Abstract

We investigate the influence of metamaterials on the scaling laws of the transmission on multilayered structures composed of random sequences of ordinary dielectric and metamaterial layers. The spectrally averaged transmission in a frequency range around the fully transparent resonant mode is shown to decay with the total number of layers as 1/N. Such thickness dependence is faster than the 1/N 1/2 decay recently reported to take place in random sequences of ordinary dielectric slabs. The interplay of strong localization and the emergence of resonant modes within the gap leads to a non-monotonous disorder dependence of the transmission that reaches a minimum at an intermediate disorder strength.

© 2008 Optical Society of America

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of permissivity and permeability," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
    [CrossRef] [PubMed]
  3. P. Kolinko and D. R. Smith, "Numerical study of electromagnetic waves interacting with negative index materials," Opt. Express 11, 640 (2003).
    [CrossRef] [PubMed]
  4. K. Guven, M. D. Caliskan, and E. Ozbay, "Experimental observation of left-handed transmission in a bilayer metamaterial under normal-to-plane propagation," Opt. Express 30, 8685 (2006).
    [CrossRef]
  5. Z. Tang, R. Peng, D. Fan, S. Wen, H. Zhang, and L. Qian, "Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal," Opt. Express 13, 9796 (2005).
    [CrossRef] [PubMed]
  6. D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 84, 4184 (2000).
    [CrossRef] [PubMed]
  7. P. Mark�?s and C. M. Soukoulis, "Transmission properties and effective electromagnetic parameters of double negative metamaterials," Opt. Express 11, 649 (2003).
    [CrossRef] [PubMed]
  8. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000)
    [CrossRef] [PubMed]
  9. J. A. Kong, B.-I. Wu, and Y. Zhang, "A unique lateral displacement of a gaussian beam transmitted through a slab with a negative permittiviy and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
    [CrossRef]
  10. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987)
    [CrossRef] [PubMed]
  11. L. Wu, S. He, and L. Shen, "Band structure for a one-dimensional photonic crystal containing left-handed materials," Phys. Rev. B 67, 235103 (2003)
    [CrossRef]
  12. J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003)
    [CrossRef] [PubMed]
  13. J. A. Monsoriu, R. A. Depine, M. L. Mart�??ınez-Ricci, and E. Silvestre, "Interaction between non-Bragg band gaps in 1D metamaterials photonic crystals," Opt. Express 14, 12958 (2006).
    [CrossRef] [PubMed]
  14. Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. Au Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220 (2006)
    [CrossRef] [PubMed]
  15. M. Ghulinyan, "Formation of optimal-order necklace modes in one-dimensional random photonic superlattices," Phys. Rev. A 76, 013822 (2007)
    [CrossRef]
  16. M. Ghulinyan, "Pediodic oscillations in transmission decay of Anderson localized one-dimensional dielectric system," Phys. Rev. Lett. 99, 063905 (2007)
    [CrossRef] [PubMed]
  17. J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, "Optical necklace states in Anderson localized 1D systems," Phys. Rev. Lett. 94, 113903 (2005)
    [CrossRef] [PubMed]
  18. E. M. Nascimento, F. A. B. F. de Moura, and M. L. Lyra, "Scaling laws for the transmission of random binary dielectric multilayered structures," Phys. Rev. B 76, 115120 (2007)
    [CrossRef]
  19. J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
    [CrossRef]
  20. M. Titov and H. Schomerus, "Nonuniversality of Anderson Localization in Short-Range Correlated Disorder," Phys. Rev. Lett. 95126602 (2005)
    [CrossRef] [PubMed]
  21. A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
    [CrossRef]

2007 (4)

M. Ghulinyan, "Formation of optimal-order necklace modes in one-dimensional random photonic superlattices," Phys. Rev. A 76, 013822 (2007)
[CrossRef]

M. Ghulinyan, "Pediodic oscillations in transmission decay of Anderson localized one-dimensional dielectric system," Phys. Rev. Lett. 99, 063905 (2007)
[CrossRef] [PubMed]

E. M. Nascimento, F. A. B. F. de Moura, and M. L. Lyra, "Scaling laws for the transmission of random binary dielectric multilayered structures," Phys. Rev. B 76, 115120 (2007)
[CrossRef]

