Abstract

The interplay between Anderson localization and total internal reflection of electromagnetic waves incident near the critical angle on randomly-stratified dielectric media is investigated theoretically. Using an exact analytical formula for the localization length for the Schrödinger equation with a Gaussian δ-correlated random potential in one dimension, we show that when the incident angle is equal to the critical angle, the localization length for an incident s wave of wavelength λ is directly proportional to λ4/3 throughout the entire range of the wavelength, for any value of the disorder strength. This result is different from that of a recent study reporting that the localization length at the critical incident angle for a binary multilayer system with random thickness variations is proportional to λ in the large λ region. We also discuss the characteristic behaviors of the localization length or the tunneling decay length for all other incident angles. Our results are confirmed by an independent numerical calculation based on the invariant imbedding method.

© 2017 Optical Society of America

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    [Crossref]
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    [Crossref]
  3. M. V. Berry and S. Klein, “Transparent mirrors: rays, waves and localization,” Eur. J. Phys. 18(3), 222–228 (1994).
    [Crossref]
  4. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: Absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
    [Crossref]
  5. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
    [Crossref] [PubMed]
  6. 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, 891–894 (2008).
    [Crossref] [PubMed]
  7. 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,” Low Temp. Phys. 38(7), 570–602 (2012).
    [Crossref]
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  12. B. I. Halperin, “Green’s functions for a particle in a one-dimensional random potential,” Phys. Rev. 139(1A), A104–A117 (1965).
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  13. B. Derrida and E. Gardner, “Lyapunov exponent of the one dimensional Anderson model: weak disorder expansions,” J. Phys. (Paris) 45(8), 1283–1295 (1984).
    [Crossref]
  14. J. M. Luck, “Non-monotonic disorder-induced enhanced tunnelling,” J. Phys. A: Math. Gen. 37(1), 259–271 (2004).
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  15. J. P. Bouchaud and P. Le Doussal, “Intermittency in random optical layers at total reflection,” J. Phys. A: Math. Gen. 19(5), 797–810 (1986).
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  16. E. Bouchaud and M. Daoud, “Reflection of light by a random layered system,” J. Phys. (Paris) 47(9), 1467–1475 (1986).
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  17. H. H. Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7, 12927 (2016).
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  20. 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]
  21. F. M. Izrailev and A. A. Krokhin, “Localization and the mobility edge in one-dimensional potentials with correlated disorder,” Phys. Rev. Lett. 82(20), 4062–4065 (1999).
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  22. B. P. Nguyen and K. Kim, “Influence of weak nonlinearity on the 1D Anderson model with long-range correlated disorder,”, Eur. Phys. J. B 84(1), 79–82 (2011).
    [Crossref]
  23. W. Choi, C. Yin, I. R. Hooper, W. L. Barnes, and J. Bertolotti, “Absence of Anderson localization in certain random lattices,” Phys. Rev. E 96(2), 022122 (2017).
    [Crossref] [PubMed]
  24. D. H. Dunlap, H.-L. Wu, and P. W. Phillips, “Absence of localization in a random-dimer model,” Phys. Rev. Lett. 65(1), 88–91 (1990).
    [Crossref] [PubMed]
  25. 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(19), 193902 (2007).
    [Crossref]
  26. K. G. Wilson and J. Kogut, “The renormalization group and the ∊ expansion,” Phys. Rep. 12C(2), 75–200 (1974).
    [Crossref]
  27. V. S. Dotsenko, “Critical phenomena and quenched disorder,” Phys. Usp. 38(5), 457–497 (1995).
    [Crossref]
  28. A. Weinrib and B. I. Halperin, “Critical phenomena with long-range-correlated quenched disorder,” Phys. Rev. B 27(1), 413–427 (1983).
    [Crossref]
  29. V. V. Prudnikov, P. V. Prudnikov, and A. A. Fedorenko, “Field-theory approach to critical behavior of systems with long-range correlated defects,” Phys. Rev. B 62(13), 8777–8786 (2000).
    [Crossref]
  30. P. C. Hohenberg and B. I. Halperin, “Theory of dynamic critical phenomena,” Rev. Mod. Phys. 49(3), 435–479 (1977).
    [Crossref]
  31. M. P. A. Fisher and G. Grinstein, “Quantum critical phenomena in charged superconductors,” Phys. Rev. Lett. 60(3), 208–211 (1988).
    [Crossref] [PubMed]
  32. V. I. Klyatskin, “The imbedding method in statistical boundary-value wave problems,” Prog. Opt. 33, 1–127 (1994).
    [Crossref]
  33. 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(6), L956–L960 (2001).
  34. K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69(2), 207–213 (2005).
    [Crossref]
  35. 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(2), 1150–1164 (2008).
    [Crossref] [PubMed]
  36. S. Kim and K. Kim, “Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic media,” J. Opt. 18(6), 065605 (2016).
    [Crossref]
  37. E. A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP 20(5), 1290–1294 (1965).
  38. K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58(10), 6153–6160 (1998).
    [Crossref]
  39. V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53(11), 7413–7416 (1996).
    [Crossref]
  40. 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(2), 024203 (2008).
    [Crossref]
  41. J. Heinrichs, “Enhanced quantum tunnelling induced by disorder,” J. Phys.: Condens. Matter 20(39), 395215 (2008).

