Abstract

Electromagnetic wave propagation in one-dimensional disordered structures composed of hyperbolic metamaterials is theoretically investigated. We find that the disordered system can suppress Anderson localization of light at long-wavelength limit under a finite range of incident angle. For isolated frequencies and for specific angles of incidence, it only occurs at areas of Brewster anomaly. Within the zero-n¯ gap, structural disorder has little impact on the localization length. In contrast, the localization length increases with the increase of the degree of disorder in the Bragg gap, giving rise to enhanced transmission of light. At the vicinities of Bragg gap edge, the localization is suppressed (enhanced) evidently outside (inside) the gap. We also find that the increase of disorder or incidence angle can result in an increase of strength and range of resonances. The role of absorption in our disordered system is also discussed.

© 2012 Optical Society of America

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2011 (2)

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B. 84, 094204(2011).
[CrossRef]

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattices,” Phys. Rev. E. 84, 036604 (2011).
[CrossRef]

2010 (4)

S. F. Liew and H. Cao, “Optical properties of 1D photonic crystals with correlated and uncorrelated disorder,” J. Opt. 12, 024011 (2010).
[CrossRef]

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

A. A. Asatryan, S. A. Gredeskul, L. C. Botten, M. A. Byrne, V. D. Freilikher, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Anderson localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B. 81, 075124 (2010).
[CrossRef]

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B. 82, 081105(R) (2010).
[CrossRef]

2009 (2)

F. M. Izrailev and N. M. Makarov, “Localization in correlated bilayer structures: from photonic crystals to metamaterials and semiconductor superlattices,” Phys. Rev. Lett. 102, 203901 (2009).
[CrossRef]

Y. Sivan, S. Xiao, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Frequency-domain simulations of a negative-index material with embedded gain,” Opt. Express 17, 24060–24074 (2009).
[CrossRef]

2008 (3)

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

K. Yu. Bliokh, Yu. P. Bliokh, V. Freilikher, S. Savelïev, and F. Nori, “Colloquium: unusual resonators: plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201–1203(2008).
[CrossRef]

2007 (3)

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007).
[CrossRef]

Y. J. Xiang, X. Y. Dai, S. C. Wen, and D. Y. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107(2007).
[CrossRef]

Y. J. Xiang, X. Y. Dai, and S. C. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[CrossRef]

2006 (3)

2005 (2)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
[CrossRef]

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102 (2005).
[CrossRef]

2004 (2)

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84, 2244–2246 (2004).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, “Omindirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B. 70, 245102 (2004).
[CrossRef]

2003 (5)

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]

R. Marqués, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments,” IEEE Trans. Antennas Propag. 51, 2572–2581 (2003).
[CrossRef]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

S. A. Ramakrishna and J. B. Pendry, “Optical gain removes absorption and increases resolution in a near-field lens,” Phys. Rev. B. 67, 201101 (2003).
[CrossRef]

D. Schurig and D. R. Smith, “Spatial filtering using media with indefinite permittivity and permeability tensors,” Appl. Phys. Lett. 82, 2215–2217 (2003).
[CrossRef]

2002 (1)

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B. 65, 144440 (2002).
[CrossRef]

2001 (1)

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

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

1999 (2)

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

H. Q. Li, G. C. Gu, and H. Chen, “Disordered dielectric high reflectors with broadband from visible to infrared,” Appl. Phys. Lett. 74, 3260–3262 (1999).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

1988 (1)

J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Asatryan, A. A.

A. A. Asatryan, S. A. Gredeskul, L. C. Botten, M. A. Byrne, V. D. Freilikher, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Anderson localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B. 81, 075124 (2010).
[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. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007).
[CrossRef]

Bliokh, K. Yu.

K. Yu. Bliokh, Yu. P. Bliokh, V. Freilikher, S. Savelïev, and F. Nori, “Colloquium: unusual resonators: plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201–1203(2008).
[CrossRef]

Bliokh, Yu. P.

