Abstract

Anomalous optical Anderson localization (AOAL) in mixed one-dimensional (1D) photonic quasicrystals with matching impedance is obtained when the average refractive index of left- and right-handed layers is approximately zero. The transport properties of ordinary and anomalous localization are investigated and compared. The difficulties in expressing analytically the scaling factors of the mixed photonic quasicrystals are illustrated from Hamiltonian-map analysis. An approach based on transfer matrix method is proposed to simulate the localization behavior. From the simulation, it is found that the narrow distribution of the phase shift is responsible for AOAL in the mixed photonic structures. The scaling factors of AOAL decrease with the broadening of the phase shift distribution. The maximum phase shifts of the mixed photonic structures determine the lower boundary of the anomalous localization.

© 2015 Optical Society of America

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    [Crossref]

2012 (5)

F. M. Izrailev, A. A. Krokhin, and N. M. Makarov, “Anomalous localization in low-dimensional systems with correlated disorder,” Phys. Rep. 512(3), 125–254 (2012).
[Crossref]

A. Maurel, A. Ourir, J. F. Mercier, and V. Pagneux, “Usual Anderson localization restored in bilayered left-and right-handed structures,” Phys. Rev. B 85(20), 205138 (2012).
[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, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85(4), 045122 (2012).
[Crossref]

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in bilayered structures,” Europhys. Lett. 98(2), 27003 (2012).
[Crossref]

E. Reyes-Gomex, A. Bruno-Alfonso, S. B. Caralcanti, and L. E. Oliveiva, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85, 205138 (2012).

2011 (2)

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Anderson Localization in metamaterials with compositional disorder,” Low Temp. Phys. 37(11), 957 (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(9), 094204 (2011).
[Crossref]

2010 (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, “Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B 82(20), 205124 (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(8), 081105 (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(7), 075124 (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(20), 203901 (2009).
[Crossref] [PubMed]

W. Tan, Y. Sun, Z. G. Wang, H. Chen, and H. Q. Lin, “Transparency induced by coupled resonances in disordered metamaterials,” Opt. Express 17(26), 24371–24376 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (2)

M. Ghulinyan, “Periodic oscillations in transmission decay of Anderson localized one-dimensional dielectric systems,” Phys. Rev. Lett. 99(6), 063905 (2007).
[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. Kivshar, “Suppression of Anderson localization in disordered metamaterals,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (3)

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (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(11), 113903 (2005).
[Crossref] [PubMed]

M. Titov and H. Schomerus, “Nonuniversality of Anderson localization in short-range correlated disorder,” Phys. Rev. Lett. 95(12), 126602 (2005).
[Crossref] [PubMed]

1998 (1)

A. A. Asatryan, N. A. Nicorovici, L. C. Botten, C. Martijn de Sterke, P. A. Robinson, and R. C. McPhedran, “Electromagnetic localization in dispersive stratified media with random loss and gain,” Phys. Rev. B 57(21), 13535–13549 (1998).
[Crossref]

1990 (1)

R. L. Weaver, “Anderson localization of ultrasound,” Wave Motion 12(2), 129–142 (1990).
[Crossref]

1969 (1)

M. Cutler and N. F. Mott, “Observation of Anderson localization in an electron gas,” Phys. Rev. 181(3), 1336–1340 (1969).
[Crossref]

Abbate, G.

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. Kivshar, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85(4), 045122 (2012).
[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, “Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B 82(20), 205124 (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(7), 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 metamaterals,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref] [PubMed]

A. A. Asatryan, N. A. Nicorovici, L. C. Botten, C. Martijn de Sterke, P. A. Robinson, and R. C. McPhedran, “Electromagnetic localization in dispersive stratified media with random loss and gain,” Phys. Rev. B 57(21), 13535–13549 (1998).
[Crossref]

Aspect, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[Crossref] [PubMed]

Bernard, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[Crossref] [PubMed]

Bertolotti, J.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[Crossref] [PubMed]

Billy, J.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[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. Kivshar, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85(4), 045122 (2012).
[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, “Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B 82(20), 205124 (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(7), 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 metamaterals,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref] [PubMed]

A. A. Asatryan, N. A. Nicorovici, L. C. Botten, C. Martijn de Sterke, P. A. Robinson, and R. C. McPhedran, “Electromagnetic localization in dispersive stratified media with random loss and gain,” Phys. Rev. B 57(21), 13535–13549 (1998).
[Crossref]

Bouyer, P.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[Crossref] [PubMed]

Braginsky, L.

