Abstract

The propagation and the Anderson localization of electromagnetic waves in a randomly-stratified slab, where both the dielectric permittivity and the magnetic permeability depend on one spatial coordinate in a random manner, is theoretically studied. The case where the wave impedance is uniform, while the refractive index is random, is considered in detail. The localization length and the disorder-averaged transmittance of s and p waves incident obliquely on the slab are calculated as a function of the incident angle θ and the strength of randomness in a numerically precise manner, using the invariant imbedding method. It is found that the waves incident perpendicularly on the slab are delocalized, while those incident obliquely are localized. As the incident angle increases from zero, the localization length decreases from infinity monotonically to some finite value. The localization length is found to depend on the incident angle as θ−4 and a simple analytical formula, which works quite well for weak disorder and small incident angles, is derived. The localization length does not depend on the wave polarization, but the disorder-averaged transmittance generally does.

© 2015 Optical Society of America

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Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses

Kihong Kim, D. K. Phung, F. Rotermund, and H. Lim
Opt. Express 16(2) 1150-1164 (2008)

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  1. S. E. Skipetrov and I. M. Sokolov, “Absence of Anderson localization of light in a random ensemble of point scatterers,” Phys. Rev. Lett. 112, 023905 (2014).
    [Crossref] [PubMed]
  2. T. Sperling, W. Bührer, M. Ackermann, C. M. Aegerter, and G. Maret, “Probing Anderson localization of light by weak nonlinear effects,“ New J. Phys. 16, 112001 (2014).
    [Crossref]
  3. A. Basiri, Y. Bromberg, A. Yamilov, H. Cao, and T. Kottos, “Light localization induced by a random imaginary refractive index,” Phys. Rev. A 90, 043815 (2014).
    [Crossref]
  4. S. Mookherjea, J. R. Ong, X. Luo, and L. Guo-Qiang, “Electronic control of optical Anderson localization modes,” Nat. Nanotechnol. 9, 365–371 (2014).
    [Crossref] [PubMed]
  5. T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Disordered animal multilayer reflectors and the localization of light,” J. R. Soc., Interface 11, 20140948 (2014).
    [Crossref]
  6. S. A. Gredeskul, Y. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Y. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media (Review Article),” Low Temp. Phys. 38, 570–602 (2012).
    [Crossref]
  7. A. I. Ignatov, A. M. Merzlikin, A. P. Vinogradov, and A. A. Lisyansky, “Effect of polarization upon light localization in random layered magnetodielectric media,” Phys. Rev. E 83, 224205 (2011).
    [Crossref]
  8. 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, 045122 (2012).
    [Crossref]
  9. E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in a matched quater stack with metamaterials,” New J. Phys. 15, 055014 (2013).
    [Crossref]
  10. I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
    [Crossref] [PubMed]
  11. K. Y. Bliokh, S. A. Gredeskul, P. Rajan, I. V. Shadrivov, and Y. S. Kivshar, “Nonreciprocal Anderson localization in magneto-optical random structures,” Phys. Rev. B 85, 014205 (2012).
    [Crossref]
  12. V. Folli and C. Conti, “Anderson localization in nonlocal nonlinear media,” Opt. Lett. 37, 332–334 (2012).
    [Crossref] [PubMed]
  13. M. Dragana Jović, C. Denz, and M. R. Belić, “Anderson localization of light in PT-symmetric optical lattices,” Opt. Lett. 37, 4455–4457 (2012).
    [Crossref]
  14. 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] [PubMed]
  15. K. Kim, F. Rotermund, D.-H. Lee, and H. Lim, “Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: random phase approximation,” Wave Random Complex 17, 43–53 (2007).
    [Crossref]
  16. K. J. Lee and K. Kim, “Universal shift of the Brewster angle and disorder-enhanced delocalization of p waves in stratified random media,” Opt. Express 19, 20817–20826 (2011).
    [Crossref] [PubMed]
  17. 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 (2010).
    [Crossref]
  18. 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]
  19. T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Suppression of Brewster delocalization anomalies in an alternating isotropic-birefringent random layered medium,” Phys. Rev. B 88, 041105 (2013).
    [Crossref]
  20. C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).
  21. C.-S. Kee, J.-E. Kim, H. Y. Park, and H. Lim, “Roles of wave impedance and refractive index in photonic crystals with magnetic and dielectric properties,” IEEE Trans. Microwave Theory Tech. 47, 2148–2150 (1999).
    [Crossref]
  22. K. Kim, H. Lim, and D.-H. Lee, “Invariant imbedding equations for electromagnetic waves in stratified magnetic media: applications to one-dimensional photonic crystals,” J. Korean Phys. Soc. 39, L956–L960 (2001).
  23. K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58, 6153–6160 (1998).
    [Crossref]
  24. R. Rammal and B. Doucot, “Invariant imbedding approach to localization. I. General framework and basic equations,” J. Physiol. 48, 509–526 (1987).
  25. V. I. Klyatskin, “The imbedding method in statistical boundary-value wave problems,” Prog. Opt. 33, 1–127 (1994).
  26. K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69, 207–213 (2005).
    [Crossref]
  27. K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses,” Opt. Express 16, 1150–1164 (2008).
    [Crossref] [PubMed]
  28. E. A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP 20, 1290–1294 (1965).
  29. V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53, 7413–7416 (1996).
    [Crossref]
  30. J. M. Luck, “Non-monotonic disorder-induced enhanced tunnelling,” J. Phys. A 37, 259–271 (2004).
    [Crossref]
  31. K. Kim, F. Rotermund, and H. Lim, “Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: exact calculation based on the invariant imbedding method,” Phys. Rev. B 77, 024203 (2008).
    [Crossref]
  32. J. Heinrichs, “Enhanced quantum tunnelling induced by disorder,” J. Phys.: Condens. Matter 20, 395215 (2008).