2017 (3)

A. Fang, Z. Q. Zhang, S. G. Louie, and C. T. Chan, “Anomalous Anderson localization behaviors in disordered pseudospin systems,” Proc. Natl. Acad. Sci. U.S.A. 114(16), 4087–4092 (2017).
[Crossref] [PubMed]

H. H. Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref] [PubMed]

W. Choi, C. Yin, I. R. Hooper, W. L. Barnes, and J. Bertolotti, “Absence of Anderson localization in certain random lattices,” Phys. Rev. E 96(2), 022122 (2017).
[Crossref] [PubMed]

2016 (2)

H. H. Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7, 12927 (2016).
[Crossref]

S. Kim and K. Kim, “Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic media,” J. Opt. 18(6), 065605 (2016).
[Crossref]

2012 (2)

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,” Low Temp. Phys. 38(7), 570–602 (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]

2011 (1)

B. P. Nguyen and K. Kim, “Influence of weak nonlinearity on the 1D Anderson model with long-range correlated disorder,”, Eur. Phys. J. B 84(1), 79–82 (2011).
[Crossref]

2009 (1)

D. Dimitropoulos and B. Jalali, “Stochastic differential equation approach for waves in a random medium,” Phys. Rev. E 79(3), 036606 (2009).
[Crossref]

2008 (4)

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, 891–894 (2008).
[Crossref] [PubMed]

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(2), 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(2), 024203 (2008).
[Crossref]

J. Heinrichs, “Enhanced quantum tunnelling induced by disorder,” J. Phys.: Condens. Matter 20(39), 395215 (2008).

2007 (2)

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(19), 193902 (2007).
[Crossref]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

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(2), 207–213 (2005).
[Crossref]

2004 (1)

J. M. Luck, “Non-monotonic disorder-induced enhanced tunnelling,” J. Phys. A: Math. Gen. 37(1), 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(6), L956–L960 (2001).

2000 (1)

V. V. Prudnikov, P. V. Prudnikov, and A. A. Fedorenko, “Field-theory approach to critical behavior of systems with long-range correlated defects,” Phys. Rev. B 62(13), 8777–8786 (2000).
[Crossref]

1999 (1)

F. M. Izrailev and A. A. Krokhin, “Localization and the mobility edge in one-dimensional potentials with correlated disorder,” Phys. Rev. Lett. 82(20), 4062–4065 (1999).
[Crossref]

1998 (1)

K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58(10), 6153–6160 (1998).
[Crossref]

1996 (1)

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53(11), 7413–7416 (1996).
[Crossref]

1995 (1)

V. S. Dotsenko, “Critical phenomena and quenched disorder,” Phys. Usp. 38(5), 457–497 (1995).
[Crossref]

1994 (3)

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

J. B. Pendry, “Symmetry and transport of waves in one-dimensional disordered systems,” Adv. Phys. 43(4), 461–542 (1994).
[Crossref]

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves and localization,” Eur. J. Phys. 18(3), 222–228 (1994).
[Crossref]

1990 (1)

