Abstract

The prediction and the engineering of the electromagnetic properties of metamaterials are increasingly important issues. Recently, several approaches have been proposed to compute these properties through appropriate averages of local fields within the unit cell. In particular, we proposed a Field Summation method that has been used successfully to determine either analytically or numerically the effective properties of different composites and metamaterials. But this method also provides interesting clues for understanding the behaviour of these materials. It helps chose appropriate planes to visualize the fields using electromagnetic simulation software, and understand behaviours leading to either positive or negative effective parameters, with either small or large values. It helps establish whether the materials can be adequately described by effective parameters.

© 2007 Optical Society of America

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  1. K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peak in metamaterials,” Opt. Lett 29,2623 (2004).
    [CrossRef] [PubMed]
  2. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
    [CrossRef] [PubMed]
  3. T. Decoopman, A. Marteau, E. Lheurette, O. Vanbésien, and D. Lippens, “Left-Handed Electromagnetic Properties of Split-Ring Resonator and Wire Loaded Transmission Line in a Fin-Line Technology,” IEEE Trans. MTT 54,1451–1457 (2006).
    [CrossRef]
  4. 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 30,3356–3358 (2005).
    [CrossRef]
  5. A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005).
    [CrossRef] [PubMed]
  6. 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]
  7. 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 (2000).
    [CrossRef] [PubMed]
  8. 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 14,11164–11177 (2006).
    [CrossRef] [PubMed]
  9. W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23,404 (2006).
    [CrossRef]
  10. O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett 84,1198–2000 (2004).
    [CrossRef]
  11. S. Tretyakov, Analytical modelling in Applied Electromagnetics, (Artech House, 2003).
  12. K. N. Rozanov and E. A. Preobrazhenskii, “Synthesis of wideband radar absorbers based on complex media composed from active electric Dipoles,” J. Commun. Technol. Electron 50,858–864 (2005).
  13. A.-L. Adenot-Engelvin, C. Dudek, and O. Acher, “Microwave permeability of metamaterials based on ferromagnetic composites,” J. Magn. Magn. Mater 300,33–37 (2006).
    [CrossRef]
  14. A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14,1557–1567 (2006).
    [CrossRef] [PubMed]
  15. R. Ziolkowski, “Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs,” Opt. Express 11,662–681 (2003).
    [CrossRef] [PubMed]
  16. 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 (2005).
    [CrossRef]
  17. B. I. Popa and S. A. Cummer, “Wave fields measured inside a negative refractive index metamaterial,” Appl. Phys. Lett 85,4564–4566 (2004).
    [CrossRef]
  18. D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B 23,391–403 (2006).
    [CrossRef]
  19. J.-M. Lerat, N. Malléjac, and O. Acher, “Determination of the effective parameters of a metamaterial by field summation method,” J. Appl. Phys 100,084908 (2006).
    [CrossRef]
  20. T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006).
    [CrossRef]
  21. A. Cho, “Voilà ! Cloak of Invisibility Unveiled,” Science 314,403 (2006).
    [CrossRef] [PubMed]
  22. 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 (2002).
    [CrossRef]
  23. O. Acher, A. -L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62,13748 (2000).
    [CrossRef]
  24. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2,466–475 (1956).
  25. A. N. Lagarkov, A. K. Sarychev, Y. R. Smychkovich, and A. P. Vinogradov, “Effective Medium Theory for microwave dielectric constant and magnetic permeability of conducting stick composites,” J. Electromagn. Waves Appl 6,1159 (1992).
  26. O. Acher, A. -L. Adenot, F. Lubrano, and F. Duverger, “Low density artificial magnetic composites,” J. Appl. Phys 85,4639–4641 (1999).
    [CrossRef]
  27. O. Reynet, A. -L. Adenot, S. Deprot, O. Acher, and M. Latrach, “Effect of the magnetic properties of inclusions on the high-frequency dielectric response of diluted composites,” Phys. Rev. B 66,94412 (2002).
    [CrossRef]
  28. M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrinov, and Y. S. Kivshar, “Effect of microscopic disorder on magnetic properties of metamaterials,” Phys. Rev. E 73,056605 (2006).
    [CrossRef]
  29. O. Acher, M. Ledieu, A.-L. Adenot, and O. Reynet, “Microwave properties of diluted composites made of magnetic wires with giant magneto-impedance effect,” IEEE Trans. Magn 39,3085–3090 (2003).
    [CrossRef]
  30. D. Maystre and S. Enoch, “Perfect lenses made with left-handed materilas: Alice’s mirror ?,” J. Opt. Soc. Am. A 21,122–131 (2004).
    [CrossRef]
  31. T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B Gralak, “Photonic Crystla Lens: From Negative Refraction and Negative Index to Negative Permittivity and Permeability,” Phys. Rev. Lett 97,073905 (2006).
    [CrossRef] [PubMed]