2014 (5)

S. E. Skipetrov and I. M. Sokolov, “Absence of Anderson localization of light in a random ensemble of point scatterers,” Phys. Rev. Lett. 112, 023905 (2014).
[Crossref] [PubMed]

T. Sperling, W. Bührer, M. Ackermann, C. M. Aegerter, and G. Maret, “Probing Anderson localization of light by weak nonlinear effects,“ New J. Phys. 16, 112001 (2014).
[Crossref]

A. Basiri, Y. Bromberg, A. Yamilov, H. Cao, and T. Kottos, “Light localization induced by a random imaginary refractive index,” Phys. Rev. A 90, 043815 (2014).
[Crossref]

S. Mookherjea, J. R. Ong, X. Luo, and L. Guo-Qiang, “Electronic control of optical Anderson localization modes,” Nat. Nanotechnol. 9, 365–371 (2014).
[Crossref] [PubMed]

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Disordered animal multilayer reflectors and the localization of light,” J. R. Soc., Interface 11, 20140948 (2014).
[Crossref]

2013 (2)

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in a matched quater stack with metamaterials,” New J. Phys. 15, 055014 (2013).
[Crossref]

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Suppression of Brewster delocalization anomalies in an alternating isotropic-birefringent random layered medium,” Phys. Rev. B 88, 041105 (2013).
[Crossref]

2012 (5)

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, 045122 (2012).
[Crossref]

S. A. Gredeskul, Y. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Y. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media (Review Article),” Low Temp. Phys. 38, 570–602 (2012).
[Crossref]

K. Y. Bliokh, S. A. Gredeskul, P. Rajan, I. V. Shadrivov, and Y. S. Kivshar, “Nonreciprocal Anderson localization in magneto-optical random structures,” Phys. Rev. B 85, 014205 (2012).
[Crossref]

V. Folli and C. Conti, “Anderson localization in nonlocal nonlinear media,” Opt. Lett. 37, 332–334 (2012).
[Crossref] [PubMed]

M. Dragana Jović, C. Denz, and M. R. Belić, “Anderson localization of light in PT-symmetric optical lattices,” Opt. Lett. 37, 4455–4457 (2012).
[Crossref]

2011 (3)

A. I. Ignatov, A. M. Merzlikin, A. P. Vinogradov, and A. A. Lisyansky, “Effect of polarization upon light localization in random layered magnetodielectric media,” Phys. Rev. E 83, 224205 (2011).
[Crossref]

K. J. Lee and K. Kim, “Universal shift of the Brewster angle and disorder-enhanced delocalization of p waves in stratified random media,” Opt. Express 19, 20817–20826 (2011).
[Crossref] [PubMed]

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 (2)

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 (2010).
[Crossref]

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[Crossref] [PubMed]

2008 (3)

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses,” Opt. Express 16, 1150–1164 (2008).
[Crossref] [PubMed]

K. Kim, F. Rotermund, and H. Lim, “Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: exact calculation based on the invariant imbedding method,” Phys. Rev. B 77, 024203 (2008).
[Crossref]

J. Heinrichs, “Enhanced quantum tunnelling induced by disorder,” J. Phys.: Condens. Matter 20, 395215 (2008).

2007 (1)

K. Kim, F. Rotermund, D.-H. Lee, and H. Lim, “Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: random phase approximation,” Wave Random Complex 17, 43–53 (2007).
[Crossref]

2005 (1)

K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69, 207–213 (2005).
[Crossref]

2004 (1)

J. M. Luck, “Non-monotonic disorder-induced enhanced tunnelling,” J. Phys. A 37, 259–271 (2004).
[Crossref]

2001 (1)

K. Kim, H. Lim, and D.-H. Lee, “Invariant imbedding equations for electromagnetic waves in stratified magnetic media: applications to one-dimensional photonic crystals,” J. Korean Phys. Soc. 39, L956–L960 (2001).