D. H. Dunlap, H.-L. Wu, and P. W. Phillips, “Absence of localization in a random-dimer model,” Phys. Rev. Lett. 65(1), 88–91 (1990).
[Crossref] [PubMed]

1988 (1)

M. P. A. Fisher and G. Grinstein, “Quantum critical phenomena in charged superconductors,” Phys. Rev. Lett. 60(3), 208–211 (1988).
[Crossref] [PubMed]

1986 (2)

J. P. Bouchaud and P. Le Doussal, “Intermittency in random optical layers at total reflection,” J. Phys. A: Math. Gen. 19(5), 797–810 (1986).
[Crossref]

E. Bouchaud and M. Daoud, “Reflection of light by a random layered system,” J. Phys. (Paris) 47(9), 1467–1475 (1986).
[Crossref]

1984 (2)

B. Derrida and E. Gardner, “Lyapunov exponent of the one dimensional Anderson model: weak disorder expansions,” J. Phys. (Paris) 45(8), 1283–1295 (1984).
[Crossref]

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
[Crossref]

1983 (1)

A. Weinrib and B. I. Halperin, “Critical phenomena with long-range-correlated quenched disorder,” Phys. Rev. B 27(1), 413–427 (1983).
[Crossref]

1979 (1)

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: Absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

1977 (1)

P. C. Hohenberg and B. I. Halperin, “Theory of dynamic critical phenomena,” Rev. Mod. Phys. 49(3), 435–479 (1977).
[Crossref]

1974 (1)

K. G. Wilson and J. Kogut, “The renormalization group and the ∊ expansion,” Phys. Rep. 12C(2), 75–200 (1974).
[Crossref]

1965 (2)

B. I. Halperin, “Green’s functions for a particle in a one-dimensional random potential,” Phys. Rev. 139(1A), A104–A117 (1965).
[Crossref]

E. A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP 20(5), 1290–1294 (1965).

1960 (1)

H. L. Frisch and S. P. Lloyd, “Electron levels in a one-dimensional random lattice,” Phys. Rev. 120(4), 1175–1189 (1960).
[Crossref]

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Abrahams, E.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: Absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

Anderson, P. W.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: Absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Ankonina, G.

H. H. Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref] [PubMed]

Asatryan, A. A.

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,” Low Temp. Phys. 38(7), 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, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[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, 891–894 (2008).
[Crossref] [PubMed]

Barnes, W. L.

W. Choi, C. Yin, I. R. Hooper, W. L. Barnes, and J. Bertolotti, “Absence of Anderson localization in certain random lattices,” Phys. Rev. E 96(2), 022122 (2017).
[Crossref] [PubMed]

Bartal, G.

H. H. Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref] [PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[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, 891–894 (2008).
[Crossref] [PubMed]

Berry, M. V.

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves and localization,” Eur. J. Phys. 18(3), 222–228 (1994).
[Crossref]

Bertolotti, J.

W. Choi, C. Yin, I. R. Hooper, W. L. Barnes, and J. Bertolotti, “Absence of Anderson localization in certain random lattices,” Phys. Rev. E 96(2), 022122 (2017).
[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, 891–894 (2008).
[Crossref] [PubMed]

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,” Low Temp. Phys. 38(7), 570–602 (2012).
[Crossref]

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,” Low Temp. Phys. 38(7), 570–602 (2012).
[Crossref]

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, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref]

Bouchaud, E.

E. Bouchaud and M. Daoud, “Reflection of light by a random layered system,” J. Phys. (Paris) 47(9), 1467–1475 (1986).
[Crossref]

Bouchaud, J. P.

J. P. Bouchaud and P. Le Doussal, “Intermittency in random optical layers at total reflection,” J. Phys. A: Math. Gen. 19(5), 797–810 (1986).
[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, 891–894 (2008).
[Crossref] [PubMed]

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, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref]

Chan, C. T.

A. Fang, Z. Q. Zhang, S. G. Louie, and C. T. Chan, “Anomalous Anderson localization behaviors in disordered pseudospin systems,” Proc. Natl. Acad. Sci. U.S.A. 114(16), 4087–4092 (2017).
[Crossref] [PubMed]

Choi, W.

