Abstract

We study theoretically the effect of a new type of blocklike positional disorder on the effective electromagnetic properties of one-dimensional chains of resonant, high-permittivity dielectric particles, where particles are arranged into perfectly well-ordered blocks whose relative position is a random variable. This creates a finite order correlation length that mimics the situation encountered in metamaterials fabricated through self-assembled techniques, whose structures often display short-range order between near neighbors but long-range disorder, due to stacking defects. Using a spectral theory approach combined with a principal component statistical analysis, we study, in the long-wavelength regime, the evolution of the electromagnetic response when the composite filling fraction and the block size are changed. Modifications in key features of the resonant response (amplitude, width, etc.) are investigated, showing a regime transition for a filling fraction around 50%.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  2. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
    [CrossRef] [PubMed]
  3. B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
    [CrossRef] [PubMed]
  4. C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
    [CrossRef]
  5. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007).
    [CrossRef]
  6. E. Shamonina and L. Solymar, “Metamaterials: how the subject started,” Metamaterials 1, 12–18 (2007).
    [CrossRef]
  7. A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: recent advances and outlook,” Metamaterials 2, 1–17 (2008).
    [CrossRef]
  8. K. Aydin, K. Guven, N. Katsarakis, C. M. Soukoulis, and E. Ozbay, “Effect of disorder on magnetic resonance band gap of split-ring resonator structures,” Opt. Express 12, 5896–5901(2004).
    [CrossRef] [PubMed]
  9. A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Suppression of left-handed properties in disordered metamaterials,” J. Appl. Phys. 97, 113906 (2005).
    [CrossRef]
  10. X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
    [CrossRef]
  11. M. V. Gorkunov, S. A. Gredeskul, I. V. Shadrivov, and Y. S. Kivshar, “Effect of microscopic disorder on magnetic properties of metamaterials,” Phys. Rev. E 73, 056605 (2006).
    [CrossRef]
  12. D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
    [CrossRef]
  13. V. Ponsinet, A. Aradian, P. Barois, and S. Ravaine,“Self-assembly and nanochemistry techniques for the fabrication of metamaterials” in Metamaterials Handbook: Applications of Metamaterials, F.Capolino, ed. (CRC Press, 2009), Vol.  2.
  14. Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
    [CrossRef]
  15. Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
    [CrossRef] [PubMed]
  16. R. Yahiaoui, H. Němec, P. Kužel, F. Kadlec, C. Kadlec, and P. Mounaix, “Broadband dielectric terahertz metamaterials with negative permeability,” Opt. Lett. 34, 3541–3543 (2009).
    [CrossRef] [PubMed]
  17. C. Noguez and R. G. Barrera, “Disorder effects on the effective dielectric response of a linear chain of polarizable spheres,” Physica A 211, 399–410 (1994).
    [CrossRef]
  18. V. N. AstratovJ. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett. 85, 5508–5510 (2004).
    [CrossRef]
  19. V. N. Astratov and S. P. Ashili, “Percolation of light through whispering gallery modes in 3D lattices of coupled microspheres,” Opt. Express 15, 17351–17361 (2007).
    [CrossRef] [PubMed]
  20. G. S. Blaustein, M. I. Gozman, O. Samoylova, I. Ya. Polishchuk, and A. L. Burin, “Guiding optical modes in chains of dielectric particles” Opt. Express 15, 17380–17391 (2007).
    [CrossRef] [PubMed]