2006 (11)

T. Decoopman, A. Marteau, E. Lheurette, O. Vanbésien, and D. Lippens, “Left-Handed Electromagnetic Properties of Split-Ring Resonator and Wire Loaded Transmission Line in a Fin-Line Technology,” IEEE Trans. MTT 54,1451–1457 (2006).
[CrossRef]

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 14,11164–11177 (2006).
[CrossRef] [PubMed]

W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23,404 (2006).
[CrossRef]

A.-L. Adenot-Engelvin, C. Dudek, and O. Acher, “Microwave permeability of metamaterials based on ferromagnetic composites,” J. Magn. Magn. Mater 300,33–37 (2006).
[CrossRef]

A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express 14,1557–1567 (2006).
[CrossRef] [PubMed]

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

J.-M. Lerat, N. Malléjac, and O. Acher, “Determination of the effective parameters of a metamaterial by field summation method,” J. Appl. Phys 100,084908 (2006).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006).
[CrossRef]

A. Cho, “Voilà ! Cloak of Invisibility Unveiled,” Science 314,403 (2006).
[CrossRef] [PubMed]

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrinov, and Y. S. Kivshar, “Effect of microscopic disorder on magnetic properties of metamaterials,” Phys. Rev. E 73,056605 (2006).
[CrossRef]

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B Gralak, “Photonic Crystla Lens: From Negative Refraction and Negative Index to Negative Permittivity and Permeability,” Phys. Rev. Lett 97,073905 (2006).
[CrossRef] [PubMed]

2005 (5)

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 (2005).
[CrossRef]

K. N. Rozanov and E. A. Preobrazhenskii, “Synthesis of wideband radar absorbers based on complex media composed from active electric Dipoles,” J. Commun. Technol. Electron 50,858–864 (2005).

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[CrossRef] [PubMed]

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 30,3356–3358 (2005).
[CrossRef]

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005).
[CrossRef] [PubMed]

2004 (4)

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peak in metamaterials,” Opt. Lett 29,2623 (2004).
[CrossRef] [PubMed]

O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett 84,1198–2000 (2004).
[CrossRef]

B. I. Popa and S. A. Cummer, “Wave fields measured inside a negative refractive index metamaterial,” Appl. Phys. Lett 85,4564–4566 (2004).
[CrossRef]

D. Maystre and S. Enoch, “Perfect lenses made with left-handed materilas: Alice’s mirror ?,” J. Opt. Soc. Am. A 21,122–131 (2004).
[CrossRef]

2003 (2)

O. Acher, M. Ledieu, A.-L. Adenot, and O. Reynet, “Microwave properties of diluted composites made of magnetic wires with giant magneto-impedance effect,” IEEE Trans. Magn 39,3085–3090 (2003).
[CrossRef]

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

2002 (2)

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 (2002).
[CrossRef]

O. Reynet, A. -L. Adenot, S. Deprot, O. Acher, and M. Latrach, “Effect of the magnetic properties of inclusions on the high-frequency dielectric response of diluted composites,” Phys. Rev. B 66,94412 (2002).
[CrossRef]

2000 (2)

O. Acher, A. -L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62,13748 (2000).
[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 (2000).
[CrossRef] [PubMed]

1999 (2)

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]

O. Acher, A. -L. Adenot, F. Lubrano, and F. Duverger, “Low density artificial magnetic composites,” J. Appl. Phys 85,4639–4641 (1999).
[CrossRef]

1992 (1)

A. N. Lagarkov, A. K. Sarychev, Y. R. Smychkovich, and A. P. Vinogradov, “Effective Medium Theory for microwave dielectric constant and magnetic permeability of conducting stick composites,” J. Electromagn. Waves Appl 6,1159 (1992).

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2,466–475 (1956).

Acher, O.