K. Yu. Bliokh, Yu. P. Bliokh, V. Freilikher, S. Savelïev, and F. Nori, “Colloquium: unusual resonators: plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201–1203(2008).
[CrossRef]

Botten, L. C.

A. A. Asatryan, S. A. Gredeskul, L. C. Botten, M. A. Byrne, V. D. Freilikher, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Anderson localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B. 81, 075124 (2010).
[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. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007).
[CrossRef]

Bruno-Alfonso, A.

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattices,” Phys. Rev. E. 84, 036604 (2011).
[CrossRef]

Byrne, M. A.

A. A. Asatryan, S. A. Gredeskul, L. C. Botten, M. A. Byrne, V. D. Freilikher, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Anderson localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B. 81, 075124 (2010).
[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. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007).
[CrossRef]

Cao, H.

S. F. Liew and H. Cao, “Optical properties of 1D photonic crystals with correlated and uncorrelated disorder,” J. Opt. 12, 024011 (2010).
[CrossRef]

Cavalcanti, S. B.

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattices,” Phys. Rev. E. 84, 036604 (2011).
[CrossRef]

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B. 84, 094204(2011).
[CrossRef]

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B. 82, 081105(R) (2010).
[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]

Chen, H.

L. G. Wang, H. Chen, and S. Y. Zhu, “Omindirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B. 70, 245102 (2004).
[CrossRef]

H. Q. Li, G. C. Gu, and H. Chen, “Disordered dielectric high reflectors with broadband from visible to infrared,” Appl. Phys. Lett. 74, 3260–3262 (1999).
[CrossRef]

Cheng, Q.

Chettiar, U. K.

Cohen, M. H.

J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988).
[CrossRef]

Cui, T. J.

Dai, X. Y.

Y. J. Xiang, X. Y. Dai, and S. C. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[CrossRef]

Y. J. Xiang, X. Y. Dai, S. C. Wen, and D. Y. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107(2007).
[CrossRef]

dos Santos, R. R.

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B. 84, 094204(2011).
[CrossRef]

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B. 82, 081105(R) (2010).
[CrossRef]

Fan, D. Y.

Y. J. Xiang, X. Y. Dai, S. C. Wen, and D. Y. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107(2007).
[CrossRef]

Fang, A.

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

Fedotov, V. A.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Freilikher, V.

K. Yu. Bliokh, Yu. P. Bliokh, V. Freilikher, S. Savelïev, and F. Nori, “Colloquium: unusual resonators: plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201–1203(2008).
[CrossRef]

Freilikher, V. D.

A. A. Asatryan, S. A. Gredeskul, L. C. Botten, M. A. Byrne, V. D. Freilikher, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Anderson localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B. 81, 075124 (2010).
[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. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007).
[CrossRef]

Gredeskul, S. A.

A. A. Asatryan, S. A. Gredeskul, L. C. Botten, M. A. Byrne, V. D. Freilikher, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Anderson localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B. 81, 075124 (2010).
[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. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007).
[CrossRef]

Gu, G. C.

H. Q. Li, G. C. Gu, and H. Chen, “Disordered dielectric high reflectors with broadband from visible to infrared,” Appl. Phys. Lett. 74, 3260–3262 (1999).
[CrossRef]

Holden, A. J.

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

Izrailev, F. M.

F. M. Izrailev and N. M. Makarov, “Localization in correlated bilayer structures: from photonic crystals to metamaterials and semiconductor superlattices,” Phys. Rev. Lett. 102, 203901 (2009).
[CrossRef]

Kildishev, A. V.

Kitano, M.

Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, “Observation of Brewster’s effect for transverse-electric electromagnetic waves in metamaterials: experiment and theory,” Phys. Rev. B. 73, 193104 (2006).
[CrossRef]

Kivshar, Y. S.