  21. C.-S. Deng, H. Xu, and L. Deych, “Effect of size disorder on the optical transport in chains of coupled microspherical resonators,” Opt. Express 19, 6923–6937 (2011).
    [CrossRef] [PubMed]
  22. Y. Park and D. Stroud, “Surface-plasmon dispersion relation in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
    [CrossRef]
  23. L. Lewin, “The electrical constants of a material loaded with spherical particles,” J. Inst. Electr. Eng. Part 3 94, 65–68(1947).
  24. C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antennas Propag. 51, 2596–2603 (2003).
    [CrossRef]
  25. L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
    [CrossRef]
  26. G. P. Ortiz, C. López-Bastidasa, J. A. Maytorena, and W. L. Mochán, “Bulk response of composites from finite samples,” Physica B 338, 54–57 (2003).
    [CrossRef]
  27. G. P. Ortiz and W. L. Mochán, “Scaling of light scattered from fractal aggregates at resonance,” Phys. Rev. B 67, 184204(2003).
    [CrossRef]
  28. V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70, 054202 (2004).
    [CrossRef]
  29. M. I. Stockman, K. B. Kurlayev, and T. F. George, “Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: dipolar spectral theory,” Phys. Rev. B 60, 17071–17083 (1999).
    [CrossRef]
  30. C. Noguez and R. Barrera, “Multipolar and disorder effects in the optical properties of granular composites,” Phys. Rev. B 57, 302–313 (1998).
    [CrossRef]
  31. D. J. Bergman and D. Stroud, “Theory of resonances in the electromagnetic scattering by macroscopic bodies,” Phys. Rev. Lett. 22, 3527–3539 (1980).
  32. J. Sancho-Parramón, V. Janicki, and H. Zorc, “On the dielectric function tuning of random metal–dielectric nanocomposites for metamaterial applications,” Opt. Express 18, 26915–26928(2010).
    [CrossRef]
  33. M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, “Effective magnetic properties of a composite material with circular conductive elements,” Eur. Phys. J. B 28, 263–269(2002).
    [CrossRef]
  34. J. M. Rico-García, J. M. López-Alonso, and J. Alda, “Characterization of photonic crystal microcavities with manufacture imperfections,” Opt. Express 13, 3802–3815 (2005).
    [CrossRef] [PubMed]
  35. J. M. López-Alonso, J. Alda, and E. Bernabéu, “Principal component characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
    [CrossRef] [PubMed]
  36. C. J. Behrend, J. N. Anker, and R. Kopelman, “Brownian modulated optical nanoprobes,” Appl. Phys. Lett. 84, 154–156(2004).
    [CrossRef]
  37. C. Macías-Romero, R. Lim, M. R. Foreman, and P. Török, “Synthesis of structured partially spatially coherent beams,” Opt. Lett. 36, 1638–1640 (2011).
    [CrossRef] [PubMed]
  38. D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGraw-Hill, 1990), Chap. 8.
  39. T. W. Du Bosq, J. M. Lopez-Alonso, and G. D. Boreman, “Millimeter wave imaging system for land mine detection,” Appl. Opt. 45, 5686–5692 (2006).
    [CrossRef] [PubMed]
  40. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express 19, 4815–4826 (2011).
    [CrossRef] [PubMed]
  41. M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies” Phys. Rev. B 73, 045105 (2006).
    [CrossRef]
  42. M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
    [CrossRef]
  43. V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17, 3717–3734 (2005).
    [CrossRef] [PubMed]
  44. B. Ersfeld and B. U. Felderhof, “Retardation correction to the Lorentz–Lorentz formula for the refractive index of a disordered system of polarizable point dipoles,” Phys. Rev. E 57, 1118–1126(1998).
    [CrossRef]
  45. J. Li and J. B. Pendry, “Non-local effective medium of metamaterial,” (2007) arXiv:cond-mat/0701332v1 [cond-mat.mtrl-sci].
  46. R. G. Barrera and R. Fuchs, “Theory of electron energy loss in a random systems of spheres,” Phys. Rev. B 52, 3256–3273 (1995).
    [CrossRef]

