Abstract

We present here the design of nano-inclusions made of properly arranged collections of plasmonic metallic nano-particles that may exhibit a resonant magnetic dipole collective response in the visible domain. When such inclusions are embedded in a host medium, they may provide metamaterials with negative effective permeability at optical frequencies. We also show how the same inclusions may provide resonant electric dipole response and, when combining the two effects at the same frequencies, left-handed materials with both negative effective permittivity and permeability may be synthesized in the optical domain with potential applications for imaging and nano-optics applications.

© 2006 Optical Society of America

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  1. R. W. Ziolkowski, and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  3. L. Landau, and E. M. Lifschitz, Electrodynamics of continuous media (Elsevier, 1984).
  4. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
    [CrossRef]
  5. A. K. Sarychev and V. M. Shalaev, "Magnetic resonance in metal nanoantennas," in Complex Mediums V: Light and Complexity, Proc. SPIE 5508, 128-137 (2004).
    [CrossRef]
  6. A. K. Sarychev and V. M. Shalaev, "Plasmonic nanowire metamaterials," in Negative Refraction Metamaterials: Fundamental Properties and Applications, G. V. Eleftheriades and K. G. Balmain, ed. (John Wiley & Sons, Inc., Hoboken, NJ, 2005), Chap. 8, pp. 313-337.
    [CrossRef]
  7. 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]
  8. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters 30, 3198-3200 (2005).
    [CrossRef] [PubMed]
  9. 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]
  10. V. A. Podolskiy, and E. E. Narimanov, "Strongly anisotropic waveguide as a nonmagnetic left-handed system," Phys. Rev. B 71, 201101 (2005).
    [CrossRef]
  11. 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]
  12. S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
    [CrossRef]
  13. G. Shvets, and Y. A. Urzhumov, "Engineering electromagnetic properties of periodic nanostructures using electrostatic resonance," Phys. Rev. Lett. 93, 243902 (2004).
    [CrossRef]
  14. M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Towards photonic crystal matematerials: Creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
    [CrossRef]
  15. A. Ishimaru, S. W. Lee, Y. Kuga, and V. Jandhyala, "Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory," IEEE Trans. Antennas Propag. 51, 2550-2557 (2003).
    [CrossRef]
  16. The forms of excitations used in Eqs. (2) and (12) are solely employed for the purpose of isolating respectively the magnetic and electric response of the nano-ring of Fig. 1 from one another, which is necessary for evaluating the polarizability coefficients separately. Once these coefficients are determined, they indeed represent the polarizability response of the material to any form of excitation (e.g., a plane wave). This approach is commonly used in the technical literature (see, e.g., [15]).
  17. J. D. Jackson, Classical Electrodyanmics (Wiley, 1998).
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  19. S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2003).
  20. I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299 (2000).
    [CrossRef]
  21. The Drude model employed here accurately describes the frequency dispersion of silver over all the visible frequencies [20]. The minimal difference between this model and realistic experimental data, possibly due to the finite size of the spheres, resonant interband transitions in the material, etc., would not significantly affect the present discussion and approach, since the inherent resonant phenomena here described may only be slightly shifted in frequency or modified in strength, still preserving the validity of the concepts pointed out here.
  22. CST Microwave StudioTM 5.0, CST of America, Inc., www.cst.com.

2005 (5)

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]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters 30, 3198-3200 (2005).
[CrossRef] [PubMed]

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]

V. A. Podolskiy, and E. E. Narimanov, "Strongly anisotropic waveguide as a nonmagnetic left-handed system," Phys. Rev. B 71, 201101 (2005).
[CrossRef]

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]

2004 (2)

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

G. Shvets, and Y. A. Urzhumov, "Engineering electromagnetic properties of periodic nanostructures using electrostatic resonance," Phys. Rev. Lett. 93, 243902 (2004).
[CrossRef]

2003 (2)

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Towards photonic crystal matematerials: Creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[CrossRef]

A. Ishimaru, S. W. Lee, Y. Kuga, and V. Jandhyala, "Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory," IEEE Trans. Antennas Propag. 51, 2550-2557 (2003).
[CrossRef]

2002 (1)

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

2001 (2)

R. W. Ziolkowski, and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (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)

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Biswas, R.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299 (2000).
[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.

Chettiar, U.K.

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Drachev, V.P.

El-Kady, I.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters 30, 3198-3200 (2005).
[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]

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]

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]

Heyman, E.

R. W. Ziolkowski, and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Ho, K. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Ishimaru, A.

A. Ishimaru, S. W. Lee, Y. Kuga, and V. Jandhyala, "Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory," IEEE Trans. Antennas Propag. 51, 2550-2557 (2003).
[CrossRef]

Jandhyala, V.