J.-M. Lerat, N. Malléjac, and O. Acher, “Determination of the effective parameters of a metamaterial by field summation method,” J. Appl. Phys 100,084908 (2006).
[CrossRef]

A.-L. Adenot-Engelvin, C. Dudek, and O. Acher, “Microwave permeability of metamaterials based on ferromagnetic composites,” J. Magn. Magn. Mater 300,33–37 (2006).
[CrossRef]

O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett 84,1198–2000 (2004).
[CrossRef]

O. Acher, M. Ledieu, A.-L. Adenot, and O. Reynet, “Microwave properties of diluted composites made of magnetic wires with giant magneto-impedance effect,” IEEE Trans. Magn 39,3085–3090 (2003).
[CrossRef]

O. Reynet, A. -L. Adenot, S. Deprot, O. Acher, and M. Latrach, “Effect of the magnetic properties of inclusions on the high-frequency dielectric response of diluted composites,” Phys. Rev. B 66,94412 (2002).
[CrossRef]

O. Acher, A. -L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62,13748 (2000).
[CrossRef]

O. Acher, A. -L. Adenot, F. Lubrano, and F. Duverger, “Low density artificial magnetic composites,” J. Appl. Phys 85,4639–4641 (1999).
[CrossRef]

Adenot, A. -L.

O. Reynet, A. -L. Adenot, S. Deprot, O. Acher, and M. Latrach, “Effect of the magnetic properties of inclusions on the high-frequency dielectric response of diluted composites,” Phys. Rev. B 66,94412 (2002).
[CrossRef]

O. Acher, A. -L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62,13748 (2000).
[CrossRef]

O. Acher, A. -L. Adenot, F. Lubrano, and F. Duverger, “Low density artificial magnetic composites,” J. Appl. Phys 85,4639–4641 (1999).
[CrossRef]

Adenot, A.-L.

O. Acher, M. Ledieu, A.-L. Adenot, and O. Reynet, “Microwave properties of diluted composites made of magnetic wires with giant magneto-impedance effect,” IEEE Trans. Magn 39,3085–3090 (2003).
[CrossRef]

Adenot-Engelvin, A.-L.

A.-L. Adenot-Engelvin, C. Dudek, and O. Acher, “Microwave permeability of metamaterials based on ferromagnetic composites,” J. Magn. Magn. Mater 300,33–37 (2006).
[CrossRef]

Alù, A.

Aydin, K.

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peak in metamaterials,” Opt. Lett 29,2623 (2004).
[CrossRef] [PubMed]

Basov, D. N.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006).
[CrossRef]

W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23,404 (2006).
[CrossRef]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[CrossRef] [PubMed]

Cai, W.

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 30,3356–3358 (2005).
[CrossRef]

Chettiar, U. 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 30,3356–3358 (2005).
[CrossRef]

Cho, A.

A. Cho, “Voilà ! Cloak of Invisibility Unveiled,” Science 314,403 (2006).
[CrossRef] [PubMed]

Cummer, S. A.

B. I. Popa and S. A. Cummer, “Wave fields measured inside a negative refractive index metamaterial,” Appl. Phys. Lett 85,4564–4566 (2004).
[CrossRef]

Decoopman, T.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B Gralak, “Photonic Crystla Lens: From Negative Refraction and Negative Index to Negative Permittivity and Permeability,” Phys. Rev. Lett 97,073905 (2006).
[CrossRef] [PubMed]

T. Decoopman, A. Marteau, E. Lheurette, O. Vanbésien, and D. Lippens, “Left-Handed Electromagnetic Properties of Split-Ring Resonator and Wire Loaded Transmission Line in a Fin-Line Technology,” IEEE Trans. MTT 54,1451–1457 (2006).
[CrossRef]

Deprot, S.

O. Reynet, A. -L. Adenot, S. Deprot, O. Acher, and M. Latrach, “Effect of the magnetic properties of inclusions on the high-frequency dielectric response of diluted composites,” Phys. Rev. B 66,94412 (2002).
[CrossRef]

Drachev, V. P.

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 30,3356–3358 (2005).
[CrossRef]

Driscoll, T.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006).
[CrossRef]

Dudek, C.

A.-L. Adenot-Engelvin, C. Dudek, and O. Acher, “Microwave permeability of metamaterials based on ferromagnetic composites,” J. Magn. Magn. Mater 300,33–37 (2006).
[CrossRef]

Duverger, F.