A. A. Asatryan, S. A. Gredeskul, L. C. Botten, M. A. Byrne, V. D. Freilikher, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Anderson localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B. 81, 075124 (2010).
[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. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
[CrossRef]

Koenderink, A. F.

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102 (2005).
[CrossRef]

Kolinko, P.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84, 2244–2246 (2004).
[CrossRef]

Koschny, T.

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

Lagendijk, A.

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102 (2005).
[CrossRef]

Li, H. Q.

H. Q. Li, G. C. Gu, and H. Chen, “Disordered dielectric high reflectors with broadband from visible to infrared,” Appl. Phys. Lett. 74, 3260–3262 (1999).
[CrossRef]

Li, J.

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]

Liew, S. F.

S. F. Liew and H. Cao, “Optical properties of 1D photonic crystals with correlated and uncorrelated disorder,” J. Opt. 12, 024011 (2010).
[CrossRef]

Makarov, N. M.

F. M. Izrailev and N. M. Makarov, “Localization in correlated bilayer structures: from photonic crystals to metamaterials and semiconductor superlattices,” Phys. Rev. Lett. 102, 203901 (2009).
[CrossRef]

Marqués, R.

R. Marqués, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments,” IEEE Trans. Antennas Propag. 51, 2572–2581 (2003).
[CrossRef]

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B. 65, 144440 (2002).
[CrossRef]

Martel, J.

R. Marqués, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments,” IEEE Trans. Antennas Propag. 51, 2572–2581 (2003).
[CrossRef]

Mayy, M.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

McPhedran, R. C.

A. A. Asatryan, S. A. Gredeskul, L. C. Botten, M. A. Byrne, V. D. Freilikher, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Anderson localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B. 81, 075124 (2010).
[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. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007).
[CrossRef]

Medina, F.

R. Marqués, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments,” IEEE Trans. Antennas Propag. 51, 2572–2581 (2003).
[CrossRef]

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B. 65, 144440 (2002).
[CrossRef]

Mesa, F.

R. Marqués, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments,” IEEE Trans. Antennas Propag. 51, 2572–2581 (2003).
[CrossRef]

Mock, J. J.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84, 2244–2246 (2004).
[CrossRef]

Mogilevtsev, D.

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B. 84, 094204(2011).
[CrossRef]

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B. 82, 081105(R) (2010).
[CrossRef]

Nakanishi, T.

Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, “Observation of Brewster’s effect for transverse-electric electromagnetic waves in metamaterials: experiment and theory,” Phys. Rev. B. 73, 193104 (2006).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Noginov, M. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Noginova, N.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Nori, F.

K. Yu. Bliokh, Yu. P. Bliokh, V. Freilikher, S. Savelïev, and F. Nori, “Colloquium: unusual resonators: plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201–1203(2008).
[CrossRef]

Oliveira, L. E.

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B. 84, 094204(2011).
[CrossRef]

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattices,” Phys. Rev. E. 84, 036604 (2011).
[CrossRef]

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B. 82, 081105(R) (2010).
[CrossRef]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Papasimakis, N.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Pendry, J. B.

S. A. Ramakrishna and J. B. Pendry, “Optical gain removes absorption and increases resolution in a near-field lens,” Phys. Rev. B. 67, 201101 (2003).
[CrossRef]

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

Pinheiro, F. A.

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B. 84, 094204(2011).
[CrossRef]

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B. 82, 081105(R) (2010).
[CrossRef]

Podolskiy, V. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Popov, A. K.

Prosvirnin, S. L.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Rafii-El-Idrissi, R.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B. 65, 144440 (2002).
[CrossRef]

Ramakrishna, S. A.

S. A. Ramakrishna and J. B. Pendry, “Optical gain removes absorption and increases resolution in a near-field lens,” Phys. Rev. B. 67, 201101 (2003).
[CrossRef]

Reyes-Gómez, E.