1999 (2)

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

C.-S. Kee, J.-E. Kim, H. Y. Park, and H. Lim, “Roles of wave impedance and refractive index in photonic crystals with magnetic and dielectric properties,” IEEE Trans. Microwave Theory Tech. 47, 2148–2150 (1999).
[Crossref]

1998 (1)

K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58, 6153–6160 (1998).
[Crossref]

1996 (1)

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53, 7413–7416 (1996).
[Crossref]

1994 (1)

V. I. Klyatskin, “The imbedding method in statistical boundary-value wave problems,” Prog. Opt. 33, 1–127 (1994).

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] [PubMed]

1987 (1)

R. Rammal and B. Doucot, “Invariant imbedding approach to localization. I. General framework and basic equations,” J. Physiol. 48, 509–526 (1987).

1965 (1)

E. A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP 20, 1290–1294 (1965).

Ackermann, M.

T. Sperling, W. Bührer, M. Ackermann, C. M. Aegerter, and G. Maret, “Probing Anderson localization of light by weak nonlinear effects,“ New J. Phys. 16, 112001 (2014).
[Crossref]

Aegerter, C. M.

T. Sperling, W. Bührer, M. Ackermann, C. M. Aegerter, and G. Maret, “Probing Anderson localization of light by weak nonlinear effects,“ New J. Phys. 16, 112001 (2014).
[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. Kivshar, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85, 045122 (2012).
[Crossref]

S. A. Gredeskul, Y. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Y. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media (Review Article),” Low Temp. Phys. 38, 570–602 (2012).
[Crossref]

Basiri, A.

A. Basiri, Y. Bromberg, A. Yamilov, H. Cao, and T. Kottos, “Light localization induced by a random imaginary refractive index,” Phys. Rev. A 90, 043815 (2014).
[Crossref]

Belic, M. R.

Bliokh, K. Y.

S. A. Gredeskul, Y. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Y. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media (Review Article),” Low Temp. Phys. 38, 570–602 (2012).
[Crossref]

K. Y. Bliokh, S. A. Gredeskul, P. Rajan, I. V. Shadrivov, and Y. S. Kivshar, “Nonreciprocal Anderson localization in magneto-optical random structures,” Phys. Rev. B 85, 014205 (2012).
[Crossref]

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[Crossref] [PubMed]

Bliokh, Y. P.

S. A. Gredeskul, Y. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Y. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media (Review Article),” Low Temp. Phys. 38, 570–602 (2012).
[Crossref]

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[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, 045122 (2012).
[Crossref]

Bromberg, Y.

A. Basiri, Y. Bromberg, A. Yamilov, H. Cao, and T. Kottos, “Light localization induced by a random imaginary refractive index,” Phys. Rev. A 90, 043815 (2014).
[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]

Bührer, W.

T. Sperling, W. Bührer, M. Ackermann, C. M. Aegerter, and G. Maret, “Probing Anderson localization of light by weak nonlinear effects,“ New J. Phys. 16, 112001 (2014).
[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. Kivshar, “Transmission and Anderson localization in dispersive metamaterials,” Phys. Rev. B 85, 045122 (2012).
[Crossref]

Cao, H.

A. Basiri, Y. Bromberg, A. Yamilov, H. Cao, and T. Kottos, “Light localization induced by a random imaginary refractive index,” Phys. Rev. A 90, 043815 (2014).
[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, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B 82, 081105 (2010).
[Crossref]

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] [PubMed]

Conti, C.

Denz, C.

dos Santos, R. R.

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 (2010).
[Crossref]

Doucot, B.

R. Rammal and B. Doucot, “Invariant imbedding approach to localization. I. General framework and basic equations,” J. Physiol. 48, 509–526 (1987).

Dragana Jovic, M.

Folli, V.

Freilikher, V.

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[Crossref] [PubMed]

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53, 7413–7416 (1996).
[Crossref]

Freilikher, V. D.

S. A. Gredeskul, Y. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Y. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media (Review Article),” Low Temp. Phys. 38, 570–602 (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, 045122 (2012).
[Crossref]

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, 045122 (2012).
[Crossref]

S. A. Gredeskul, Y. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Y. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media (Review Article),” Low Temp. Phys. 38, 570–602 (2012).
[Crossref]

K. Y. Bliokh, S. A. Gredeskul, P. Rajan, I. V. Shadrivov, and Y. S. Kivshar, “Nonreciprocal Anderson localization in magneto-optical random structures,” Phys. Rev. B 85, 014205 (2012).
[Crossref]

Guo-Qiang, L.

S. Mookherjea, J. R. Ong, X. Luo, and L. Guo-Qiang, “Electronic control of optical Anderson localization modes,” Nat. Nanotechnol. 9, 365–371 (2014).
[Crossref] [PubMed]

Heinrichs, J.