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, “Negative refractive index materials,” J. Comput. Theor. Nanosci. 3, 1 (2006).

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Bruno-Alfonso, A.

E. Reyes-Gomex, A. Bruno-Alfonso, S. B. Caralcanti, and L. E. Oliveiva, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85, 205138 (2012).

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. Kivshar, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85(4), 045122 (2012).
[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, “Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B 82(20), 205124 (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(7), 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 metamaterals,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref] [PubMed]

Caralcanti, S. B.

E. Reyes-Gomex, A. Bruno-Alfonso, S. B. Caralcanti, and L. E. Oliveiva, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85, 205138 (2012).

Cavalcanti, S. B.

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(9), 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(8), 081105 (2010).
[Crossref]

Chen, H.

Clément, D.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[Crossref] [PubMed]

Cutler, M.

M. Cutler and N. F. Mott, “Observation of Anderson localization in an electron gas,” Phys. Rev. 181(3), 1336–1340 (1969).
[Crossref]

de Moura, F. A. B. F.

De Stefano, L.

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(9), 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(8), 081105 (2010).
[Crossref]

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

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. Kivshar, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85(4), 045122 (2012).
[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, “Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B 82(20), 205124 (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(7), 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 metamaterals,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref] [PubMed]

Ghulinyan, M.

M. Ghulinyan, “Periodic oscillations in transmission decay of Anderson localized one-dimensional dielectric systems,” Phys. Rev. Lett. 99(6), 063905 (2007).
[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(11), 113903 (2005).
[Crossref] [PubMed]

Gibbs, H. M.

Gottardo, S.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 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. Kivshar, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85(4), 045122 (2012).
[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, “Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B 82(20), 205124 (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(7), 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 metamaterals,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref] [PubMed]

Hafner, C.

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, “Negative refractive index materials,” J. Comput. Theor. Nanosci. 3, 1 (2006).

Hambrecht, B.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[Crossref] [PubMed]

Hendrickson, J.

Ivchenko, E. L.

Izrailev, F. M.

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in bilayered structures,” Europhys. Lett. 98(2), 27003 (2012).
[Crossref]

F. M. Izrailev, A. A. Krokhin, and N. M. Makarov, “Anomalous localization in low-dimensional systems with correlated disorder,” Phys. Rep. 512(3), 125–254 (2012).
[Crossref]

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Anderson Localization in metamaterials with compositional disorder,” Low Temp. Phys. 37(11), 957 (2011).
[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(20), 203901 (2009).
[Crossref] [PubMed]

Josse, V.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[Crossref] [PubMed]

Khitrova, G.

Kivshar, 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. Kivshar, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85(4), 045122 (2012).
[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, “Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B 82(20), 205124 (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(7), 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 metamaterals,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref] [PubMed]

Krokhin, A. A.

F. M. Izrailev, A. A. Krokhin, and N. M. Makarov, “Anomalous localization in low-dimensional systems with correlated disorder,” Phys. Rep. 512(3), 125–254 (2012).
[Crossref]

Lin, H. Q.

Lugan, P.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[Crossref] [PubMed]

Lyra, M. L.

Makarov, N. M.

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in bilayered structures,” Europhys. Lett. 98(2), 27003 (2012).
[Crossref]

F. M. Izrailev, A. A. Krokhin, and N. M. Makarov, “Anomalous localization in low-dimensional systems with correlated disorder,” Phys. Rep. 512(3), 125–254 (2012).
[Crossref]

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Anderson Localization in metamaterials with compositional disorder,” Low Temp. Phys. 37(11), 957 (2011).
[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(20), 203901 (2009).
[Crossref] [PubMed]

Malloy, K. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Marino, A.

Martijn de Sterke, C.