O. Acher, A. -L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62,13748 (2000).
[CrossRef]

O. Acher, A. -L. Adenot, F. Lubrano, and F. Duverger, “Low density artificial magnetic composites,” J. Appl. Phys 85,4639–4641 (1999).
[CrossRef]

Engheta, N.

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[CrossRef] [PubMed]

Enoch, S.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B Gralak, “Photonic Crystla Lens: From Negative Refraction and Negative Index to Negative Permittivity and Permeability,” Phys. Rev. Lett 97,073905 (2006).
[CrossRef] [PubMed]

D. Maystre and S. Enoch, “Perfect lenses made with left-handed materilas: Alice’s mirror ?,” J. Opt. Soc. Am. A 21,122–131 (2004).
[CrossRef]

Fainman, Y.

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005).
[CrossRef] [PubMed]

Geim, A. K.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005).
[CrossRef] [PubMed]

Gleeson, H. F.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005).
[CrossRef] [PubMed]

Gorkunov, M. V.

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrinov, and Y. S. Kivshar, “Effect of microscopic disorder on magnetic properties of metamaterials,” Phys. Rev. E 73,056605 (2006).
[CrossRef]

Gralak, B

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B Gralak, “Photonic Crystla Lens: From Negative Refraction and Negative Index to Negative Permittivity and Permeability,” Phys. Rev. Lett 97,073905 (2006).
[CrossRef] [PubMed]

Gredeskul, S. A.

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrinov, and Y. S. Kivshar, “Effect of microscopic disorder on magnetic properties of metamaterials,” Phys. Rev. E 73,056605 (2006).
[CrossRef]

Grigorenko, A. N.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005).
[CrossRef] [PubMed]

Guven, K.

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peak in metamaterials,” Opt. Lett 29,2623 (2004).
[CrossRef] [PubMed]

Holden, A. J.

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

Kafesaki, M.

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peak in metamaterials,” Opt. Lett 29,2623 (2004).
[CrossRef] [PubMed]

Khrushchev, I. Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005).
[CrossRef] [PubMed]

Kildishev, A. V.

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 30,3356–3358 (2005).
[CrossRef]

Kivshar, Y. S.

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrinov, and Y. S. Kivshar, “Effect of microscopic disorder on magnetic properties of metamaterials,” Phys. Rev. E 73,056605 (2006).
[CrossRef]

Koschny, Th.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[CrossRef] [PubMed]

Lagarkov, A. N.

A. N. Lagarkov, A. K. Sarychev, Y. R. Smychkovich, and A. P. Vinogradov, “Effective Medium Theory for microwave dielectric constant and magnetic permeability of conducting stick composites,” J. Electromagn. Waves Appl 6,1159 (1992).

Latrach, M.

O. Reynet, A. -L. Adenot, S. Deprot, O. Acher, and M. Latrach, “Effect of the magnetic properties of inclusions on the high-frequency dielectric response of diluted composites,” Phys. Rev. B 66,94412 (2002).
[CrossRef]

Ledieu, M.

O. Acher, M. Ledieu, A.-L. Adenot, and O. Reynet, “Microwave properties of diluted composites made of magnetic wires with giant magneto-impedance effect,” IEEE Trans. Magn 39,3085–3090 (2003).
[CrossRef]

Lerat, J.-M.

J.-M. Lerat, N. Malléjac, and O. Acher, “Determination of the effective parameters of a metamaterial by field summation method,” J. Appl. Phys 100,084908 (2006).
[CrossRef]

Lheurette, E.

T. Decoopman, A. Marteau, E. Lheurette, O. Vanbésien, and D. Lippens, “Left-Handed Electromagnetic Properties of Split-Ring Resonator and Wire Loaded Transmission Line in a Fin-Line Technology,” IEEE Trans. MTT 54,1451–1457 (2006).
[CrossRef]

Linden, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[CrossRef] [PubMed]

Lippens, D.

T. Decoopman, A. Marteau, E. Lheurette, O. Vanbésien, and D. Lippens, “Left-Handed Electromagnetic Properties of Split-Ring Resonator and Wire Loaded Transmission Line in a Fin-Line Technology,” IEEE Trans. MTT 54,1451–1457 (2006).
[CrossRef]

Lomakin, V.

Lubrano, F.

O. Acher, A. -L. Adenot, F. Lubrano, and F. Duverger, “Low density artificial magnetic composites,” J. Appl. Phys 85,4639–4641 (1999).
[CrossRef]

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 (2005).
[CrossRef]

Malléjac, N.