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
[CrossRef]

2006 (4)

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
[CrossRef]

K. Guven, M. D. Caliskan, and E. Ozbay, "Experimental observation of left-handed transmission in a bilayer metamaterial under normal-to-plane propagation," Opt. Express 30, 8685 (2006).
[CrossRef]

Y. Yuan, L. Ran, J. Huangfu, H. Chen, L. Shen, and J. Au Kong, "Experimental verification of zero order bandgap in a layered stack of left-handed and right-handed materials," Opt. Express 14, 2220 (2006)
[CrossRef] [PubMed]

J. A. Monsoriu, R. A. Depine, M. L. Mart�??ınez-Ricci, and E. Silvestre, "Interaction between non-Bragg band gaps in 1D metamaterials photonic crystals," Opt. Express 14, 12958 (2006).
[CrossRef] [PubMed]

2005 (3)

Z. Tang, R. Peng, D. Fan, S. Wen, H. Zhang, and L. Qian, "Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal," Opt. Express 13, 9796 (2005).
[CrossRef] [PubMed]

M. Titov and H. Schomerus, "Nonuniversality of Anderson Localization in Short-Range Correlated Disorder," Phys. Rev. Lett. 95126602 (2005)
[CrossRef] [PubMed]

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, "Optical necklace states in Anderson localized 1D systems," Phys. Rev. Lett. 94, 113903 (2005)
[CrossRef] [PubMed]

2003 (4)

P. Kolinko and D. R. Smith, "Numerical study of electromagnetic waves interacting with negative index materials," Opt. Express 11, 640 (2003).
[CrossRef] [PubMed]

P. Mark�?s and C. M. Soukoulis, "Transmission properties and effective electromagnetic parameters of double negative metamaterials," Opt. Express 11, 649 (2003).
[CrossRef] [PubMed]

L. Wu, S. He, and L. Shen, "Band structure for a one-dimensional photonic crystal containing left-handed materials," Phys. Rev. B 67, 235103 (2003)
[CrossRef]

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003)
[CrossRef] [PubMed]

2002 (1)

J. A. Kong, B.-I. Wu, and Y. Zhang, "A unique lateral displacement of a gaussian beam transmitted through a slab with a negative permittiviy and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
[CrossRef]

2000 (2)

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

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

1996 (1)

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

1987 (1)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987)
[CrossRef] [PubMed]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of permissivity and permeability," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Andreani, L. C.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
[CrossRef]

Asatryan, A. A.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
[CrossRef]

Au Kong, J.

Bertolotti, J.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
[CrossRef]

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, "Optical necklace states in Anderson localized 1D systems," Phys. Rev. Lett. 94, 113903 (2005)
[CrossRef] [PubMed]

Botten, L. C.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
[CrossRef]

Byrne, M. A.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
[CrossRef]

Caliskan, M. D.

K. Guven, M. D. Caliskan, and E. Ozbay, "Experimental observation of left-handed transmission in a bilayer metamaterial under normal-to-plane propagation," Opt. Express 30, 8685 (2006).
[CrossRef]

Chan, C. T.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003)
[CrossRef] [PubMed]

Chen, H.

de Moura, F. A. B. F.

E. M. Nascimento, F. A. B. F. de Moura, and M. L. Lyra, "Scaling laws for the transmission of random binary dielectric multilayered structures," Phys. Rev. B 76, 115120 (2007)
[CrossRef]

Depine, R. A.

Fan, D.

Freilikher, V. D.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
[CrossRef]

Galli, M.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
[CrossRef]

Ghulinyan, M.

M. Ghulinyan, "Formation of optimal-order necklace modes in one-dimensional random photonic superlattices," Phys. Rev. A 76, 013822 (2007)
[CrossRef]

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
[CrossRef]

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, "Optical necklace states in Anderson localized 1D systems," Phys. Rev. Lett. 94, 113903 (2005)
[CrossRef] [PubMed]

Ghulinyan, Mher

M. Ghulinyan, "Pediodic oscillations in transmission decay of Anderson localized one-dimensional dielectric system," Phys. Rev. Lett. 99, 063905 (2007)
[CrossRef] [PubMed]

Gottardo, S.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
[CrossRef]

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, "Optical necklace states in Anderson localized 1D systems," Phys. Rev. Lett. 94, 113903 (2005)
[CrossRef] [PubMed]

Gredeskul, S. A.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
[CrossRef]

Guven, K.