A. Ishimaru, S. W. Lee, Y. Kuga, and V. Jandhyala, "Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory," IEEE Trans. Antennas Propag. 51, 2550-2557 (2003).
[CrossRef]

Joannopoulos, J. D.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Towards photonic crystal matematerials: Creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[CrossRef]

Johnson, S. G.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Towards photonic crystal matematerials: Creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[CrossRef]

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.

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]

Kuga, Y.

A. Ishimaru, S. W. Lee, Y. Kuga, and V. Jandhyala, "Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory," IEEE Trans. Antennas Propag. 51, 2550-2557 (2003).
[CrossRef]

Lee, S. W.

A. Ishimaru, S. W. Lee, Y. Kuga, and V. Jandhyala, "Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory," IEEE Trans. Antennas Propag. 51, 2550-2557 (2003).
[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]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters 30, 3198-3200 (2005).
[CrossRef] [PubMed]

McPeake, D.

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Narimanov, E. E.

V. A. Podolskiy, and E. E. Narimanov, "Strongly anisotropic waveguide as a nonmagnetic left-handed system," Phys. Rev. B 71, 201101 (2005).
[CrossRef]

O’Brien, S.

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Pendry, J. B.

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Towards photonic crystal matematerials: Creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[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]

Podolskiy, V. A.

V. A. Podolskiy, and E. E. Narimanov, "Strongly anisotropic waveguide as a nonmagnetic left-handed system," Phys. Rev. B 71, 201101 (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. Mater. 11, 65-74 (2002).
[CrossRef]

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Towards photonic crystal matematerials: Creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[CrossRef]

Ramakrishna, S. A.

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Sarychev, A. K.

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

Sarychev, A.K.

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.

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

Shalaev, V. M.

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

Shalaev, V.M.

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]

Shvets, G.

G. Shvets, and Y. A. Urzhumov, "Engineering electromagnetic properties of periodic nanostructures using electrostatic resonance," Phys. Rev. Lett. 93, 243902 (2004).
[CrossRef]

Sigalas, M. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Smith, D. R.

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

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]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters 30, 3198-3200 (2005).
[CrossRef] [PubMed]

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Urzhumov, Y. A.

G. Shvets, and Y. A. Urzhumov, "Engineering electromagnetic properties of periodic nanostructures using electrostatic resonance," Phys. Rev. Lett. 93, 243902 (2004).
[CrossRef]

Wegener, M.

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters 30, 3198-3200 (2005).
[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]

Yuan, H.-K.

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.

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters 30, 3198-3200 (2005).
[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]

Ziolkowski, R. W.

R. W. Ziolkowski, and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

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. (1)

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Towards photonic crystal matematerials: Creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Ishimaru, S. W. Lee, Y. Kuga, and V. Jandhyala, "Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory," IEEE Trans. Antennas Propag. 51, 2550-2557 (2003).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

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

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. Lett. (1)

Optics Letters (1)

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Optics Letters 30, 3198-3200 (2005).
[CrossRef] [PubMed]

Phys. Rev. B (3)

V. A. Podolskiy, and E. E. Narimanov, "Strongly anisotropic waveguide as a nonmagnetic left-handed system," Phys. Rev. B 71, 201101 (2005).
[CrossRef]

S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Phys. Rev. E (1)

R. W. Ziolkowski, and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Phys. Rev. Lett. (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]

G. Shvets, and Y. A. Urzhumov, "Engineering electromagnetic properties of periodic nanostructures using electrostatic resonance," Phys. Rev. Lett. 93, 243902 (2004).
[CrossRef]

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]

Other (9)

L. Landau, and E. M. Lifschitz, Electrodynamics of continuous media (Elsevier, 1984).

A. K. Sarychev and V. M. Shalaev, "Magnetic resonance in metal nanoantennas," in Complex Mediums V: Light and Complexity, Proc. SPIE 5508, 128-137 (2004).
[CrossRef]

A. K. Sarychev and V. M. Shalaev, "Plasmonic nanowire metamaterials," in Negative Refraction Metamaterials: Fundamental Properties and Applications, G. V. Eleftheriades and K. G. Balmain, ed. (John Wiley & Sons, Inc., Hoboken, NJ, 2005), Chap. 8, pp. 313-337.
[CrossRef]

The Drude model employed here accurately describes the frequency dispersion of silver over all the visible frequencies [20]. The minimal difference between this model and realistic experimental data, possibly due to the finite size of the spheres, resonant interband transitions in the material, etc., would not significantly affect the present discussion and approach, since the inherent resonant phenomena here described may only be slightly shifted in frequency or modified in strength, still preserving the validity of the concepts pointed out here.

CST Microwave StudioTM 5.0, CST of America, Inc., www.cst.com.