2011 (3)

2010 (2)

J. Sancho-Parramón, V. Janicki, and H. Zorc, “On the dielectric function tuning of random metal–dielectric nanocomposites for metamaterial applications,” Opt. Express 18, 26915–26928(2010).
[CrossRef]

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

2009 (2)

2008 (4)

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: recent advances and outlook,” Metamaterials 2, 1–17 (2008).
[CrossRef]

2007 (4)

2006 (5)

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[CrossRef]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

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

T. W. Du Bosq, J. M. Lopez-Alonso, and G. D. Boreman, “Millimeter wave imaging system for land mine detection,” Appl. Opt. 45, 5686–5692 (2006).
[CrossRef] [PubMed]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

2005 (5)

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17, 3717–3734 (2005).
[CrossRef] [PubMed]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Suppression of left-handed properties in disordered metamaterials,” J. Appl. Phys. 97, 113906 (2005).
[CrossRef]

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[CrossRef]

J. M. Rico-García, J. M. López-Alonso, and J. Alda, “Characterization of photonic crystal microcavities with manufacture imperfections,” Opt. Express 13, 3802–3815 (2005).
[CrossRef] [PubMed]

2004 (5)

C. J. Behrend, J. N. Anker, and R. Kopelman, “Brownian modulated optical nanoprobes,” Appl. Phys. Lett. 84, 154–156(2004).
[CrossRef]

Y. Park and D. Stroud, “Surface-plasmon dispersion relation in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70, 054202 (2004).
[CrossRef]

V. N. AstratovJ. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett. 85, 5508–5510 (2004).
[CrossRef]

K. Aydin, K. Guven, N. Katsarakis, C. M. Soukoulis, and E. Ozbay, “Effect of disorder on magnetic resonance band gap of split-ring resonator structures,” Opt. Express 12, 5896–5901(2004).
[CrossRef] [PubMed]

2003 (3)

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antennas Propag. 51, 2596–2603 (2003).
[CrossRef]

G. P. Ortiz, C. López-Bastidasa, J. A. Maytorena, and W. L. Mochán, “Bulk response of composites from finite samples,” Physica B 338, 54–57 (2003).
[CrossRef]

G. P. Ortiz and W. L. Mochán, “Scaling of light scattered from fractal aggregates at resonance,” Phys. Rev. B 67, 184204(2003).
[CrossRef]

2002 (2)

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, “Effective magnetic properties of a composite material with circular conductive elements,” Eur. Phys. J. B 28, 263–269(2002).
[CrossRef]

J. M. López-Alonso, J. Alda, and E. Bernabéu, “Principal component characterization of noise for infrared images,” Appl. Opt. 41, 320–331 (2002).
[CrossRef] [PubMed]

2000 (1)

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

1999 (1)

M. I. Stockman, K. B. Kurlayev, and T. F. George, “Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: dipolar spectral theory,” Phys. Rev. B 60, 17071–17083 (1999).
[CrossRef]

1998 (2)

C. Noguez and R. Barrera, “Multipolar and disorder effects in the optical properties of granular composites,” Phys. Rev. B 57, 302–313 (1998).
[CrossRef]

B. Ersfeld and B. U. Felderhof, “Retardation correction to the Lorentz–Lorentz formula for the refractive index of a disordered system of polarizable point dipoles,” Phys. Rev. E 57, 1118–1126(1998).
[CrossRef]

1995 (1)

R. G. Barrera and R. Fuchs, “Theory of electron energy loss in a random systems of spheres,” Phys. Rev. B 52, 3256–3273 (1995).
[CrossRef]

1994 (1)

C. Noguez and R. G. Barrera, “Disorder effects on the effective dielectric response of a linear chain of polarizable spheres,” Physica A 211, 399–410 (1994).
[CrossRef]

1980 (1)

D. J. Bergman and D. Stroud, “Theory of resonances in the electromagnetic scattering by macroscopic bodies,” Phys. Rev. Lett. 22, 3527–3539 (1980).

1947 (1)

L. Lewin, “The electrical constants of a material loaded with spherical particles,” J. Inst. Electr. Eng. Part 3 94, 65–68(1947).

Aitchison, J. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

Aizpurua, J.

Alda, J.

Alu, A.

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Anker, J. N.

C. J. Behrend, J. N. Anker, and R. Kopelman, “Brownian modulated optical nanoprobes,” Appl. Phys. Lett. 84, 154–156(2004).
[CrossRef]

Aradian, A.

V. Ponsinet, A. Aradian, P. Barois, and S. Ravaine,“Self-assembly and nanochemistry techniques for the fabrication of metamaterials” in Metamaterials Handbook: Applications of Metamaterials, F.Capolino, ed. (CRC Press, 2009), Vol.  2.

Ashili, S. P.

V. N. Astratov and S. P. Ashili, “Percolation of light through whispering gallery modes in 3D lattices of coupled microspheres,” Opt. Express 15, 17351–17361 (2007).
[CrossRef] [PubMed]

V. N. AstratovJ. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett. 85, 5508–5510 (2004).
[CrossRef]

Astratov, V. N.

V. N. Astratov and S. P. Ashili, “Percolation of light through whispering gallery modes in 3D lattices of coupled microspheres,” Opt. Express 15, 17351–17361 (2007).
[CrossRef] [PubMed]

V. N. AstratovJ. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett. 85, 5508–5510 (2004).
[CrossRef]

Aydin, K.

