line matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55(12), 2930–2941 (2007).
[CrossRef]

Sailing, H.

C. R. Simovski and H. Sailing, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting omega particles,” Phys. Lett. A 311(2-3), 254–263 (2003).
[CrossRef]

Sarychev, A.

Sarychev, A. K.

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes in metal nanowires and left-handed materials,” J. Nonlinear Opt. Phys. 11(1), 65–74 (2002).
[CrossRef]

Sauleau,, R

D. Seetharamdoo, R Sauleau, K Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys . 98, 063505/1–4 (2005).
[CrossRef]

Schuchinsky, A.

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

A. Vallecchi, F. Capolino, and A. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microwave Wireless Comp. Lett. 19(5), 269–271 (2009).
[CrossRef]

Schultz, S.

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]

Seetharamdoo,, D.

D. Seetharamdoo, R Sauleau, K Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys . 98, 063505/1–4 (2005).
[CrossRef]

Shalaev, V.

Shalaev, V. M.

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes in metal nanowires and left-handed materials,” J. Nonlinear Opt. Phys. 11(1), 65–74 (2002).
[CrossRef]

Shvets, G.

V. Lomakin, Y. Fainman, Y. Urzhumov, and G. Shvets, “Doubly negative metamaterials in the near infrared and visible regimes based on thin film nanocomposites,” Opt. Express 14(23), 11164–11177 (2006).
[CrossRef] [PubMed]

G. Shvets and Y. A. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A, Pure Appl. Opt. 8(4), S122–S130 (2006).
[CrossRef]

Simovski, C. R.

C. R. Simovski, “Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials (Amst.) 1(2), 62–80 (2007).
[CrossRef]

C. R. Simovski and H. Sailing, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting omega particles,” Phys. Lett. A 311(2-3), 254–263 (2003).
[CrossRef]

Smith, D. R.

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.

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]

Tarot, A.C

D. Seetharamdoo, R Sauleau, K Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys . 98, 063505/1–4 (2005).
[CrossRef]

Urzhumov, Y.

Urzhumov, Y. A.

G. Shvets and Y. A. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A, Pure Appl. Opt. 8(4), S122–S130 (2006).
[CrossRef]

Vallecchi, A.

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

A. Vallecchi, F. Capolino, and A. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microwave Wireless Comp. Lett. 19(5), 269–271 (2009).
[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]

Wongkasemand, N.

N. Wongkasemand, A. Akyurtlu, and K. A. Marx, “Group theory based design of isotropic negative refractive index metamaterials,” Progress in Electromagnetics Research 63, 295–310 (2006).
[CrossRef]

Yuan, H.-K.

Zedler, M.

M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmission-line matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55(12), 2930–2941 (2007).
[CrossRef]

Zengerle, R.

Zhang, L.

Zhou, J.

IEEE Antennas Wirel. Propag. Lett.

L. Markley and G. V. Eleftheriades, “A negative-refractive-index metamaterial for incident plane waves of arbitrary polarization,” IEEE Antennas Wirel. Propag. Lett. 6(11), 28–32 (2007).
[CrossRef]

IEEE Microwave Wireless Comp. Lett.

A. Vallecchi, F. Capolino, and A. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microwave Wireless Comp. Lett. 19(5), 269–271 (2009).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

M. Zedler, C. Caloz, and P. Russer, “A 3-D isotropic left-handed metamaterial based on the rotated transmission-line matrix (TLM) scheme,” IEEE Trans. Microw. Theory Tech. 55(12), 2930–2941 (2007).
[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. Appl. Phys

D. Seetharamdoo, R Sauleau, K Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: Interpretation and validity,” J. Appl. Phys . 98, 063505/1–4 (2005).
[CrossRef]

J. Nonlinear Opt. Phys.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes in metal nanowires and left-handed materials,” J. Nonlinear Opt. Phys. 11(1), 65–74 (2002).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

G. Shvets and Y. A. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A, Pure Appl. Opt. 8(4), S122–S130 (2006).
[CrossRef]

Metamaterials (Amst.)

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

C. R. Simovski, “Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials (Amst.) 1(2), 62–80 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

C. R. Simovski and H. Sailing, “Frequency range and explicit expressions for negative permittivity and permeability for an isotropic medium formed by a lattice of perfectly conducting omega particles,” Phys. Lett. A 311(2-3), 254–263 (2003).
[CrossRef]

Phys. Rev. Lett.

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]

Progress in Electromagnetics Research

N. Wongkasemand, A. Akyurtlu, and K. A. Marx, “Group theory based design of isotropic negative refractive index metamaterials,” Progress in Electromagnetics Research 63, 295–310 (2006).
[CrossRef]

Other

A. Grbica, G. V. Eleftheriades, “An isotropic three-dimensional negative-refractive-index transmission-line metamaterial,” J. Appl. Phys. 98, 043106/1–5 (2005).

J. Zhou, T. Koschny, L. Zhang, G. Tuttle, and C. M. Soukoulis, “Experimental demonstration of negative index of refraction,” Appl. Phys. Lett. 88, 221,103/1–3 (2006).

A. Vallecchi, and F. Capolino, “Metamaterials based on pairs of tightly-coupled scatterers,” in Theory and Phenomena of Metamaterials, chap. 19 (CRC Press, Boca Raton, FL, 2009).