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattices,” Phys. Rev. E. 84, 036604 (2011).
[CrossRef]

Ritzo, B. A.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Robbins, D. J.

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

Rye, P.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84, 2244–2246 (2004).
[CrossRef]

Savelïev, S.

K. Yu. Bliokh, Yu. P. Bliokh, V. Freilikher, S. Savelïev, and F. Nori, “Colloquium: unusual resonators: plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201–1203(2008).
[CrossRef]

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]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Schurig, D.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84, 2244–2246 (2004).
[CrossRef]

D. Schurig and D. R. Smith, “Spatial filtering using media with indefinite permittivity and permeability tensors,” Appl. Phys. Lett. 82, 2215–2217 (2003).
[CrossRef]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Shadrivov, I. V.

A. A. Asatryan, S. A. Gredeskul, L. C. Botten, M. A. Byrne, V. D. Freilikher, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Anderson localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B. 81, 075124 (2010).
[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. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
[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]

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]

J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988).
[CrossRef]

P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Springer, 1995).

Sipe, J. E.

J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988).
[CrossRef]

Sivan, Y.

Smith, D. R.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84, 2244–2246 (2004).
[CrossRef]

D. Schurig and D. R. Smith, “Spatial filtering using media with indefinite permittivity and permeability tensors,” Appl. Phys. Lett. 82, 2215–2217 (2003).
[CrossRef]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Soukoulis, C. M.

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

Stewart, W. J.

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

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

Sugiyama, K.

Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, “Observation of Brewster’s effect for transverse-electric electromagnetic waves in metamaterials: experiment and theory,” Phys. Rev. B. 73, 193104 (2006).
[CrossRef]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
[CrossRef]

Tamayama, Y.

Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, “Observation of Brewster’s effect for transverse-electric electromagnetic waves in metamaterials: experiment and theory,” Phys. Rev. B. 73, 193104 (2006).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Vos, W. L.

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102 (2005).
[CrossRef]

Wang, L. G.

L. G. Wang, H. Chen, and S. Y. Zhu, “Omindirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B. 70, 245102 (2004).
[CrossRef]

Wen, S. C.

Y. J. Xiang, X. Y. Dai, and S. C. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[CrossRef]

Y. J. Xiang, X. Y. Dai, S. C. Wen, and D. Y. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107(2007).
[CrossRef]

White, B. S.

J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988).
[CrossRef]

Xiang, Y. J.

Y. J. Xiang, X. Y. Dai, S. C. Wen, and D. Y. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107(2007).
[CrossRef]

Y. J. Xiang, X. Y. Dai, and S. C. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[CrossRef]

Xiao, S.

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

Zheludev, N. I.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[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]

Zhu, G.

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Zhu, S. Y.

L. G. Wang, H. Chen, and S. Y. Zhu, “Omindirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B. 70, 245102 (2004).
[CrossRef]

Appl. Phys. Lett. (3)

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84, 2244–2246 (2004).
[CrossRef]

H. Q. Li, G. C. Gu, and H. Chen, “Disordered dielectric high reflectors with broadband from visible to infrared,” Appl. Phys. Lett. 74, 3260–3262 (1999).
[CrossRef]

D. Schurig and D. R. Smith, “Spatial filtering using media with indefinite permittivity and permeability tensors,” Appl. Phys. Lett. 82, 2215–2217 (2003).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

R. Marqués, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments,” IEEE Trans. Antennas Propag. 51, 2572–2581 (2003).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (1)

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

J. Appl. Phys. (1)

Y. J. Xiang, X. Y. Dai, S. C. Wen, and D. Y. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107(2007).
[CrossRef]

J. Opt. (2)

S. F. Liew and H. Cao, “Optical properties of 1D photonic crystals with correlated and uncorrelated disorder,” J. Opt. 12, 024011 (2010).
[CrossRef]