Baker-Jarvis, J.

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antennas Propag. 51, 2596–2603 (2003).
[CrossRef]

Barois, P.

V. Ponsinet, A. Aradian, P. Barois, and S. Ravaine,“Self-assembly and nanochemistry techniques for the fabrication of metamaterials” in Metamaterials Handbook: Applications of Metamaterials, F.Capolino, ed. (CRC Press, 2009), Vol.  2.

Barrera, R.

C. Noguez and R. Barrera, “Multipolar and disorder effects in the optical properties of granular composites,” Phys. Rev. B 57, 302–313 (1998).
[CrossRef]

Barrera, R. G.

R. G. Barrera and R. Fuchs, “Theory of electron energy loss in a random systems of spheres,” Phys. Rev. B 52, 3256–3273 (1995).
[CrossRef]

C. Noguez and R. G. Barrera, “Disorder effects on the effective dielectric response of a linear chain of polarizable spheres,” Physica A 211, 399–410 (1994).
[CrossRef]

Behrend, C. J.

C. J. Behrend, J. N. Anker, and R. Kopelman, “Brownian modulated optical nanoprobes,” Appl. Phys. Lett. 84, 154–156(2004).
[CrossRef]

Bergman, D. J.

D. J. Bergman and D. Stroud, “Theory of resonances in the electromagnetic scattering by macroscopic bodies,” Phys. Rev. Lett. 22, 3527–3539 (1980).

Bernabéu, E.

Blaustein, G. S.

Boltasseva, A.

A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: recent advances and outlook,” Metamaterials 2, 1–17 (2008).
[CrossRef]

Boreman, G. D.

Burin, A. L.

Chantada, L.

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Deng, C.-S.

Deych, L.

Du, B.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Du Bosq, T. W.

Economou, E. N.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

Edwards, B.

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Engheta, N.

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Ersfeld, B.

B. Ersfeld and B. U. Felderhof, “Retardation correction to the Lorentz–Lorentz formula for the refractive index of a disordered system of polarizable point dipoles,” Phys. Rev. E 57, 1118–1126(1998).
[CrossRef]

Felderhof, B. U.

B. Ersfeld and B. U. Felderhof, “Retardation correction to the Lorentz–Lorentz formula for the refractive index of a disordered system of polarizable point dipoles,” Phys. Rev. E 57, 1118–1126(1998).
[CrossRef]

Foreman, M. R.

Franchak, J. P.

V. N. AstratovJ. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett. 85, 5508–5510 (2004).
[CrossRef]

Froufe-Pérez, L. S.

Fu, Q. H.

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[CrossRef]

Fuchs, R.

R. G. Barrera and R. Fuchs, “Theory of electron energy loss in a random systems of spheres,” Phys. Rev. B 52, 3256–3273 (1995).
[CrossRef]

García-Etxarri, A.

George, T. F.

M. I. Stockman, K. B. Kurlayev, and T. F. George, “Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: dipolar spectral theory,” Phys. Rev. B 60, 17071–17083 (1999).
[CrossRef]

Gerasimov, V. S.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70, 054202 (2004).
[CrossRef]

Gómez-Medina, R.

Gorkunov, M.

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, “Effective magnetic properties of a composite material with circular conductive elements,” Eur. Phys. J. B 28, 263–269(2002).
[CrossRef]

Gorkunov, M. V.

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

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

Gozman, M. I.

Gredeskul, S. A.

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

Guven, K.

Holloway, C. L.

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antennas Propag. 51, 2596–2603 (2003).
[CrossRef]

Huang, X.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Isaev, I. L.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70, 054202 (2004).
[CrossRef]

Janicki, V.

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Jylhä, L.

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[CrossRef]

Kabos, P.

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antennas Propag. 51, 2596–2603 (2003).
[CrossRef]

Kadlec, C.

Kadlec, F.

Kafesaki, M.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

Kang, L.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[CrossRef]

Karpov, S. V.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70, 054202 (2004).
[CrossRef]

Katsarakis, N.

Kivshar, Y. S.

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

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

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Suppression of left-handed properties in disordered metamaterials,” J. Appl. Phys. 97, 113906 (2005).
[CrossRef]

Kolmakov, I.

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[CrossRef]

Kopelman, R.