J.-M. Lerat, N. Malléjac, and O. Acher, “Determination of the effective parameters of a metamaterial by field summation method,” J. Appl. Phys 100,084908 (2006).
[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 (2002).
[CrossRef]

Marteau, A.

T. Decoopman, A. Marteau, E. Lheurette, O. Vanbésien, and D. Lippens, “Left-Handed Electromagnetic Properties of Split-Ring Resonator and Wire Loaded Transmission Line in a Fin-Line Technology,” IEEE Trans. MTT 54,1451–1457 (2006).
[CrossRef]

Maystre, D.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B Gralak, “Photonic Crystla Lens: From Negative Refraction and Negative Index to Negative Permittivity and Permeability,” Phys. Rev. Lett 97,073905 (2006).
[CrossRef] [PubMed]

D. Maystre and S. Enoch, “Perfect lenses made with left-handed materilas: Alice’s mirror ?,” J. Opt. Soc. Am. A 21,122–131 (2004).
[CrossRef]

Nemat-Nasser, S.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (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 84,4184 (2000).
[CrossRef] [PubMed]

Ozbay, E.

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peak in metamaterials,” Opt. Lett 29,2623 (2004).
[CrossRef] [PubMed]

Padilla, W. J.

W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23,404 (2006).
[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 (2000).
[CrossRef] [PubMed]

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, 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]

Petrovic, J.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005).
[CrossRef] [PubMed]

Popa, B. I.

B. I. Popa and S. A. Cummer, “Wave fields measured inside a negative refractive index metamaterial,” Appl. Phys. Lett 85,4564–4566 (2004).
[CrossRef]

Preobrazhenskii, E. A.

K. N. Rozanov and E. A. Preobrazhenskii, “Synthesis of wideband radar absorbers based on complex media composed from active electric Dipoles,” J. Commun. Technol. Electron 50,858–864 (2005).

Reynet, O.

O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett 84,1198–2000 (2004).
[CrossRef]

O. Acher, M. Ledieu, A.-L. Adenot, and O. Reynet, “Microwave properties of diluted composites made of magnetic wires with giant magneto-impedance effect,” IEEE Trans. Magn 39,3085–3090 (2003).
[CrossRef]

O. Reynet, A. -L. Adenot, S. Deprot, O. Acher, and M. Latrach, “Effect of the magnetic properties of inclusions on the high-frequency dielectric response of diluted composites,” Phys. Rev. B 66,94412 (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. Microwave Theory Tech 47,2075–2084 (1999).
[CrossRef]

Rozanov, K. N.

K. N. Rozanov and E. A. Preobrazhenskii, “Synthesis of wideband radar absorbers based on complex media composed from active electric Dipoles,” J. Commun. Technol. Electron 50,858–864 (2005).

Rye, P. M.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006).
[CrossRef]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2,466–475 (1956).

Salandrino, 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 30,3356–3358 (2005).
[CrossRef]

A. N. Lagarkov, A. K. Sarychev, Y. R. Smychkovich, and A. P. Vinogradov, “Effective Medium Theory for microwave dielectric constant and magnetic permeability of conducting stick composites,” J. Electromagn. Waves Appl 6,1159 (1992).

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 (2005).
[CrossRef]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[CrossRef] [PubMed]

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 (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 (2000).
[CrossRef] [PubMed]

Schurig, D.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006).
[CrossRef]

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 (2005).
[CrossRef]

Shadrinov, I. V.

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrinov, and Y. S. Kivshar, “Effect of microscopic disorder on magnetic properties of metamaterials,” Phys. Rev. E 73,056605 (2006).
[CrossRef]

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 30,3356–3358 (2005).
[CrossRef]

Shvets, G.

Smith, D. R.

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

W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23,404 (2006).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006).
[CrossRef]

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 (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 (2000).
[CrossRef] [PubMed]

Smychkovich, Y. R.

A. N. Lagarkov, A. K. Sarychev, Y. R. Smychkovich, and A. P. Vinogradov, “Effective Medium Theory for microwave dielectric constant and magnetic permeability of conducting stick composites,” J. Electromagn. Waves Appl 6,1159 (1992).

Soukoulis, C. M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[CrossRef] [PubMed]

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peak in metamaterials,” Opt. Lett 29,2623 (2004).
[CrossRef] [PubMed]

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 (2002).
[CrossRef]

Starr, A. F.