J. Heinrichs, “Enhanced quantum tunnelling induced by disorder,” J. Phys.: Condens. Matter 20, 395215 (2008).

Ignatov, A. I.

A. I. Ignatov, A. M. Merzlikin, A. P. Vinogradov, and A. A. Lisyansky, “Effect of polarization upon light localization in random layered magnetodielectric media,” Phys. Rev. E 83, 224205 (2011).
[Crossref]

Izrailev, F. M.

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in a matched quater stack with metamaterials,” New J. Phys. 15, 055014 (2013).
[Crossref]

Jordan, T. M.

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Disordered animal multilayer reflectors and the localization of light,” J. R. Soc., Interface 11, 20140948 (2014).
[Crossref]

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Suppression of Brewster delocalization anomalies in an alternating isotropic-birefringent random layered medium,” Phys. Rev. B 88, 041105 (2013).
[Crossref]

Kee, C.-S.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

C.-S. Kee, J.-E. Kim, H. Y. Park, and H. Lim, “Roles of wave impedance and refractive index in photonic crystals with magnetic and dielectric properties,” IEEE Trans. Microwave Theory Tech. 47, 2148–2150 (1999).
[Crossref]

Kim, J.-E.

C.-S. Kee, J.-E. Kim, H. Y. Park, and H. Lim, “Roles of wave impedance and refractive index in photonic crystals with magnetic and dielectric properties,” IEEE Trans. Microwave Theory Tech. 47, 2148–2150 (1999).
[Crossref]

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

Kim, K.

K. J. Lee and K. Kim, “Universal shift of the Brewster angle and disorder-enhanced delocalization of p waves in stratified random media,” Opt. Express 19, 20817–20826 (2011).
[Crossref] [PubMed]

K. Kim, F. Rotermund, and H. Lim, “Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: exact calculation based on the invariant imbedding method,” Phys. Rev. B 77, 024203 (2008).
[Crossref]

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses,” Opt. Express 16, 1150–1164 (2008).
[Crossref] [PubMed]

K. Kim, F. Rotermund, D.-H. Lee, and H. Lim, “Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: random phase approximation,” Wave Random Complex 17, 43–53 (2007).
[Crossref]

K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69, 207–213 (2005).
[Crossref]

K. Kim, H. Lim, and D.-H. Lee, “Invariant imbedding equations for electromagnetic waves in stratified magnetic media: applications to one-dimensional photonic crystals,” J. Korean Phys. Soc. 39, L956–L960 (2001).

K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58, 6153–6160 (1998).
[Crossref]

Kim, S. J.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

Kivshar, Y. S.

K. Y. Bliokh, S. A. Gredeskul, P. Rajan, I. V. Shadrivov, and Y. S. Kivshar, “Nonreciprocal Anderson localization in magneto-optical random structures,” Phys. Rev. B 85, 014205 (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, 045122 (2012).
[Crossref]

S. A. Gredeskul, Y. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Y. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media (Review Article),” Low Temp. Phys. 38, 570–602 (2012).
[Crossref]

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[Crossref] [PubMed]

Klyatskin, V. I.

V. I. Klyatskin, “The imbedding method in statistical boundary-value wave problems,” Prog. Opt. 33, 1–127 (1994).

Kottos, T.

A. Basiri, Y. Bromberg, A. Yamilov, H. Cao, and T. Kottos, “Light localization induced by a random imaginary refractive index,” Phys. Rev. A 90, 043815 (2014).
[Crossref]

Kwon, Y. S.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

Lee, D.-H.

K. Kim, F. Rotermund, D.-H. Lee, and H. Lim, “Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: random phase approximation,” Wave Random Complex 17, 43–53 (2007).
[Crossref]

K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69, 207–213 (2005).
[Crossref]

K. Kim, H. Lim, and D.-H. Lee, “Invariant imbedding equations for electromagnetic waves in stratified magnetic media: applications to one-dimensional photonic crystals,” J. Korean Phys. Soc. 39, L956–L960 (2001).

Lee, K. J.

Lim, H.

K. Kim, F. Rotermund, and H. Lim, “Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: exact calculation based on the invariant imbedding method,” Phys. Rev. B 77, 024203 (2008).
[Crossref]

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses,” Opt. Express 16, 1150–1164 (2008).
[Crossref] [PubMed]

K. Kim, F. Rotermund, D.-H. Lee, and H. Lim, “Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: random phase approximation,” Wave Random Complex 17, 43–53 (2007).
[Crossref]

K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69, 207–213 (2005).
[Crossref]

K. Kim, H. Lim, and D.-H. Lee, “Invariant imbedding equations for electromagnetic waves in stratified magnetic media: applications to one-dimensional photonic crystals,” J. Korean Phys. Soc. 39, L956–L960 (2001).