K. Guven, M. D. Caliskan, and E. Ozbay, "Experimental observation of left-handed transmission in a bilayer metamaterial under normal-to-plane propagation," Opt. Express 30, 8685 (2006).
[CrossRef]

He, S.

L. Wu, S. He, and L. Shen, "Band structure for a one-dimensional photonic crystal containing left-handed materials," Phys. Rev. B 67, 235103 (2003)
[CrossRef]

Holden, A. J.

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

Huangfu, J.

Kivsharet, Y. S.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
[CrossRef]

Kolinko, P.

Kong, J. A.

J. A. Kong, B.-I. Wu, and Y. Zhang, "A unique lateral displacement of a gaussian beam transmitted through a slab with a negative permittiviy and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
[CrossRef]

Kroll, N.

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

Li, Jensen

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003)
[CrossRef] [PubMed]

Lyra, M. L.

E. M. Nascimento, F. A. B. F. de Moura, and M. L. Lyra, "Scaling laws for the transmission of random binary dielectric multilayered structures," Phys. Rev. B 76, 115120 (2007)
[CrossRef]

Mark??s, P.

Mart???inez-Ricci, M. L.

McPhedran, R. C.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
[CrossRef]

Monsoriu, J. A.

Nascimento, E. M.

E. M. Nascimento, F. A. B. F. de Moura, and M. L. Lyra, "Scaling laws for the transmission of random binary dielectric multilayered structures," Phys. Rev. B 76, 115120 (2007)
[CrossRef]

Ozbay, E.

K. Guven, M. D. Caliskan, and E. Ozbay, "Experimental observation of left-handed transmission in a bilayer metamaterial under normal-to-plane propagation," Opt. Express 30, 8685 (2006).
[CrossRef]

Pavesi, L.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
[CrossRef]

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, "Optical necklace states in Anderson localized 1D systems," Phys. Rev. Lett. 94, 113903 (2005)
[CrossRef] [PubMed]

Pendry, J. B.

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

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

Peng, R.

Qian, L.

Ran, L.

Sapienza, R.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
[CrossRef]

Schomerus, H.

M. Titov and H. Schomerus, "Nonuniversality of Anderson Localization in Short-Range Correlated Disorder," Phys. Rev. Lett. 95126602 (2005)
[CrossRef] [PubMed]

Shadrivov, I. V.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
[CrossRef]

Shen, L.

Sheng, P.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003)
[CrossRef] [PubMed]

Silvestre, E.

Smith, D. R.

Soukoulis, C. M.

Stewart, W. J.

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

Tang, Z.

Titov, M.

M. Titov and H. Schomerus, "Nonuniversality of Anderson Localization in Short-Range Correlated Disorder," Phys. Rev. Lett. 95126602 (2005)
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of permissivity and permeability," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Wen, S.

Wiersma, D. S.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
[CrossRef]

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, "Optical necklace states in Anderson localized 1D systems," Phys. Rev. Lett. 94, 113903 (2005)
[CrossRef] [PubMed]

Wu, B.-I.

J. A. Kong, B.-I. Wu, and Y. Zhang, "A unique lateral displacement of a gaussian beam transmitted through a slab with a negative permittiviy and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
[CrossRef]

Wu, L.

L. Wu, S. He, and L. Shen, "Band structure for a one-dimensional photonic crystal containing left-handed materials," Phys. Rev. B 67, 235103 (2003)
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987)
[CrossRef] [PubMed]

Youngs, I.

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

Yuan, Y.

Zhang, H.

Zhang, Y.