W. Choi, C. Yin, I. R. Hooper, W. L. Barnes, and J. Bertolotti, “Absence of Anderson localization in certain random lattices,” Phys. Rev. E 96(2), 022122 (2017).
[Crossref] [PubMed]

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, 891–894 (2008).
[Crossref] [PubMed]

Daoud, M.

E. Bouchaud and M. Daoud, “Reflection of light by a random layered system,” J. Phys. (Paris) 47(9), 1467–1475 (1986).
[Crossref]

Derrida, B.

B. Derrida and E. Gardner, “Lyapunov exponent of the one dimensional Anderson model: weak disorder expansions,” J. Phys. (Paris) 45(8), 1283–1295 (1984).
[Crossref]

Dimitropoulos, D.

D. Dimitropoulos and B. Jalali, “Stochastic differential equation approach for waves in a random medium,” Phys. Rev. E 79(3), 036606 (2009).
[Crossref]

Dotsenko, V. S.

V. S. Dotsenko, “Critical phenomena and quenched disorder,” Phys. Usp. 38(5), 457–497 (1995).
[Crossref]

Dunlap, D. H.

D. H. Dunlap, H.-L. Wu, and P. W. Phillips, “Absence of localization in a random-dimer model,” Phys. Rev. Lett. 65(1), 88–91 (1990).
[Crossref] [PubMed]

Fang, A.

A. Fang, Z. Q. Zhang, S. G. Louie, and C. T. Chan, “Anomalous Anderson localization behaviors in disordered pseudospin systems,” Proc. Natl. Acad. Sci. U.S.A. 114(16), 4087–4092 (2017).
[Crossref] [PubMed]

Fedorenko, A. A.

V. V. Prudnikov, P. V. Prudnikov, and A. A. Fedorenko, “Field-theory approach to critical behavior of systems with long-range correlated defects,” Phys. Rev. B 62(13), 8777–8786 (2000).
[Crossref]

Fisher, M. P. A.

M. P. A. Fisher and G. Grinstein, “Quantum critical phenomena in charged superconductors,” Phys. Rev. Lett. 60(3), 208–211 (1988).
[Crossref] [PubMed]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Freilikher, V.

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53(11), 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,” Low Temp. Phys. 38(7), 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, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref]

Frisch, H. L.

H. L. Frisch and S. P. Lloyd, “Electron levels in a one-dimensional random lattice,” Phys. Rev. 120(4), 1175–1189 (1960).
[Crossref]

Gardner, E.

B. Derrida and E. Gardner, “Lyapunov exponent of the one dimensional Anderson model: weak disorder expansions,” J. Phys. (Paris) 45(8), 1283–1295 (1984).
[Crossref]

Genack, A. Z.

H. H. Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref] [PubMed]

H. H. Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7, 12927 (2016).
[Crossref]

Gredeskul, S. A.

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,” Low Temp. Phys. 38(7), 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, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref]

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

Grinstein, G.

M. P. A. Fisher and G. Grinstein, “Quantum critical phenomena in charged superconductors,” Phys. Rev. Lett. 60(3), 208–211 (1988).
[Crossref] [PubMed]

Halperin, B. I.

A. Weinrib and B. I. Halperin, “Critical phenomena with long-range-correlated quenched disorder,” Phys. Rev. B 27(1), 413–427 (1983).
[Crossref]

P. C. Hohenberg and B. I. Halperin, “Theory of dynamic critical phenomena,” Rev. Mod. Phys. 49(3), 435–479 (1977).
[Crossref]

B. I. Halperin, “Green’s functions for a particle in a one-dimensional random potential,” Phys. Rev. 139(1A), A104–A117 (1965).
[Crossref]

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, 891–894 (2008).
[Crossref] [PubMed]

Heinrichs, J.

J. Heinrichs, “Enhanced quantum tunnelling induced by disorder,” J. Phys.: Condens. Matter 20(39), 395215 (2008).

Hohenberg, P. C.

P. C. Hohenberg and B. I. Halperin, “Theory of dynamic critical phenomena,” Rev. Mod. Phys. 49(3), 435–479 (1977).
[Crossref]

Hooper, I. R.