A. Fang, T. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. 12, 024013 (2010).
[CrossRef]

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

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

Nat. Photonics (1)

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72, 153102 (2005).
[CrossRef]

Phys. Rev. B. (7)

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B. 65, 144440 (2002).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, “Omindirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B. 70, 245102 (2004).
[CrossRef]

A. A. Asatryan, S. A. Gredeskul, L. C. Botten, M. A. Byrne, V. D. Freilikher, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Anderson localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B. 81, 075124 (2010).
[CrossRef]

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B. 82, 081105(R) (2010).
[CrossRef]

D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Light propagation and Anderson localization in disordered superlattices containing dispersive metamaterials: effects of correlated disorder,” Phys. Rev. B. 84, 094204(2011).
[CrossRef]

S. A. Ramakrishna and J. B. Pendry, “Optical gain removes absorption and increases resolution in a near-field lens,” Phys. Rev. B. 67, 201101 (2003).
[CrossRef]

Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, “Observation of Brewster’s effect for transverse-electric electromagnetic waves in metamaterials: experiment and theory,” Phys. Rev. B. 73, 193104 (2006).
[CrossRef]

Phys. Rev. E. (1)

E. Reyes-Gómez, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattices,” Phys. Rev. E. 84, 036604 (2011).
[CrossRef]

Phys. Rev. Lett. (9)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Complete band gaps in one-dimensional left-handed periodic structures,” Phys. Rev. Lett. 95, 193903 (2005).
[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. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99, 193902 (2007).
[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]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

F. M. Izrailev and N. M. Makarov, “Localization in correlated bilayer structures: from photonic crystals to metamaterials and semiconductor superlattices,” Phys. Rev. Lett. 102, 203901 (2009).
[CrossRef]

J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988).
[CrossRef]

M. A. Noginov, G. Zhu, M. Mayy, B. A. Ritzo, N. Noginova, and V. A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[CrossRef]

Rev. Mod. Phys. (1)

K. Yu. Bliokh, Yu. P. Bliokh, V. Freilikher, S. Savelïev, and F. Nori, “Colloquium: unusual resonators: plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201–1203(2008).
[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]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Other (1)

P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Springer, 1995).

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Figures (4)

Fig. 1.
Fig. 1.

Geometry of a disordered multilayered system containing hyperbolic metamaterials.

Fig. 2.
Fig. 2.

(a) Band structures of the TE wave, at incidence angle θ=π/6, for perfectly ordered superlattice. (b) Localization length ξ (in units of system size) for the TE wave with different disorder strength.

Fig. 3.
Fig. 3.

Ratio S(λ) versus wavelength for (a) Δ=1mm, 6 mm, 12 mm and (b) θ=0, π/100, π/12, π/6, π/3.

Fig. 4.
Fig. 4.

Localization length ξ (in units of system size), obtained by numerical simulations with different values of the absorption γe, as a function of frequency at incidence angle θ=π/6, when Δ=1mm.

Equations (10)

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ε=(εBx000εBy000εBz),μ=(μBx000μBy000μBz).
XN(ω)=ΠjNM(dj,ω),
MA,B(dA,B,ω)=(cos(kA,BzdA,B)ipA,BkA,Bzsin(kA,BzdA,B)ikA,BzpA,Bsin(kA,BzdA,B)cos(kA,BzdA,B)),
T(ω)=2q0(qsx11+q0x22)+(q0qsx12+x21),
cos(qd)=cos(kAzdA)cos(kBzdB)12(kBzμAkAzμBx+kAzμBxkBzμA)sin(kAzdA)sin(kBzdB),
cos(qd)=cos(kAzdA)cos(kBzdB)12(kBzϵAkAzϵBx+kAzϵBxkBzϵA)sin(kAzdA)sin(kBzdB),
lL=ln|T|L.
ξ1=limLlL1,
cosθ2=1μBzϵBy1μBzμBx.
S=ln|T|2/ln|T|2.

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