The forms of excitations used in Eqs. (2) and (12) are solely employed for the purpose of isolating respectively the magnetic and electric response of the nano-ring of Fig. 1 from one another, which is necessary for evaluating the polarizability coefficients separately. Once these coefficients are determined, they indeed represent the polarizability response of the material to any form of excitation (e.g., a plane wave). This approach is commonly used in the technical literature (see, e.g., [15]).

J. D. Jackson, Classical Electrodyanmics (Wiley, 1998).

C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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

Supplementary Material (1)

» Media 1: GIF (2580 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

A circular array of equi-spaced nano-spheres in the x-y plane excited by: (a) a local time-varying magnetic field directed along z; (b) a local time-varying electric field directed along y. The vectors on each particle indicate the induced electric dipole moments in the two cases.

Fig. 2.
Fig. 2.

Effective relative magnetic permeability μeff(p)/μ 0 for bulk media with the following parameters for the geometry of nano-inclusion: (a) R = 40nm, a = 16nm, N = 6, Nd = (108nm)-3; (b) R = 38nm, a = 16nm, N = 4, Nd = (95nm)-3. Following [20], in this range of frequency the permittivity of silver has been assumed to follow the Drude model with fpAg = 2175 THz, fτAg = 4.35 THz and ε = 5ε 0. The background material in this example is glass with εb = 2.2ε 0.

Fig. 3.
Fig. 3.

(2.5 MB) Movie (simulated with CST Microwave StudioTM [22]) of the time-domain electric field distribution for the nano-ring of Fig. 2(b), composed of four plasmonic nano-spheres, at f = 655THz. [Media 1]

Fig. 4.
Fig. 4.

Effective relative electric permittivity εeff(p) / ε 0 for the bulk media with the parameters of Fig. 2(a) and 2(b). The dot-lines represent the effective permittivity of another bulk medium that could be formed by embedding the same number density of silver nano-spheres as in the simulations, but in a regular periodic cubic lattice, not collected in loop arrangement.

Fig. 5.
Fig. 5.

Effective index of refraction for the material composed as in Fig. 2(b) and Fig. 4(b)

Fig. 6.
Fig. 6.

(a) Effective magnetic permeability μeff(p)/μ 0, and (b) effective electric permittivity εeff(p)/ε 0, for the following parameters: R = 22nm, a = 9.5nm, N = 4, Nd = (55nm)-3. The background material here is SiC with εb = 6.5ε 0.

Equations (14)

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r n = x ̂ [ R cos ( ( n 1 ) 2 π N ) ] + y ̂ [ R sin ( ( n 1 ) 2 π N ) ] = R r ̂ ( r n ) ,
H 0 = z ̂ n = 1 N H 0 N e i k n r , E 0 = n = 1 N E 0 n e i k n r ,
{ k n = k b r ̂ ( r n ) E 0 n = η b H 0 N φ ̂ ( r n ) ,
p n = α E loc ( r n ) = p φ ̂ ( r n ) ,
E loc ( r n ) = E 0 ( r n ) + p l n N Q ̅ ln φ ̂ ( r l ) ,
p = E 0 ( r n ) φ ̂ ( r n ) α 1 l n N Q ̅ ln φ ̂ ( r l ) φ ̂ ( r n ) .
E i N k b 3 R 8 π ε b e i k b r r p sin θ φ ̂ H i N k b 3 R 8 π ε b η b e i k b r r p sin θ θ ̂ ,
m H = iωpNR 2 z ̂ .
α m m 1 = 4 ε b N k b 2 R 2 α 1 i ( k b 3 6 π 2 k b 3 π N R 2 ) + 1 16 π N k b 2 R 5 l n N 3 + cos [ 2 π ( l n ) / N ] sin [ π ( l n ) / N ] 3 .
α = [ ( 4 π ε b a 3 ε ε b ε + 2 ε b ) 1 i k b 3 6 π ε b ] 1 .
μ eff ( r ) = μ 0 ( 1 + 1 N d 1 α m m 1 1 / 3 ) , μ eff ( p ) = μ 0 ( 1 + 1 N d 1 [ α m m 1 + i ( k b 3 / 6 π ) ] 1 / 3 ) ,
E 0 = E 0 cos ( k b x ) y ̂ H 0 = i E 0 sin ( k b x ) η b z ̂ ,
p n = α E loc = α [ E 0 ( r n ) + l n N Q ̅ ln p l ] .
ε eff ( r ) = ε 0 ( 1 + 1 ε 0 N d 1 α e e 1 1 / 3 ) , ε eff ( p ) = ε 0 ( 1 + 1 ε 0 N d 1 [ α e e 1 + i ( k 0 3 / 6 π ε 0 ) ] 1 / 3 ) .

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