W. Choi, C. Yin, I. R. Hooper, W. L. Barnes, and J. Bertolotti, “Absence of Anderson localization in certain random lattices,” Phys. Rev. E 96(2), 022122 (2017).
[Crossref] [PubMed]

Izrailev, F. M.

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]

F. M. Izrailev and A. A. Krokhin, “Localization and the mobility edge in one-dimensional potentials with correlated disorder,” Phys. Rev. Lett. 82(20), 4062–4065 (1999).
[Crossref]

Jalali, B.

D. Dimitropoulos and B. Jalali, “Stochastic differential equation approach for waves in a random medium,” Phys. Rev. E 79(3), 036606 (2009).
[Crossref]

John, S.

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
[Crossref]

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, 891–894 (2008).
[Crossref] [PubMed]

Kaminer, I.

H. H. Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7, 12927 (2016).
[Crossref]

Kim, K.

S. Kim and K. Kim, “Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic media,” J. Opt. 18(6), 065605 (2016).
[Crossref]

B. P. Nguyen and K. Kim, “Influence of weak nonlinearity on the 1D Anderson model with long-range correlated disorder,”, Eur. Phys. J. B 84(1), 79–82 (2011).
[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(2), 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(2), 1150–1164 (2008).
[Crossref] [PubMed]

K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69(2), 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(6), L956–L960 (2001).

K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58(10), 6153–6160 (1998).
[Crossref]

Kim, S.

S. Kim and K. Kim, “Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic media,” J. Opt. 18(6), 065605 (2016).
[Crossref]

Kivshar, Y. S.

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,” Low Temp. Phys. 38(7), 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, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref]

Klein, S.

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves and localization,” Eur. J. Phys. 18(3), 222–228 (1994).
[Crossref]

Klyatskin, V. I.

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

Kogut, J.

K. G. Wilson and J. Kogut, “The renormalization group and the ∊ expansion,” Phys. Rep. 12C(2), 75–200 (1974).
[Crossref]

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]

F. M. Izrailev and A. A. Krokhin, “Localization and the mobility edge in one-dimensional potentials with correlated disorder,” Phys. Rev. Lett. 82(20), 4062–4065 (1999).
[Crossref]

Le Doussal, P.

J. P. Bouchaud and P. Le Doussal, “Intermittency in random optical layers at total reflection,” J. Phys. A: Math. Gen. 19(5), 797–810 (1986).
[Crossref]

Lee, D.-H.

K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69(2), 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(6), L956–L960 (2001).

Licciardello, D. C.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: Absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

Lifshits, I. M.

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

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(2), 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(2), 1150–1164 (2008).
[Crossref] [PubMed]

K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69(2), 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(6), L956–L960 (2001).

Lloyd, S. P.

H. L. Frisch and S. P. Lloyd, “Electron levels in a one-dimensional random lattice,” Phys. Rev. 120(4), 1175–1189 (1960).
[Crossref]

Louie, S. G.

A. Fang, Z. Q. Zhang, S. G. Louie, and C. T. Chan, “Anomalous Anderson localization behaviors in disordered pseudospin systems,” Proc. Natl. Acad. Sci. U.S.A. 114(16), 4087–4092 (2017).
[Crossref] [PubMed]

Luck, J. M.

J. M. Luck, “Non-monotonic disorder-induced enhanced tunnelling,” J. Phys. A: Math. Gen. 37(1), 259–271 (2004).
[Crossref]

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, 891–894 (2008).
[Crossref] [PubMed]

Lumer, Y.

H. H. Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref] [PubMed]

Makarov, N. M.

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]

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, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref]

Nguyen, B. P.

B. P. Nguyen and K. Kim, “Influence of weak nonlinearity on the 1D Anderson model with long-range correlated disorder,”, Eur. Phys. J. B 84(1), 79–82 (2011).
[Crossref]

Novikov, E. A.

E. A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP 20(5), 1290–1294 (1965).

Pastur, L. A.

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

Pendry, J. B.

J. B. Pendry, “Symmetry and transport of waves in one-dimensional disordered systems,” Adv. Phys. 43(4), 461–542 (1994).
[Crossref]

Phillips, P. W.