C.-S. Kee, J.-E. Kim, H. Y. Park, and H. Lim, “Roles of wave impedance and refractive index in photonic crystals with magnetic and dielectric properties,” IEEE Trans. Microwave Theory Tech. 47, 2148–2150 (1999).
[Crossref]

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

Lisyansky, A. A.

A. I. Ignatov, A. M. Merzlikin, A. P. Vinogradov, and A. A. Lisyansky, “Effect of polarization upon light localization in random layered magnetodielectric media,” Phys. Rev. E 83, 224205 (2011).
[Crossref]

Luck, J. M.

J. M. Luck, “Non-monotonic disorder-induced enhanced tunnelling,” J. Phys. A 37, 259–271 (2004).
[Crossref]

Luo, X.

S. Mookherjea, J. R. Ong, X. Luo, and L. Guo-Qiang, “Electronic control of optical Anderson localization modes,” Nat. Nanotechnol. 9, 365–371 (2014).
[Crossref] [PubMed]

Makarov, N. M.

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in a matched quater stack with metamaterials,” New J. Phys. 15, 055014 (2013).
[Crossref]

Maret, G.

T. Sperling, W. Bührer, M. Ackermann, C. M. Aegerter, and G. Maret, “Probing Anderson localization of light by weak nonlinear effects,“ New J. Phys. 16, 112001 (2014).
[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, 045122 (2012).
[Crossref]

Merzlikin, A. M.

A. I. Ignatov, A. M. Merzlikin, A. P. Vinogradov, and A. A. Lisyansky, “Effect of polarization upon light localization in random layered magnetodielectric media,” Phys. Rev. E 83, 224205 (2011).
[Crossref]

Mogilevtsev, D.

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 (2010).
[Crossref]

Mookherjea, S.

S. Mookherjea, J. R. Ong, X. Luo, and L. Guo-Qiang, “Electronic control of optical Anderson localization modes,” Nat. Nanotechnol. 9, 365–371 (2014).
[Crossref] [PubMed]

Myung, N. H.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

Novikov, E. A.

E. A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP 20, 1290–1294 (1965).

Oliveira, L. 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]

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 (2010).
[Crossref]

Ong, J. R.

S. Mookherjea, J. R. Ong, X. Luo, and L. Guo-Qiang, “Electronic control of optical Anderson localization modes,” Nat. Nanotechnol. 9, 365–371 (2014).
[Crossref] [PubMed]

Park, H. Y.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

C.-S. Kee, J.-E. Kim, H. Y. Park, and H. Lim, “Roles of wave impedance and refractive index in photonic crystals with magnetic and dielectric properties,” IEEE Trans. Microwave Theory Tech. 47, 2148–2150 (1999).
[Crossref]

Partridge, J. C.

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Disordered animal multilayer reflectors and the localization of light,” J. R. Soc., Interface 11, 20140948 (2014).
[Crossref]

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Suppression of Brewster delocalization anomalies in an alternating isotropic-birefringent random layered medium,” Phys. Rev. B 88, 041105 (2013).
[Crossref]

Phung, D. K.

Pinheiro, F. A.

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 (2010).
[Crossref]

Pustilnik, M.

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53, 7413–7416 (1996).
[Crossref]

Rajan, P.

K. Y. Bliokh, S. A. Gredeskul, P. Rajan, I. V. Shadrivov, and Y. S. Kivshar, “Nonreciprocal Anderson localization in magneto-optical random structures,” Phys. Rev. B 85, 014205 (2012).
[Crossref]

Rammal, R.

R. Rammal and B. Doucot, “Invariant imbedding approach to localization. I. General framework and basic equations,” J. Physiol. 48, 509–526 (1987).

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]

Roberts, N. W.

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Disordered animal multilayer reflectors and the localization of light,” J. R. Soc., Interface 11, 20140948 (2014).
[Crossref]

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Suppression of Brewster delocalization anomalies in an alternating isotropic-birefringent random layered medium,” Phys. Rev. B 88, 041105 (2013).
[Crossref]

Rotermund, F.

K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses,” Opt. Express 16, 1150–1164 (2008).
[Crossref] [PubMed]

K. Kim, F. Rotermund, and H. Lim, “Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: exact calculation based on the invariant imbedding method,” Phys. Rev. B 77, 024203 (2008).
[Crossref]

K. Kim, F. Rotermund, D.-H. Lee, and H. Lim, “Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: random phase approximation,” Wave Random Complex 17, 43–53 (2007).
[Crossref]

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, 045122 (2012).
[Crossref]

S. A. Gredeskul, Y. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Y. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media (Review Article),” Low Temp. Phys. 38, 570–602 (2012).
[Crossref]

K. Y. Bliokh, S. A. Gredeskul, P. Rajan, I. V. Shadrivov, and Y. S. Kivshar, “Nonreciprocal Anderson localization in magneto-optical random structures,” Phys. Rev. B 85, 014205 (2012).
[Crossref]

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[Crossref] [PubMed]

Sheng, P.