A. A. Asatryan, N. A. Nicorovici, L. C. Botten, C. Martijn de Sterke, P. A. Robinson, and R. C. McPhedran, “Electromagnetic localization in dispersive stratified media with random loss and gain,” Phys. Rev. B 57(21), 13535–13549 (1998).
[Crossref]

Maurel, A.

A. Maurel, A. Ourir, J. F. Mercier, and V. Pagneux, “Usual Anderson localization restored in bilayered left-and right-handed structures,” Phys. Rev. B 85(20), 205138 (2012).
[Crossref]

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. Kivshar, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85(4), 045122 (2012).
[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, “Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B 82(20), 205124 (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(7), 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 metamaterals,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref] [PubMed]

A. A. Asatryan, N. A. Nicorovici, L. C. Botten, C. Martijn de Sterke, P. A. Robinson, and R. C. McPhedran, “Electromagnetic localization in dispersive stratified media with random loss and gain,” Phys. Rev. B 57(21), 13535–13549 (1998).
[Crossref]

Mercier, J. F.

A. Maurel, A. Ourir, J. F. Mercier, and V. Pagneux, “Usual Anderson localization restored in bilayered left-and right-handed structures,” Phys. Rev. B 85(20), 205138 (2012).
[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(9), 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(8), 081105 (2010).
[Crossref]

Moretti, L.

Mott, N. F.

M. Cutler and N. F. Mott, “Observation of Anderson localization in an electron gas,” Phys. Rev. 181(3), 1336–1340 (1969).
[Crossref]

Nascimento, E. M.

Nicorovici, N. A.

A. A. Asatryan, N. A. Nicorovici, L. C. Botten, C. Martijn de Sterke, P. A. Robinson, and R. C. McPhedran, “Electromagnetic localization in dispersive stratified media with random loss and gain,” Phys. Rev. B 57(21), 13535–13549 (1998).
[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(9), 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(8), 081105 (2010).
[Crossref]

Oliveiva, L. E.

E. Reyes-Gomex, A. Bruno-Alfonso, S. B. Caralcanti, and L. E. Oliveiva, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85, 205138 (2012).

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Ourir, A.

A. Maurel, A. Ourir, J. F. Mercier, and V. Pagneux, “Usual Anderson localization restored in bilayered left-and right-handed structures,” Phys. Rev. B 85(20), 205138 (2012).
[Crossref]

Pagneux, V.

A. Maurel, A. Ourir, J. F. Mercier, and V. Pagneux, “Usual Anderson localization restored in bilayered left-and right-handed structures,” Phys. Rev. B 85(20), 205138 (2012).
[Crossref]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Pavesi, L.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[Crossref] [PubMed]

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(9), 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(8), 081105 (2010).
[Crossref]

Poddubny, A. N.

Rea, I.

Rendina, I.

Reyes-Gomex, E.

E. Reyes-Gomex, A. Bruno-Alfonso, S. B. Caralcanti, and L. E. Oliveiva, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85, 205138 (2012).

Richards, B. C.

Robinson, P. A.

A. A. Asatryan, N. A. Nicorovici, L. C. Botten, C. Martijn de Sterke, P. A. Robinson, and R. C. McPhedran, “Electromagnetic localization in dispersive stratified media with random loss and gain,” Phys. Rev. B 57(21), 13535–13549 (1998).
[Crossref]

Rotiroti, L.

Sanchez-Palencia, L.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[Crossref] [PubMed]

Schomerus, H.

M. Titov and H. Schomerus, “Nonuniversality of Anderson localization in short-range correlated disorder,” Phys. Rev. Lett. 95(12), 126602 (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. Kivshar, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85(4), 045122 (2012).
[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, “Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B 82(20), 205124 (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(7), 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 metamaterals,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref] [PubMed]

Shklover, V.

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, “Negative refractive index materials,” J. Comput. Theor. Nanosci. 3, 1 (2006).

Sun, Y.

Sweet, J.

Tan, W.

Titov, M.

M. Titov and H. Schomerus, “Nonuniversality of Anderson localization in short-range correlated disorder,” Phys. Rev. Lett. 95(12), 126602 (2005).
[Crossref] [PubMed]

Torres-Herrera, E. J.