D. H. Dunlap, H.-L. Wu, and P. W. Phillips, “Absence of localization in a random-dimer model,” Phys. Rev. Lett. 65(1), 88–91 (1990).
[Crossref] [PubMed]

Phung, D. K.

Prudnikov, P. V.

V. V. Prudnikov, P. V. Prudnikov, and A. A. Fedorenko, “Field-theory approach to critical behavior of systems with long-range correlated defects,” Phys. Rev. B 62(13), 8777–8786 (2000).
[Crossref]

Prudnikov, V. V.

V. V. Prudnikov, P. V. Prudnikov, and A. A. Fedorenko, “Field-theory approach to critical behavior of systems with long-range correlated defects,” Phys. Rev. B 62(13), 8777–8786 (2000).
[Crossref]

Pustilnik, M.

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53(11), 7413–7416 (1996).
[Crossref]

Ramakrishnan, T. V.

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: Absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

Rotermund, F.

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(2), 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(2), 1150–1164 (2008).
[Crossref] [PubMed]

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, 891–894 (2008).
[Crossref] [PubMed]

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Segev, M.

H. H. Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref] [PubMed]

H. H. Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7, 12927 (2016).
[Crossref]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Shadrivov, I. V.

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,” Low Temp. Phys. 38(7), 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, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref]

Sheinfux, H. H.

H. H. Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref] [PubMed]

H. H. Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7, 12927 (2016).
[Crossref]

Weinrib, A.

A. Weinrib and B. I. Halperin, “Critical phenomena with long-range-correlated quenched disorder,” Phys. Rev. B 27(1), 413–427 (1983).
[Crossref]

Wilson, K. G.

K. G. Wilson and J. Kogut, “The renormalization group and the ∊ expansion,” Phys. Rep. 12C(2), 75–200 (1974).
[Crossref]

Wu, H.-L.

D. H. Dunlap, H.-L. Wu, and P. W. Phillips, “Absence of localization in a random-dimer model,” Phys. Rev. Lett. 65(1), 88–91 (1990).
[Crossref] [PubMed]

Yin, C.

W. Choi, C. Yin, I. R. Hooper, W. L. Barnes, and J. Bertolotti, “Absence of Anderson localization in certain random lattices,” Phys. Rev. E 96(2), 022122 (2017).
[Crossref] [PubMed]

Yurkevich, I.

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53(11), 7413–7416 (1996).
[Crossref]

Zhang, Z. Q.

A. Fang, Z. Q. Zhang, S. G. Louie, and C. T. Chan, “Anomalous Anderson localization behaviors in disordered pseudospin systems,” Proc. Natl. Acad. Sci. U.S.A. 114(16), 4087–4092 (2017).
[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, 891–894 (2008).
[Crossref] [PubMed]

Adv. Phys. (1)

J. B. Pendry, “Symmetry and transport of waves in one-dimensional disordered systems,” Adv. Phys. 43(4), 461–542 (1994).
[Crossref]

Eur. J. Phys. (1)

M. V. Berry and S. Klein, “Transparent mirrors: rays, waves and localization,” Eur. J. Phys. 18(3), 222–228 (1994).
[Crossref]

Eur. Phys. J. B (1)

B. P. Nguyen and K. Kim, “Influence of weak nonlinearity on the 1D Anderson model with long-range correlated disorder,”, Eur. Phys. J. B 84(1), 79–82 (2011).
[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(2), 207–213 (2005).
[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(6), L956–L960 (2001).

J. Opt. (1)

S. Kim and K. Kim, “Invariant imbedding theory of wave propagation in arbitrarily inhomogeneous stratified bi-isotropic media,” J. Opt. 18(6), 065605 (2016).
[Crossref]

J. Phys. (Paris) (2)

B. Derrida and E. Gardner, “Lyapunov exponent of the one dimensional Anderson model: weak disorder expansions,” J. Phys. (Paris) 45(8), 1283–1295 (1984).
[Crossref]

E. Bouchaud and M. Daoud, “Reflection of light by a random layered system,” J. Phys. (Paris) 47(9), 1467–1475 (1986).
[Crossref]