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] [PubMed]

Shin, S. Y.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

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] [PubMed]

Skipetrov, S. E.

S. E. Skipetrov and I. M. Sokolov, “Absence of Anderson localization of light in a random ensemble of point scatterers,” Phys. Rev. Lett. 112, 023905 (2014).
[Crossref] [PubMed]

Sokolov, I. M.

S. E. Skipetrov and I. M. Sokolov, “Absence of Anderson localization of light in a random ensemble of point scatterers,” Phys. Rev. Lett. 112, 023905 (2014).
[Crossref] [PubMed]

Song, H. C.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

Sperling, T.

T. Sperling, W. Bührer, M. Ackermann, C. M. Aegerter, and G. Maret, “Probing Anderson localization of light by weak nonlinear effects,“ New J. Phys. 16, 112001 (2014).
[Crossref]

Torres-Herrera, E. J.

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in a matched quater stack with metamaterials,” New J. Phys. 15, 055014 (2013).
[Crossref]

Vinogradov, A. P.

A. I. Ignatov, A. M. Merzlikin, A. P. Vinogradov, and A. A. Lisyansky, “Effect of polarization upon light localization in random layered magnetodielectric media,” Phys. Rev. E 83, 224205 (2011).
[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] [PubMed]

Yamilov, A.

A. Basiri, Y. Bromberg, A. Yamilov, H. Cao, and T. Kottos, “Light localization induced by a random imaginary refractive index,” Phys. Rev. A 90, 043815 (2014).
[Crossref]

Yurkevich, I.

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53, 7413–7416 (1996).
[Crossref]

Europhys. Lett. (1)

K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69, 207–213 (2005).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

C.-S. Kee, J.-E. Kim, H. Y. Park, and H. Lim, “Roles of wave impedance and refractive index in photonic crystals with magnetic and dielectric properties,” IEEE Trans. Microwave Theory Tech. 47, 2148–2150 (1999).
[Crossref]

J. Korean Phys. Soc. (1)

K. Kim, H. Lim, and D.-H. Lee, “Invariant imbedding equations for electromagnetic waves in stratified magnetic media: applications to one-dimensional photonic crystals,” J. Korean Phys. Soc. 39, L956–L960 (2001).

J. Phys. A (1)

J. M. Luck, “Non-monotonic disorder-induced enhanced tunnelling,” J. Phys. A 37, 259–271 (2004).
[Crossref]

J. Phys.: Condens. Matter (1)

J. Heinrichs, “Enhanced quantum tunnelling induced by disorder,” J. Phys.: Condens. Matter 20, 395215 (2008).

J. Physiol. (1)

R. Rammal and B. Doucot, “Invariant imbedding approach to localization. I. General framework and basic equations,” J. Physiol. 48, 509–526 (1987).

J. R. Soc., Interface (1)

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Disordered animal multilayer reflectors and the localization of light,” J. R. Soc., Interface 11, 20140948 (2014).
[Crossref]

Low Temp. Phys. (1)

S. A. Gredeskul, Y. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Y. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media (Review Article),” Low Temp. Phys. 38, 570–602 (2012).
[Crossref]

Nat. Nanotechnol. (1)

S. Mookherjea, J. R. Ong, X. Luo, and L. Guo-Qiang, “Electronic control of optical Anderson localization modes,” Nat. Nanotechnol. 9, 365–371 (2014).
[Crossref] [PubMed]

New J. Phys. (2)

T. Sperling, W. Bührer, M. Ackermann, C. M. Aegerter, and G. Maret, “Probing Anderson localization of light by weak nonlinear effects,“ New J. Phys. 16, 112001 (2014).
[Crossref]

E. J. Torres-Herrera, F. M. Izrailev, and N. M. Makarov, “Non-conventional Anderson localization in a matched quater stack with metamaterials,” New J. Phys. 15, 055014 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. (1)

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. 59, 4695–4698 (1999).

Phys. Rev. A (1)

A. Basiri, Y. Bromberg, A. Yamilov, H. Cao, and T. Kottos, “Light localization induced by a random imaginary refractive index,” Phys. Rev. A 90, 043815 (2014).
[Crossref]

Phys. Rev. B (7)

K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58, 6153–6160 (1998).
[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, 045122 (2012).
[Crossref]

T. M. Jordan, J. C. Partridge, and N. W. Roberts, “Suppression of Brewster delocalization anomalies in an alternating isotropic-birefringent random layered medium,” Phys. Rev. B 88, 041105 (2013).
[Crossref]

K. Y. Bliokh, S. A. Gredeskul, P. Rajan, I. V. Shadrivov, and Y. S. Kivshar, “Nonreciprocal Anderson localization in magneto-optical random structures,” Phys. Rev. B 85, 014205 (2012).
[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 (2010).
[Crossref]