C. J. Behrend, J. N. Anker, and R. Kopelman, “Brownian modulated optical nanoprobes,” Appl. Phys. Lett. 84, 154–156(2004).
[CrossRef]

Koschny, T.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

Kuester, E. F.

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antennas Propag. 51, 2596–2603 (2003).
[CrossRef]

Kurlayev, K. B.

M. I. Stockman, K. B. Kurlayev, and T. F. George, “Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: dipolar spectral theory,” Phys. Rev. B 60, 17071–17083 (1999).
[CrossRef]

Kužel, P.

Lapine, M.

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, “Effective magnetic properties of a composite material with circular conductive elements,” Eur. Phys. J. B 28, 263–269(2002).
[CrossRef]

Lewin, L.

L. Lewin, “The electrical constants of a material loaded with spherical particles,” J. Inst. Electr. Eng. Part 3 94, 65–68(1947).

Li, B.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Li, J.

J. Li and J. B. Pendry, “Non-local effective medium of metamaterial,” (2007) arXiv:cond-mat/0701332v1 [cond-mat.mtrl-sci].

Li, L.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Lim, R.

Lippens, D.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
[CrossRef]

López, C.

Lopez-Alonso, J. M.

López-Alonso, J. M.

López-Bastidasa, C.

G. P. Ortiz, C. López-Bastidasa, J. A. Maytorena, and W. L. Mochán, “Bulk response of composites from finite samples,” Physica B 338, 54–57 (2003).
[CrossRef]

Macías-Romero, C.

Markel, V. A.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70, 054202 (2004).
[CrossRef]

Maslovski, S.

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[CrossRef]

Maytorena, J. A.

G. P. Ortiz, C. López-Bastidasa, J. A. Maytorena, and W. L. Mochán, “Bulk response of composites from finite samples,” Physica B 338, 54–57 (2003).
[CrossRef]

Mochán, W. L.

G. P. Ortiz, C. López-Bastidasa, J. A. Maytorena, and W. L. Mochán, “Bulk response of composites from finite samples,” Physica B 338, 54–57 (2003).
[CrossRef]

G. P. Ortiz and W. L. Mochán, “Scaling of light scattered from fractal aggregates at resonance,” Phys. Rev. B 67, 184204(2003).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Mojahedi, M.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

Moroz, A.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17, 3717–3734 (2005).
[CrossRef] [PubMed]

Morrison, D. F.

D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGraw-Hill, 1990), Chap. 8.

Mounaix, P.

Nemec, H.

Nieto-Vesperinas, M.

Noguez, C.

C. Noguez and R. Barrera, “Multipolar and disorder effects in the optical properties of granular composites,” Phys. Rev. B 57, 302–313 (1998).
[CrossRef]

C. Noguez and R. G. Barrera, “Disorder effects on the effective dielectric response of a linear chain of polarizable spheres,” Physica A 211, 399–410 (1994).
[CrossRef]

Obuschenko, A. V.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70, 054202 (2004).
[CrossRef]

Ortiz, G. P.

G. P. Ortiz and W. L. Mochán, “Scaling of light scattered from fractal aggregates at resonance,” Phys. Rev. B 67, 184204(2003).
[CrossRef]

G. P. Ortiz, C. López-Bastidasa, J. A. Maytorena, and W. L. Mochán, “Bulk response of composites from finite samples,” Physica B 338, 54–57 (2003).
[CrossRef]

Ozbay, E.

Park, Y.

Y. Park and D. Stroud, “Surface-plasmon dispersion relation in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

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

J. Li and J. B. Pendry, “Non-local effective medium of metamaterial,” (2007) arXiv:cond-mat/0701332v1 [cond-mat.mtrl-sci].

Polishchuk, I. Ya.

Ponsinet, V.

V. Ponsinet, A. Aradian, P. Barois, and S. Ravaine,“Self-assembly and nanochemistry techniques for the fabrication of metamaterials” in Metamaterials Handbook: Applications of Metamaterials, F.Capolino, ed. (CRC Press, 2009), Vol.  2.

Powell, D. A.

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

Pustovit, V. N.

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70, 054202 (2004).
[CrossRef]

Ravaine, S.

V. Ponsinet, A. Aradian, P. Barois, and S. Ravaine,“Self-assembly and nanochemistry techniques for the fabrication of metamaterials” in Metamaterials Handbook: Applications of Metamaterials, F.Capolino, ed. (CRC Press, 2009), Vol.  2.