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in bilayered structures,” Europhys. Lett. 98(2), 27003 (2012).
[Crossref]

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Anderson Localization in metamaterials with compositional disorder,” Low Temp. Phys. 37(11), 957 (2011).
[Crossref]

Veselago, V.

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, “Negative refractive index materials,” J. Comput. Theor. Nanosci. 3, 1 (2006).

Wang, Z. G.

Weaver, R. L.

R. L. Weaver, “Anderson localization of ultrasound,” Wave Motion 12(2), 129–142 (1990).
[Crossref]

Wegener, M.

Wiersma, D. S.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[Crossref] [PubMed]

Zhang, S.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Zuo, Z.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[Crossref] [PubMed]

Europhys. Lett. (1)

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in bilayered structures,” Europhys. Lett. 98(2), 27003 (2012).
[Crossref]

J. Comput. Theor. Nanosci. (1)

V. Veselago, L. Braginsky, V. Shklover, and C. Hafner, “Negative refractive index materials,” J. Comput. Theor. Nanosci. 3, 1 (2006).

Low Temp. Phys. (1)

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Anderson Localization in metamaterials with compositional disorder,” Low Temp. Phys. 37(11), 957 (2011).
[Crossref]

Nature (1)

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453(7197), 891–894 (2008).
[Crossref] [PubMed]

Opt. Express (4)

Phys. Rep. (1)

F. M. Izrailev, A. A. Krokhin, and N. M. Makarov, “Anomalous localization in low-dimensional systems with correlated disorder,” Phys. Rep. 512(3), 125–254 (2012).
[Crossref]

Phys. Rev. (1)

M. Cutler and N. F. Mott, “Observation of Anderson localization in an electron gas,” Phys. Rev. 181(3), 1336–1340 (1969).
[Crossref]

Phys. Rev. B (7)

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(8), 081105 (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(7), 075124 (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(9), 094204 (2011).
[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, “Effects of polarization on the transmission and localization of classical waves in weakly scattering metamaterials,” Phys. Rev. B 82(20), 205124 (2010).
[Crossref]

A. Maurel, A. Ourir, J. F. Mercier, and V. Pagneux, “Usual Anderson localization restored in bilayered left-and right-handed structures,” Phys. Rev. B 85(20), 205138 (2012).
[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, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85(4), 045122 (2012).
[Crossref]

A. A. Asatryan, N. A. Nicorovici, L. C. Botten, C. Martijn de Sterke, P. A. Robinson, and R. C. McPhedran, “Electromagnetic localization in dispersive stratified media with random loss and gain,” Phys. Rev. B 57(21), 13535–13549 (1998).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

E. Reyes-Gomex, A. Bruno-Alfonso, S. B. Caralcanti, and L. E. Oliveiva, “Anderson localization and Brewster anomalies in photonic disordered quasiperiodic lattice,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 85, 205138 (2012).

Phys. Rev. Lett. (6)

F. M. Izrailev and N. M. Makarov, “Localization in correlated bilayer structures: from photonic crystals to metamaterials and semiconductor superlattices,” Phys. Rev. Lett. 102(20), 203901 (2009).
[Crossref] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

M. Ghulinyan, “Periodic oscillations in transmission decay of Anderson localized one-dimensional dielectric systems,” Phys. Rev. Lett. 99(6), 063905 (2007).
[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(11), 113903 (2005).
[Crossref] [PubMed]

M. Titov and H. Schomerus, “Nonuniversality of Anderson localization in short-range correlated disorder,” Phys. Rev. Lett. 95(12), 126602 (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. Kivshar, “Suppression of Anderson localization in disordered metamaterals,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref] [PubMed]

Wave Motion (1)

R. L. Weaver, “Anderson localization of ultrasound,” Wave Motion 12(2), 129–142 (1990).
[Crossref]

Other (3)

P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopoc Phenomena, Second Edition (Springer, 2006).

M. F. Limonv and R. M. De La Rue, Optical Properties of Photonic Structures: Interplay of Order and Disorder (CRC, 2012).