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53, 7413–7416 (1996).
[Crossref]

K. Kim, F. Rotermund, and H. Lim, “Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: exact calculation based on the invariant imbedding method,” Phys. Rev. B 77, 024203 (2008).
[Crossref]

Phys. Rev. E (2)

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]

A. I. Ignatov, A. M. Merzlikin, A. P. Vinogradov, and A. A. Lisyansky, “Effect of polarization upon light localization in random layered magnetodielectric media,” Phys. Rev. E 83, 224205 (2011).
[Crossref]

Phys. Rev. Lett. (3)

I. V. Shadrivov, K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, and Y. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[Crossref] [PubMed]

S. E. Skipetrov and I. M. Sokolov, “Absence of Anderson localization of light in a random ensemble of point scatterers,” Phys. Rev. Lett. 112, 023905 (2014).
[Crossref] [PubMed]

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] [PubMed]

Prog. Opt. (1)

V. I. Klyatskin, “The imbedding method in statistical boundary-value wave problems,” Prog. Opt. 33, 1–127 (1994).

Sov. Phys. JETP (1)

E. A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP 20, 1290–1294 (1965).

Wave Random Complex (1)

K. Kim, F. Rotermund, D.-H. Lee, and H. Lim, “Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: random phase approximation,” Wave Random Complex 17, 43–53 (2007).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 (a) Normalized localization length, , and (b) its inverse versus incident angle, θ, when a = b = 1 and g = 0.001, 0.01. Due to symmetry, the localization length is identical for both s and p waves. In (a), the numerical results obtained using the invariant imbedding method are compared with the approximate analytical formula, Eq. (23).
Fig. 2
Fig. 2 (a) Normalized localization length and (b) its inverse plotted versus incident angle when a = 2 and b = 1. The disorder parameter g is equal to 0.001 and 0.01. The localization length is identical for both s and p waves. In (a), the numerical results obtained using the invariant imbedding method are compared with the approximate analytical formula, Eq. (24).
Fig. 3
Fig. 3 Normalized localization length versus incident angle in a log-log plot for three different sets of values of a and b, when g = 0.01. The localization length is identical for both s and p waves in all cases. The results obtained using the invariant imbedding method are compared with the approximate analytical formula, Eq. (24).
Fig. 4
Fig. 4 Normalized localization length versus disorder parameter, g, in a log-log plot, when a = b = 1 and θ = 5°, 50°. The localization length is identical for both s and p waves. The results obtained using the invariant imbedding method are compared with the approximate analytical formula, Eq. (24).
Fig. 5
Fig. 5 Disorder-averaged transmittance, 〈T〉, versus incident angle, when a = b = 1, kL = 40 and g = 0.001, 0.01. Due to symmetry, the results are identical for both s and p waves.
Fig. 6
Fig. 6 Disorder-averaged transmittance versus incident angle, when a = 2, b = 1, kL = 40 and g = 0.001, 0.01. The results for the s wave case are compared with those for the p wave case.

Equations (25)