Rico-García, J. M.

Ringhofer, K. H.

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, “Effective magnetic properties of a composite material with circular conductive elements,” Eur. Phys. J. B 28, 263–269(2002).
[CrossRef]

Sáenz, J. J.

Samoylova, O.

Sancho-Parramón, J.

Scheffold, F.

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Shadrivov, I. V.

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

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

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Suppression of left-handed properties in disordered metamaterials,” J. Appl. Phys. 97, 113906 (2005).
[CrossRef]

Shalaev, V. M.

A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: recent advances and outlook,” Metamaterials 2, 1–17 (2008).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007).
[CrossRef]

Shamonina, E.

E. Shamonina and L. Solymar, “Metamaterials: how the subject started,” Metamaterials 1, 12–18 (2007).
[CrossRef]

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, “Effective magnetic properties of a composite material with circular conductive elements,” Eur. Phys. J. B 28, 263–269(2002).
[CrossRef]

Silveirinha, M.

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Solymar, L.

E. Shamonina and L. Solymar, “Metamaterials: how the subject started,” Metamaterials 1, 12–18 (2007).
[CrossRef]

Song, J.

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

K. Aydin, K. Guven, N. Katsarakis, C. M. Soukoulis, and E. Ozbay, “Effect of disorder on magnetic resonance band gap of split-ring resonator structures,” Opt. Express 12, 5896–5901(2004).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Stockman, M. I.

M. I. Stockman, K. B. Kurlayev, and T. F. George, “Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: dipolar spectral theory,” Phys. Rev. B 60, 17071–17083 (1999).
[CrossRef]

Stroud, D.

Y. Park and D. Stroud, “Surface-plasmon dispersion relation in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

D. J. Bergman and D. Stroud, “Theory of resonances in the electromagnetic scattering by macroscopic bodies,” Phys. Rev. Lett. 22, 3527–3539 (1980).

Török, P.

Tretyakov, S.

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[CrossRef]

Wheeler, M. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

Xie, Q.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Xu, H.

Yahiaoui, R.

Yannopapas, V.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17, 3717–3734 (2005).
[CrossRef] [PubMed]

Young, M. E.

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Zhang, F.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
[CrossRef]

Zhao, H.

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Zhao, Q.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
[CrossRef]

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[CrossRef]

Zhao, X. P.

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[CrossRef]

Zharov, A. A.

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Suppression of left-handed properties in disordered metamaterials,” J. Appl. Phys. 97, 113906 (2005).
[CrossRef]

Zhou, J.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
[CrossRef]

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

Zorc, H.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

C. J. Behrend, J. N. Anker, and R. Kopelman, “Brownian modulated optical nanoprobes,” Appl. Phys. Lett. 84, 154–156(2004).
[CrossRef]

V. N. AstratovJ. P. Franchak, and S. P. Ashili, “Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder,” Appl. Phys. Lett. 85, 5508–5510 (2004).
[CrossRef]

Eur. Phys. J. B (1)

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, “Effective magnetic properties of a composite material with circular conductive elements,” Eur. Phys. J. B 28, 263–269(2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antennas Propag. 51, 2596–2603 (2003).
[CrossRef]

J. Appl. Phys. (2)

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Suppression of left-handed properties in disordered metamaterials,” J. Appl. Phys. 97, 113906 (2005).
[CrossRef]

J. Inst. Electr. Eng. Part 3 (1)

L. Lewin, “The electrical constants of a material loaded with spherical particles,” J. Inst. Electr. Eng. Part 3 94, 65–68(1947).