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech 47,2075–2084 (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 (2005).
[CrossRef]

Tayeb, G.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B Gralak, “Photonic Crystla Lens: From Negative Refraction and Negative Index to Negative Permittivity and Permeability,” Phys. Rev. Lett 97,073905 (2006).
[CrossRef] [PubMed]

Tretyakov, S.

S. Tretyakov, Analytical modelling in Applied Electromagnetics, (Artech House, 2003).

Urzhumov, Y.

Vanbésien, O.

T. Decoopman, A. Marteau, E. Lheurette, O. Vanbésien, and D. Lippens, “Left-Handed Electromagnetic Properties of Split-Ring Resonator and Wire Loaded Transmission Line in a Fin-Line Technology,” IEEE Trans. MTT 54,1451–1457 (2006).
[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 84,4184 (2000).
[CrossRef] [PubMed]

Vinogradov, A. P.

A. N. Lagarkov, A. K. Sarychev, Y. R. Smychkovich, and A. P. Vinogradov, “Effective Medium Theory for microwave dielectric constant and magnetic permeability of conducting stick composites,” J. Electromagn. Waves Appl 6,1159 (1992).

Wegener, M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[CrossRef] [PubMed]

Yuan, H.-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 30,3356–3358 (2005).
[CrossRef]

Zhang, L.

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peak in metamaterials,” Opt. Lett 29,2623 (2004).
[CrossRef] [PubMed]

Zhang, Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005).
[CrossRef] [PubMed]

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[CrossRef] [PubMed]

Ziolkowski, R.

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett (3)

O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett 84,1198–2000 (2004).
[CrossRef]

B. I. Popa and S. A. Cummer, “Wave fields measured inside a negative refractive index metamaterial,” Appl. Phys. Lett 85,4564–4566 (2004).
[CrossRef]

T. Driscoll, D. N. Basov, A. F. Starr, P. M. Rye, S. Nemat-Nasser, D. Schurig, and D. R. Smith, “Free-space microwave focusing by a negative-index gradient lens,” Appl. Phys. Lett 88,081101 (2006).
[CrossRef]

IEEE Trans. Magn (1)

O. Acher, M. Ledieu, A.-L. Adenot, and O. Reynet, “Microwave properties of diluted composites made of magnetic wires with giant magneto-impedance effect,” IEEE Trans. Magn 39,3085–3090 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech (1)

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]

IEEE Trans. MTT (1)

T. Decoopman, A. Marteau, E. Lheurette, O. Vanbésien, and D. Lippens, “Left-Handed Electromagnetic Properties of Split-Ring Resonator and Wire Loaded Transmission Line in a Fin-Line Technology,” IEEE Trans. MTT 54,1451–1457 (2006).
[CrossRef]

J. Appl. Phys (3)

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 (2005).
[CrossRef]

O. Acher, A. -L. Adenot, F. Lubrano, and F. Duverger, “Low density artificial magnetic composites,” J. Appl. Phys 85,4639–4641 (1999).
[CrossRef]

J.-M. Lerat, N. Malléjac, and O. Acher, “Determination of the effective parameters of a metamaterial by field summation method,” J. Appl. Phys 100,084908 (2006).
[CrossRef]

J. Commun. Technol. Electron (1)

K. N. Rozanov and E. A. Preobrazhenskii, “Synthesis of wideband radar absorbers based on complex media composed from active electric Dipoles,” J. Commun. Technol. Electron 50,858–864 (2005).

J. Electromagn. Waves Appl (1)

A. N. Lagarkov, A. K. Sarychev, Y. R. Smychkovich, and A. P. Vinogradov, “Effective Medium Theory for microwave dielectric constant and magnetic permeability of conducting stick composites,” J. Electromagn. Waves Appl 6,1159 (1992).