J. A. Kong, B.-I. Wu, and Y. Zhang, "A unique lateral displacement of a gaussian beam transmitted through a slab with a negative permittiviy and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
[CrossRef]

Zhou, L.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003)
[CrossRef] [PubMed]

Microwave Opt. Technol. Lett. (1)

J. A. Kong, B.-I. Wu, and Y. Zhang, "A unique lateral displacement of a gaussian beam transmitted through a slab with a negative permittiviy and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
[CrossRef]

Opt. Express (6)

Phys. Rev. A (1)

M. Ghulinyan, "Formation of optimal-order necklace modes in one-dimensional random photonic superlattices," Phys. Rev. A 76, 013822 (2007)
[CrossRef]

Phys. Rev. B (2)

E. M. Nascimento, F. A. B. F. de Moura, and M. L. Lyra, "Scaling laws for the transmission of random binary dielectric multilayered structures," Phys. Rev. B 76, 115120 (2007)
[CrossRef]

L. Wu, S. He, and L. Shen, "Band structure for a one-dimensional photonic crystal containing left-handed materials," Phys. Rev. B 67, 235103 (2003)
[CrossRef]

Phys. Rev. E (1)

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, "Wave transport in random systems: Multiple resonance character of necklace modes and their statistical behavior," Phys. Rev. E 74035602(R) (2006)
[CrossRef]

Phys. Rev. Lett. (9)

M. Titov and H. Schomerus, "Nonuniversality of Anderson Localization in Short-Range Correlated Disorder," Phys. Rev. Lett. 95126602 (2005)
[CrossRef] [PubMed]

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivsharet, "Suppression of Anderson localization in disordered metamaterials," Phys. Rev. Lett. 99193902 (2007)
[CrossRef]

D. R. Smith and N. Kroll, "Negative refractive index in left-handed materials," Phys. Rev. Lett. 84, 4184 (2000).
[CrossRef] [PubMed]

J. Li, L. Zhou, C. T. Chan, and P. Sheng, "Photonic band gap from a stack of positive and negative index materials," Phys. Rev. Lett. 90, 083901 (2003)
[CrossRef] [PubMed]

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987)
[CrossRef] [PubMed]

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

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Figures (4)

Fig. 1.
Fig. 1.

Transmission spectrum of (a) an ordinary multilayered structure (composed uniquely of ordinary dielectric layers) and (b) a mixed one (composed of metamaterial and ordinary dielectric layers) for the particular case of n a d a = 5 3 n b d b . Both cases have a similar transmission peaks pattern. Peaks with finite transmission occur whenever a multiple of the mode half-wavelength equals the optical length of just one constituent layer. At the vicinity of the fully transparent resonant modes ω 0,0 and ω 5,3, the transmission band width is much narrower for the mixed case indicating a stronger finite-size scaling of these transmission peaks.

Fig. 2.
Fig. 2.

(a) Spectral average of the transmission versus the number of layers N in a frequency range around the fully resonant mode of an ordinary structure. The transmission decays as 1/N 1/2. (b) Same as before for a structure composed of ordinary and metamaterial layers. In this case, the finite-size dependence is stronger, with the transmission decaying asymptotically as 1/N. (c) Localization length near the resonant mode ω 5,3 of a mixed structure containing N=104 layers. The quadratic divergence reproduces the same scaling law found in purely ordinary structures.

Fig. 3.
Fig. 3.

Spectral and disorder averaged transmission in the vicinity of the fully transparent mode as a function of the disorder strength q. Average was performed over 5×103 disorder configurations in structures containing 102 layers. The mixed case (M) shows a minimum transmission at a finite disorder strength. Since the structure containing a metamaterial is more sensitive to disorder than the ordinary structure, it exhibits a smaller average transmission than the purely ordinary (O) structure

Fig. 4.
Fig. 4.

Transmission spectra in the vicinity of the ω 5,3 mode for different values of the disorder strength. We considered structures with N=102 layers and averaged over 105 realizations of disorder. Figure (a) shows the spectra of ordinary structures. In this case, the transmission monotonously decreases with the disorder strength. Figure (b) shows the weak disorder region of a mixed structure, where the predominant effect is the strong Anderson localization which leads to a faster decrease of the transmission as the disorder strength is increased. In the strong disorder region (c), the transmission of a mixed structure is enhanced by increasing disorder strengths as the number of resonant necklace modes also increases.

Equations (3)

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( E 1 B 1 ) = M 2 ( E 2 B 2 ) = ( cos δ i p sin δ i p sin δ cos δ ) ( E 2 B 2 )
( E 0 B 0 ) = M 1 M 2 . . . M N ( E N B N ) = M ( E N B N )
t ( ω ) = 2 p i ( m 11 + m 12 p o ) p i + ( m 21 + m 22 p o )

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