J. Phys. Condens. Matter (2)

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17, 3717–3734 (2005).
[CrossRef] [PubMed]

Mater. Today (1)

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12, 60–69 (2009).
[CrossRef]

Metamaterials (2)

E. Shamonina and L. Solymar, “Metamaterials: how the subject started,” Metamaterials 1, 12–18 (2007).
[CrossRef]

A. Boltasseva and V. M. Shalaev, “Fabrication of optical negative-index metamaterials: recent advances and outlook,” Metamaterials 2, 1–17 (2008).
[CrossRef]

Nat. Photon. (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1, 41–48 (2007).
[CrossRef]

Opt. Express (7)

Opt. Lett. (2)

Phys. Lett. A (1)

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[CrossRef]

Phys. Rev. B (9)

Y. Park and D. Stroud, “Surface-plasmon dispersion relation in chains of metallic nanoparticles: an exact quasistatic calculation,” Phys. Rev. B 69, 125418 (2004).
[CrossRef]

D. A. Powell, M. Lapine, M. V. Gorkunov, I. V. Shadrivov, and Y. S. Kivshar, “Metamaterial tuning by manipulation of near-field interaction,” Phys. Rev. B 82, 155128 (2010).
[CrossRef]

G. P. Ortiz and W. L. Mochán, “Scaling of light scattered from fractal aggregates at resonance,” Phys. Rev. B 67, 184204(2003).
[CrossRef]

V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70, 054202 (2004).
[CrossRef]

M. I. Stockman, K. B. Kurlayev, and T. F. George, “Linear and nonlinear optical susceptibilities of Maxwell Garnett composites: dipolar spectral theory,” Phys. Rev. B 60, 17071–17083 (1999).
[CrossRef]

C. Noguez and R. Barrera, “Multipolar and disorder effects in the optical properties of granular composites,” Phys. Rev. B 57, 302–313 (1998).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[CrossRef]

R. G. Barrera and R. Fuchs, “Theory of electron energy loss in a random systems of spheres,” Phys. Rev. B 52, 3256–3273 (1995).
[CrossRef]

Phys. Rev. E (2)

B. Ersfeld and B. U. Felderhof, “Retardation correction to the Lorentz–Lorentz formula for the refractive index of a disordered system of polarizable point dipoles,” Phys. Rev. E 57, 1118–1126(1998).
[CrossRef]

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

Phys. Rev. Lett. (4)

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

Q. Zhao, L. Kang, B. Du, H. Zhao, Q. Xie, X. Huang, B. Li, J. Zhou, and L. Li, “Experimental demonstration of isotropic negative permeability in a three-dimensional dielectric composite,” Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

D. J. Bergman and D. Stroud, “Theory of resonances in the electromagnetic scattering by macroscopic bodies,” Phys. Rev. Lett. 22, 3527–3539 (1980).

B. Edwards, A. Alu, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef] [PubMed]

Physica A (1)

C. Noguez and R. G. Barrera, “Disorder effects on the effective dielectric response of a linear chain of polarizable spheres,” Physica A 211, 399–410 (1994).
[CrossRef]

Physica B (1)

G. P. Ortiz, C. López-Bastidasa, J. A. Maytorena, and W. L. Mochán, “Bulk response of composites from finite samples,” Physica B 338, 54–57 (2003).
[CrossRef]

Science (1)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Other (3)

V. Ponsinet, A. Aradian, P. Barois, and S. Ravaine,“Self-assembly and nanochemistry techniques for the fabrication of metamaterials” in Metamaterials Handbook: Applications of Metamaterials, F.Capolino, ed. (CRC Press, 2009), Vol.  2.

D. F. Morrison, Multivariate Statistical Methods, 3rd ed. (McGraw-Hill, 1990), Chap. 8.

J. Li and J. B. Pendry, “Non-local effective medium of metamaterial,” (2007) arXiv:cond-mat/0701332v1 [cond-mat.mtrl-sci].

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Toy model under study. Mie-resonant particles are placed in the chain into ordered blocks. The interparticle distance inside a well-ordered block of particles, d, is fixed. The number of particles per block, p, rules the amount of order in the chain, since it is proportional to the chain correlation length, as is explained in the text. In the picture, p = 3 . X is a random variable representing the distance between ordered blocks in the chain.

Fig. 2
Fig. 2

Eigenvalues of the covariance matrix of the couplings for dimers at Φ = 0.5 . We indicate both the percentage of the variance carried by each one of them and the statistical uncertainty in their values.

Fig. 3
Fig. 3

Reconstruction of the couplings ensemble for dimers at Φ = 0.5 . We show the mean values of the reconstructed data with the three processes mentioned in Fig. 2. At the bottom, we show an enlarged picture of the reconstruction with process 2 and process 3, far less important than process 1.

Fig. 4
Fig. 4

Eigenvalues of the covariance matrix of the ensemble of the MFT of the chain modes for dimers at Φ = 0.5 There are three processes. Only processes P1 and P2 are significant because the third one can be considered noise, as explained in the text. The eigenvalues are displayed with their statistical uncertainty.