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

d 2 E d z 2 1 μ ( z ) d μ d z d E d z + [ k 0 2 ε ( z ) μ ( z ) q 2 ] E = 0 ,
d 2 H d z 2 1 ε ( z ) d ε d z d H d z + [ k 0 2 ε ( z ) μ ( z ) q 2 ] H = 0.
ε = ε ¯ + δ ε ( z ) , μ = μ ¯ + δ μ ( z ) ,
n 2 = ( ε ¯ + δ ε ) ( μ ¯ + δ μ ) = ε ¯ μ ¯ ( 1 + δ ε ε ¯ + δ μ μ ¯ + δ ε ε ¯ δ μ μ ¯ ) , Z 2 = μ ¯ + δ μ ε ¯ + δ ε = μ ¯ ε ¯ 1 + δ μ μ ¯ 1 + δ ε ε ¯ .
δ ε ε ¯ = δ μ μ ¯ .
n 2 ε ¯ μ ¯ ( 1 + 2 δ ε ε ¯ ) , Z 2 = μ ¯ ε ¯ ,
ε ˜ ε ε 1 = a + δ ε ˜ ( z ) , μ ˜ μ μ 1 = b + δ μ ˜ ( z ) ,
a = ε ¯ ε 1 , b = μ ¯ μ 1 , δ ε ˜ ( z ) = δ ε ( z ) ε 1 , δ μ ˜ ( z ) = δ μ ( z ) μ 1 .
δ μ ˜ = b a δ ε ˜ .
δ ε ˜ ( z ) δ ε ˜ ( z ) = g ˜ δ ( z z ) , δ ε ˜ ( z ) = 0 ,
H ˜ ( x , z ) = { [ e i p ( L z ) + r e i p ( z L ) ] e i q x , z > L t e i p z + i q x , z < 0 .
d r d l = 2 i p ε ˜ r + i 2 p [ μ ˜ ε ˜ + ( μ ˜ 1 ε ˜ ) tan 2 θ ] ( 1 + r ) 2 , d t d l = i p ε ˜ t + i 2 p [ μ ˜ ε ˜ + ( μ ˜ 1 ε ˜ ) tan 2 θ ] ( 1 + r ) t ,
ξ = lim L ( L ln T ) .
d r d l = 2 i p μ ˜ r + i 2 p [ ε ˜ μ ˜ + ( ε ˜ 1 μ ˜ ) tan 2 θ ] ( 1 + r ) 2 , d t d l = i p μ ˜ t + i 2 p [ ε ˜ μ ˜ + ( ε ˜ 1 μ ˜ ) tan 2 θ ] ( 1 + r ) t .
1 ε ˜ = 1 a + δ ε ˜ 1 a δ ε ˜ a 2 , 1 μ ˜ = 1 b + δ μ ˜ 1 b δ μ ˜ b 2 .
1 i k cos θ d r d l = 2 ( a + δ ε ˜ ) r + 1 2 [ b cos 2 θ + δ μ ˜ cos 2 θ ( a + tan 2 θ a ) ( 1 tan 2 θ a 2 ) δ ε ˜ ] ( 1 + r ) 2 , 1 i k cos θ d t d l = ( a + δ ε ˜ ) t + 1 2 [ b cos 2 θ + δ μ ˜ cos 2 θ ( a + tan 2 θ a ) ( 1 tan 2 θ a 2 ) δ ε ˜ ] ( 1 + r ) t .
1 i k cos θ d r d l = 2 ( a + δ ε ˜ ) r + 1 2 [ b cos 2 θ a tan 2 θ a + ( b a cos 2 θ 1 + tan 2 θ a 2 ) δ ε ˜ ] ( 1 + r ) 2 , 1 i k cos θ d t d l = ( a + δ ε ˜ ) t + 1 2 [ b cos 2 θ a tan 2 θ a + ( b a cos 2 θ 1 + tan 2 θ a 2 ) δ ε ˜ ] ( 1 + r ) t .
1 k d Z n n ˜ d l = i ( n n ˜ ) cos θ ( a tan 2 θ a + b cos 2 θ ) Z n n ˜ i 2 n C 0 ( Z n + 1 , n ˜ + Z n 1 , n ˜ ) + i 2 n ˜ C 0 ( Z n , n ˜ + 1 + Z n , n ˜ 1 ) g { [ 2 ( 1 + tan 2 θ a 2 ) ( n n ˜ ) 2 + ( 1 tan 2 θ a 2 ) 2 ( n 2 + n ˜ 2 ) ] cos 2 θ + b a [ ( 3 n 2 4 n n ˜ + 3 n ˜ 2 ) ( 2 tan 2 θ a 2 + b a cos 2 θ ) + 2 n 2 + 2 n ˜ 2 8 n n ˜ ] } Z n n ˜ + g ( 2 n 2 n ˜ + 1 ) n C 1 Z n + 1 , n ˜ g ( 2 n 2 n ˜ 1 ) n ˜ C 1 Z n , n ˜ + 1 + g ( 2 n 2 n ˜ 1 ) n C 1 Z n 1 , n ˜ g ( 2 n 2 n ˜ + 1 ) n ˜ C 1 Z n , n ˜ 1 g 2 n ( n + 1 ) C 2 Z n + 2 , n ˜ g 2 n ˜ ( n ˜ + 1 ) C 2 Z n , n ˜ + 2 g 2 n ( n 1 ) C 2 Z n 2 , n ˜ g 2 n ˜ ( n ˜ 1 ) C 2 Z n , n ˜ 2 + g n n ˜ C 2 ( Z n + 1 , n ˜ + 1 + Z n 1 , n ˜ 1 + Z n + 1 , n ˜ 1 + Z n 1 , n ˜ + 1 ) ,
g = g ˜ k 4
C 0 = ( a + tan 2 θ a b cos 2 θ ) cos θ , C 1 = ( 1 tan 2 θ a 4 ) cos 2 θ b a ( 2 tan 2 θ a 2 + b a cos 2 θ ) , C 2 = ( 1 tan 2 θ a 2 b a cos 2 θ ) 2 cos 2 θ .
1 k d ln T d l = g C 2 i 2 C 0 ( Z 10 + Z 01 ) + g C 1 ( Z 10 + Z 01 ) g 2 C 2 ( Z 20 + Z 02 ) ,
1 k ξ = g C 2 + Re [ ( i C 0 2 g C 1 ) Z 10 ( l ) + g C 2 Z 20 ( l ) ]
1 k ξ 4 g sin 2 θ tan 2 θ ,
k ξ a 3 b 4 g θ 4 ,
ξ g ˜ 1 k 2 g ˜ 1 ω 2 ,

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