Z. Knittl, Optics of Thin Films: an Optical Multilayer Theory (Wiley, London, 1976).

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Figures (7)

Fig. 1
Fig. 1 Structure of the 5th generation Fibonacci 11-quasicrystal. A and B denote for right- and left-handed layers, respectively. R and T denote optical reflectance and transmittance, respectively.
Fig. 2
Fig. 2 Localization length versus thickness ratio for 11- (red) and 12-quasicrystal (black) at wavelength 10(da + db). Generation order is 18 for 11- and 12 for 12-quasicrystals, respectively. The localization length is calculated from average of 1000 configurations with different disorder realizations. The disorder strength ξ is 0.5.
Fig. 3
Fig. 3 Localization length spectra for the mixed 11-quasicrystal with thickness ratios 1 (black) and 1.618 (red), 12-quasicrystal (blue), and mixed photonic crystal (cyan) with thickness ratios 1. The spectra of solid lines are from average of 1000 configurations with different disorder realization of about 10000 layers. The dashed lines are the localization length spectra for the four structures with layer number about 107 from average of 5 configurations. The dashed lines denote the linear fit of AOAL versus wavelength. F, G and H denote the lower wavelength boundaries of AOAL for the mixed photonic crystal with thickness ratio 1, 11-quasicrystal with thickness ratio 1.618, and 12-quasicrystal with thickness ratio 1, respectively.
Fig. 4
Fig. 4 Field distribution |u|2 and transmittance spectra of mixed 11-quasicrystal with thickness ratios 1 (a) and 1.618 (b) for single realization of refractive index disorder. The total thicknesses of the multilayer are normalized.
Fig. 5
Fig. 5 Phase space trajectories of (Qn, Pn) for a single realization of disorder. (a). Mixed photonic crystal with thickness ratio 1; (b). 11-quasicystal with thickness ratio 1.618; (c). 12-quasicrystal with thickness ratio 1; (d). 11-quasicystal with thickness ratio 1. The numbers of the layers are approximately 10000. The wavelength is optimized for the four structures for clarity of the images. Disorder strength ξ is 0.5.
Fig. 6
Fig. 6 Normalized phase shift distributions for the mixed 11-quasicrystal with thickness ratio 1.618 (red), 12-quasicrystal with thickness ratio 1(black), and the mixed photonic crystal with thickness ratios 1 (blue) without disorder. The wavelength for phase shift calculation is 2π.
Fig. 7
Fig. 7 Simulated localization length spectra for phase shift distributions similar to 11-quasicrystal with thickness ratio 1.618. The maximum phase shifts are 2, 5 and 15 for black (dashed), red (solid) and blue (dashed) lines, respectively.

Equations (10)

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

d 2 d x 2 u ( x ) + k 2 ( ε 0 + δ ε ( x ) ) u ( x ) = 0 ,
u ( x ) = e χ ( x ) sin φ ( x ) , d d x u ( x ) = k e χ ( x ) cos φ ( x ) .
γ = lim x χ ( x ) x ,
l 1 2 γ = lim N N ln | T N | ,
( u 0 , R u 0 , L ) = S ( u N + 1 , R u N + 1 , L ) = ( v = 1 N W v 1 , v U v ) W N , N + 1 ( u N + 1 , R u N + 1 , L ) .
W v 1 , v = 1 t v ( ( 1 0 0 1 ) + ( 0 r v r v 0 ) ) .
S 11 = ( v = 1 N 1 t v ) × ( 1 + N 0 < N 1 r N 0 r N 1 e v = 1 N j ϕ v 2 v = N 0 N 1 j ϕ v + ) ,
Q n + 1 = a n Q n + b n P n , P n + 1 = c n Q n + d n P n .
a n = cos ( ϕ p ) cos ( ϕ q ) Z p 1 Z q sin ( ϕ p ) sin ( ϕ q ) , b n = Z p sin ( ϕ p ) cos ( ϕ q ) Z q cos ( ϕ p ) sin ( ϕ q ) , c n = Z p 1 sin ( ϕ p ) cos ( ϕ q ) Z q 1 cos ( ϕ p ) sin ( ϕ q ) , d n = cos ( ϕ p ) cos ( ϕ q ) Z p Z q 1 sin ( ϕ p ) sin ( ϕ q ) ,
l = ln R n + 1 R n ,

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