Fig. 5
Fig. 5

Mean and STD values of the MFT ensemble. Compare this figure with the computations shown in Fig. 6.

Fig. 6
Fig. 6

(Top) Reconstructed ensemble of the MFT with the process P1. (Middle) Reconstructed ensemble of the MFT with the process P2. (Bottom) Reconstructed ensemble of the MFT with the process P3. We show both the mean and the STD computed from the reconstructed ensembles by each process. Compare with Fig. 5.

Fig. 7
Fig. 7

(a) Susceptibility ensemble reconstructed with the first process. (b) Susceptibility ensemble reconstructed with the second processes in the data set. Adding (a) and (b), we recover the whole ensemble in (c). We show some samples retrieved in this way.

Fig. 8
Fig. 8

We show here for the sake of comparison the ordered absorption peak (black) at Φ = 0.5 with the dimer (red) at the same filling fraction. The asymmetry, as noted in the text, comes from the influence of the second process. Some samples retrieved only with the latter are shown. An important remark should be taken into account here: the samples reconstructed with the second process have nothing to do with real part of the susceptibility since they are the deviations from the mean absorption curve given by the first process. They must be added to the samples reconstructed with the first process to get the original samples in the ensemble of susceptibilities.

Fig. 9
Fig. 9

Histograms of resonant frequencies for dimers at different filling fractions. (Left) Dimer histograms for Φ = 0.1 , Φ = 0.5 , and Φ = 0.9 . (Right) Decamer histograms for Φ = 0.1 , Φ = 0.5 ,and Φ = 0.9 . The filling fraction increases from top to bottom in the figure.

Fig. 10
Fig. 10

Reconstruction of the coupling data of (left) dimers and (right) decamers at Φ = 0.1 , Φ = 0.5 , and Φ = 0.9 with the first PCA.

Fig. 11
Fig. 11

Reconstruction of the external susceptibility with the first principal component for Φ = 0.1 , 0.5 , 0.9 . Dotted lines correspond to decamer chains. Continuous lines refer to dimer chains. For the sake of comparison, we show below the same quantities for the ordered structure.

Fig. 12
Fig. 12

First PCA of the MFT for (left) dimers and (right) decamers. (Top)  Φ = 0.1 , (center)  Φ = 0.5 , and (bottom)  Φ = 0.9 . The order in the composite (chain) increases from top to bottom. The coupled modes are those with a low k value in the pictures.

Fig. 13
Fig. 13

(Top) Resonant frequency, (middle) resonant width, and (center) maximum of the absorption peak in terms of Φ and p. We consider a set of ensembles going from very disordered blocks to highly ordered blocks. Trends observed therein are explained in the text.

Fig. 14
Fig. 14

Uncertainty in the peak position. The trends showed here are explained in the text.

Equations (15)

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

m i = α m { H 0 + j T i j m j } ,
T i j = 1 4 π ( 1 δ i j ) · 3 x i j x i j x i j 2 I x i j 5 .
| m = α m { | H 0 + T | m } .
α m ( ω ) = 4 π a 3 F ( ω ) 1 F ( ω ) + 2 ,
u ( ω ) = 1 1 F ( ω ) ,
α m = 4 π a 3 ( 1 3 u ) 1 .
| m = 4 π a 3 [ ( 1 3 u ) I Dielectric Properties 4 π a 3 T Geometry ] 1 R ( u ; a ) | H 0 .
H 0 | m = V H 0 M = V χ 0 m H 0 2 ,
χ 0 m = 4 π a 3 V H 0 | R ( u ; a ) | H 0 H 0 2 = 2 Φ 0 | R ( u ; a ) | 0 ,
χ 0 m = 2 3 Φ n C n u s n ,
P C k = m = 1 N e k ( m ) E m .
E m = k = 1 N e k ( m ) P C k .
| H 0 = H 0 N | 0 .
F ( ω ) = 2 sin θ ( ω ) θ ( ω ) cos θ ( ω ) [ θ ( ω ) 2 1 ] sin θ ( ω ) + θ ( ω ) cos θ ( ω ) ,
θ ( ω ) = 2 π λ a ϵ ( ω ) .

Metrics