J. Magn. Magn. Mater (1)

A.-L. Adenot-Engelvin, C. Dudek, and O. Acher, “Microwave permeability of metamaterials based on ferromagnetic composites,” J. Magn. Magn. Mater 300,33–37 (2006).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

Nature (1)

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438,335–338 (2005).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett (2)

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 30,3356–3358 (2005).
[CrossRef]

K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, “Experimental observation of true left-handed transmission peak in metamaterials,” Opt. Lett 29,2623 (2004).
[CrossRef] [PubMed]

Phys. Rev. B (3)

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 (2002).
[CrossRef]

O. Acher, A. -L. Adenot, and F. Duverger, “Fresnel coefficients at an interface with a lamellar composite material,” Phys. Rev. B 62,13748 (2000).
[CrossRef]

O. Reynet, A. -L. Adenot, S. Deprot, O. Acher, and M. Latrach, “Effect of the magnetic properties of inclusions on the high-frequency dielectric response of diluted composites,” Phys. Rev. B 66,94412 (2002).
[CrossRef]

Phys. Rev. E (1)

M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrinov, and Y. S. Kivshar, “Effect of microscopic disorder on magnetic properties of metamaterials,” Phys. Rev. E 73,056605 (2006).
[CrossRef]

Phys. Rev. Lett (3)

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B Gralak, “Photonic Crystla Lens: From Negative Refraction and Negative Index to Negative Permittivity and Permeability,” Phys. Rev. Lett 97,073905 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett 95,203901 (2005).
[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 (2000).
[CrossRef] [PubMed]

Science (1)

A. Cho, “Voilà ! Cloak of Invisibility Unveiled,” Science 314,403 (2006).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2,466–475 (1956).

Other (1)

S. Tretyakov, Analytical modelling in Applied Electromagnetics, (Artech House, 2003).

Supplementary Material (8)

» Media 1: AVI (812 KB)     
» Media 2: AVI (1556 KB)     
» Media 3: AVI (2306 KB)     
» Media 4: AVI (1888 KB)     
» Media 5: AVI (754 KB)     
» Media 6: AVI (2107 KB)     
» Media 7: AVI (2481 KB)     
» Media 8: AVI (2381 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Slab of periodic medium illuminated by an incoming wave: notations, and averaging zones used in different Field Summation Methods.

Fig. 2.
Fig. 2.

(a). Permeability and permittivity obtained by field averaging on a single scatterer thick metamaterial slab; (b). Reflection and Transmission coefficients for the metamaterial slab, calculated using the effective parameters obtained by Field Summation (full curve); and computed in the numerical experiment (S11, S12). Red markers correspond to frequencies of Figs. 3–6.

Fig. 3.
Fig. 3.

H field as a function of time on the P and M planes in a metamaterial: (a). (0.81 MB movie) at 0.9 GHz, the permeability is slightly larger than unity; [Media 1] (b). (1.56 MB movie) at 0.98 GHz, the permeability is large and positive. [Media 2]

Fig. 4.
Fig. 4.

(2.31 MB movie) H field as a function of time on the P and M planes in a metamaterial at the resonance frequency F=0.99 GHz [Media 3]

Fig. 5.
Fig. 5.

H field as a function of time on the P and M planes in a metamaterial: (a) (1.89 MB movie) at 1 GHz, the permeability is negative; [Media 4] (b) (0.75 MB movie) at 1.1 GHz, the permeability is slightly lower than unity. [Media 5]

Fig. 6.
Fig. 6.

(a). Permeability of a 4-scatterer thick metamaterial made with a resistive metal, computed using the Field Summation method; red markers correspond to frequencies illustrated on Fig. 7; (b). Reflection and Transmission coefficients computed from the effective parameters obtained by the field averaging method, and comparison with S11 and S12 values obtained directly from the simulation software.

Fig. 7.
Fig. 7.

H field in a 4-scaterrer thick metamaterial slab made with a resistive metal; (a) (2.10 MB movie) at 0.85 GHz (μ>1); [Media 6] (b) (2.48 MB movie) at 0.96 GHz (μ is imaginary); [Media 7] (c) (2.38 MB movie) at 1.05 GHz (μ <1). [Media 8]

Fig. 8.
Fig. 8.

Reflection and Transmission coefficients for a 4-scatterrer thick slab consisting of highly resonant patterns, computed using the simulation software.

Fig. 9.
Fig. 9.

H field in a 4-scatterrer thick slab consisting of highly resonant patterns, at a frequency 1.04 GHz; (a) Top view of the P plane; (b) Top view of the M plane.

Equations (5)

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

μ 0 μ V V = B x xyz H x xyz ε 0 ε V V = D z xyz E z xyz
μ 0 μ S L = B x xy H x x n y kd sin ( n y kd )
ε 0 ε S L = D z xy E z z n y kd sin ( n y kd )
μ 0 μ V S = B x xyz H x xy ε 0 ε S V = D z xy E z xyz
μ V S = H x xyz H x xy

Metrics