J. Phys. A: Math. Gen. (2)

J. M. Luck, “Non-monotonic disorder-induced enhanced tunnelling,” J. Phys. A: Math. Gen. 37(1), 259–271 (2004).
[Crossref]

J. P. Bouchaud and P. Le Doussal, “Intermittency in random optical layers at total reflection,” J. Phys. A: Math. Gen. 19(5), 797–810 (1986).
[Crossref]

J. Phys.: Condens. Matter (1)

J. Heinrichs, “Enhanced quantum tunnelling induced by disorder,” J. Phys.: Condens. Matter 20(39), 395215 (2008).

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,” Low Temp. Phys. 38(7), 570–602 (2012).
[Crossref]

Nat. Commun. (1)

H. H. Sheinfux, I. Kaminer, A. Z. Genack, and M. Segev, “Interplay between evanescence and disorder in deep subwavelength photonic structures,” Nat. Commun. 7, 12927 (2016).
[Crossref]

Nature (2)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

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, 891–894 (2008).
[Crossref] [PubMed]

Opt. Express (1)

Phys. Rep. (2)

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]

K. G. Wilson and J. Kogut, “The renormalization group and the ∊ expansion,” Phys. Rep. 12C(2), 75–200 (1974).
[Crossref]

Phys. Rev. (3)

H. L. Frisch and S. P. Lloyd, “Electron levels in a one-dimensional random lattice,” Phys. Rev. 120(4), 1175–1189 (1960).
[Crossref]

B. I. Halperin, “Green’s functions for a particle in a one-dimensional random potential,” Phys. Rev. 139(1A), A104–A117 (1965).
[Crossref]

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Phys. Rev. B (5)

A. Weinrib and B. I. Halperin, “Critical phenomena with long-range-correlated quenched disorder,” Phys. Rev. B 27(1), 413–427 (1983).
[Crossref]

V. V. Prudnikov, P. V. Prudnikov, and A. A. Fedorenko, “Field-theory approach to critical behavior of systems with long-range correlated defects,” Phys. Rev. B 62(13), 8777–8786 (2000).
[Crossref]

K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58(10), 6153–6160 (1998).
[Crossref]

V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53(11), 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(2), 024203 (2008).
[Crossref]

Phys. Rev. E (2)

D. Dimitropoulos and B. Jalali, “Stochastic differential equation approach for waves in a random medium,” Phys. Rev. E 79(3), 036606 (2009).
[Crossref]

W. Choi, C. Yin, I. R. Hooper, W. L. Barnes, and J. Bertolotti, “Absence of Anderson localization in certain random lattices,” Phys. Rev. E 96(2), 022122 (2017).
[Crossref] [PubMed]

Phys. Rev. Lett. (6)

D. H. Dunlap, H.-L. Wu, and P. W. Phillips, “Absence of localization in a random-dimer model,” Phys. Rev. Lett. 65(1), 88–91 (1990).
[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 metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[Crossref]

M. P. A. Fisher and G. Grinstein, “Quantum critical phenomena in charged superconductors,” Phys. Rev. Lett. 60(3), 208–211 (1988).
[Crossref] [PubMed]

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
[Crossref]

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, “Scaling theory of localization: Absence of quantum diffusion in two dimensions,” Phys. Rev. Lett. 42(10), 673–676 (1979).
[Crossref]

F. M. Izrailev and A. A. Krokhin, “Localization and the mobility edge in one-dimensional potentials with correlated disorder,” Phys. Rev. Lett. 82(20), 4062–4065 (1999).
[Crossref]

Phys. Usp. (1)

V. S. Dotsenko, “Critical phenomena and quenched disorder,” Phys. Usp. 38(5), 457–497 (1995).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

A. Fang, Z. Q. Zhang, S. G. Louie, and C. T. Chan, “Anomalous Anderson localization behaviors in disordered pseudospin systems,” Proc. Natl. Acad. Sci. U.S.A. 114(16), 4087–4092 (2017).
[Crossref] [PubMed]

Prog. Opt. (1)

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

Rev. Mod. Phys. (1)

P. C. Hohenberg and B. I. Halperin, “Theory of dynamic critical phenomena,” Rev. Mod. Phys. 49(3), 435–479 (1977).
[Crossref]

Science (1)

H. H. Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, “Observation of Anderson localization in disordered nanophotonic structures,” Science 356(6341), 953–956 (2017).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

E. A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP 20(5), 1290–1294 (1965).

Other (1)

I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).