J. C. Vardaxoglou, Frequency Selective Surfaces: Analysis and Design (Research Studies Press, NewYork, 1997).

B. A. Munk, Frequency selective surfaces: Theory and Design (Wiley, New York, 2000).

Th. Koschny, L. Zhang and C. M. Soukoulis, “Isotropic three-dimensional left-handed metamaterials,” Phys. Rev. B 71, 121103/1–4 (2005).

C. R. Simovski, S.A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B 75, 195111/1–9 (2007).

C. R. Simovski, “On the extraction of local material parameters of meta-materials from experimental or simulated data,” in Theory and Phenomena of Metamaterials, Chap. 11 (CRC Press, Boca Raton, FL, 2009).

X. 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 70, 016608/1–7 (2004).

M. Kafesaki, I. Tsiapa, N. Katsarakis, T. Koschny, C. M. Soukoulis, and E. N. Economou, “Left-handed metamaterials: The fishnet structure and its variations,” Phys. Rev. B 75, 235114/1–9 (2007).

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Figures (8)

Fig. 1
Fig. 1

(a) Perspective view of a layer of the 2D-isotropic metamaterial formed by a periodic arrangement of tightly coupled pairs of loaded tripoles, which exhibit an antisymmetric (magnetic) resonance for any incident linear polarization. (b) Top view of the metamaterial unit cell with geometrical parameters quoted and lattice vectors (dashed). In the simulations, we have set A = 5 mm, A1 = 0.5 mm, B2 = 0.5mm, A2 = 4.885 mm, and B1 = 4 mm.

Fig. 2
Fig. 2

(a) Simulated transmission coefficients vs. frequency for a layer of periodically arranged LTPs (Fig. 1) at different thicknesses H (H = 1, 2, 3 mm) of the dielectric substrate supporting the top and bottom conductors. Solid and dashed lines, almost superimposed, correspond to CST simulations of lossy and lossless structures, respectively; circles represent HFSS results for the respective lossy structure only. (b) LTPs’ transmission characteristics when the lateral arms of the tripole particles are short-circuited (see the inset): the magnetic resonance (providing the passband) is suppressed by the short circuits and only the FSS-like stopband electric resonance is present.

Fig. 3
Fig. 3

Antisymmeyric surface current distribution on the unit cell of the LTP from Fig. 1 (H = 2 mm) calculated by CST MWS at the frequency f = 4.6 GHz, near the magnetic resonance fm . The illuminating plane wave with the horizontally polarized electric field (electric field polarized along the y-axis) is normally incident on the structure from the left-hand side.

Fig. 4
Fig. 4

Simulation setups for: (a) variable polarization at normal incidence; (b) TE (transverse-to-z electric field) obliquely incident plane wave; (c) TM (transverse-to-z magnetic field) obliquely incident plane wave. In (b) and (c) the plane wave is impinging from the direction (θi,ϕi) .

Fig. 5
Fig. 5

Simulated (CST MWS) transmission coefficients versus frequency for a layer of periodically arranged LTPs (Fig. 1) with H = 2 mm in the different illumination setups displayed in Fig. 4. (a) Normally incident plane waves whose polarization is rotated by the angles ϕpol=0°,30°,60°,90° ; (b) TE plane waves incident at ϕi=0° and varying θi ; (c) TM plane waves incident at ϕi=0° and varying θi ; (d) TE plane waves incident at ϕi=30° and varying θi ; (e) TM plane waves incident at ϕi=30° and varying θi ; (f) TE plane waves incident at ϕi=0°,30°,60°,90° and θi=30° .

Fig. 6
Fig. 6

Effective material parameters for a layer of periodically arranged LTPs (Fig. 1) at normal incidence. The unit cell size along the propagation direction is C = 6 mm and the thickness of the dielectric substrate is H = 2 mm. The real and imaginary parts of the effective parameters are plotted in solid blue and dashed red lines, respectively. Shaded areas highlight double-negative, i.e. NRI transmission, frequency bands for the considered dielectric substrate thicknesses. (a) Effective impedance; (b) effective refractive index; (c) effective relative permittivity; (d) effective relative permeability.

Fig. 7
Fig. 7

Dispersion curves for a wave with propagation constant kM in the infinite periodic metamaterial formed by the LTP structure of Fig. 1 stacked with period C = 6 mm along the z-direction at different thicknesses H (H = 1, 2, 3 mm) of the dielectric substrate supporting the pairs of conductors. (a) Low-frequency dispersion diagram of the paired tripole lattice as calculated by CST MWS. (b) Enlargement of the NRI passband with comparison of CST MWS (solid black, dashed blue, and solid red lines) and HFSS (circular, square, and triangular markers) results. If the lateral arms of the pair of tripoles would be short circuited, or, in an analogous manner, the tripole pairs in each cell would be replaced by a single tripole conductor, the second passband with negative slope would disappear (cf. Fig. 2(b)).

Fig. 8
Fig. 8

(a) Center frequency, associated to the very close magnetic resonance fm , and (b) fractional bandwidth Δf/fm of the backward wave passband vs. thickness H of the dielectric substrate supporting the tripole pairs at a few values of the unit cell size C along the propagation direction as retrieved by CST MWS dispersion analyses.

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