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Figures (3)

Fig. 1
Fig. 1 Normalized inverse localization length (or tunneling decay length if θ > θc), 1/(), versus dimensionless disorder parameter g in a log-log plot for various values of the incident angle θ, when 〈〉/1 = 0.75 and θc = 60°. The curves obtained from the analytical formula, Eq. (15), are compared with the numerical results obtained using the invariant imbedding method, which are designated by square dots.
Fig. 2
Fig. 2 Comparison between Fig. 2(b) of Ref. 17 and the localization length versus incident angle curve obtained from Eq. (15), when λ = 1 μm and g0 = 0.00225 μm.
Fig. 3
Fig. 3 Comparison between Fig. 2(a) of Ref. 17 (colored lines) and the localization length versus wavelength curves (black lines) obtained from Eq. (15), when θ = 58°, 59°, 59.5° and 60°, and when (a) g0 = 0.0003 μm and (b) g0 = 0.000072 μm.

Tables (1)

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Table 1 Correspondence between the electromagnetic wave equation for obliquely incident s waves [Eq. (6)] and the Schrödinger equation in one dimension [Eq. (7)].

Equations (37)

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d 2 d z 2 + [ k 0 2 ( z ) q 2 ] = 0 ,
= + δ ( z ) ,
˜ = 1 = 1 + a + δ ˜ ( z ) ,
a = 1 1 , δ ˜ ( z ) = δ ( z ) 1 .
δ ˜ ( z ) δ ˜ ( z ) = 2 g 0 δ ( z z ) , δ ˜ ( z ) = 0 ,
d 2 d z 2 + ( k cos θ ) 2 [ 1 + a + δ ˜ ( z ) cos 2 θ ] = 0 .
d 2 ψ d z 2 + κ 2 [ 1 V ( z ) E ] ψ = 0 ,
δ V ( z ) δ V ( z ) = 2 D δ ( z z ) , δ V ( z ) = 0 .
ψ ( z ) = { e i κ ( L z ) + r ( L ) e i κ ( z L ) , z > L t ( L ) e i κ z , z < 0 .
lim L ln T 2 L = γ ,
γ = 1 2 ξ .
γ = D ˜ 1 / 3 F ( X ) ,
D ˜ = κ 4 D E 2 , X = ( E κ D ) 2 / 3 ( V 0 E 1 ) ,
F ( X ) = Ai ( X ) A i ( X ) + Bi ( X ) Bi ( X ) [ Ai ( X ) ] 2 + [ Bi ( X ) ] 2 .
1 ξ = 2 k ( k g 0 ) 1 / 3 F ( sin 2 θ 1 ( k g 0 ) 2 / 3 ) .
1 ξ f = 2 F ( 0 ) k 4 / 3 g 0 1 / 3 ω 4 / 3
ξ c = 1 2 ( 2 π ) 4 / 3 F ( 0 ) g 0 1 / 3 λ 4 / 3 0.1183 g 0 1 / 3 λ 4 / 3 λ 4 / 3 ,
1 k ξ c = 2 4 / 3 F ( 0 ) g 1 / 3 0.9185 g 1 / 3 ,
lim X F ( X ) = 1 4 X ,
ln ( 1 k ξ ) ln g ln ( a + cos 2 θ )
ξ k 2 ω 2 λ 2 ,
ξ a + cos 2 θ 2 π 2 g 0 λ 2 .
ξ c ζ 2 / 3 ,
ξ ζ 2
S ( k ) = 2 g 0 ,
δ ˜ ( z ) δ ˜ ( z ) = σ 2 exp ( | z z | / l c ) ,
S ( k ) = 2 σ 2 l c 1 + ( k l c ) 2 .
S ( k ) = n = 0 a n k 2 n .
˜ ( 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 k cos θ r ( l ) + i k 2 cos θ [ a + δ ˜ ( l ) ] [ 1 + r ( l ) ] 2 , d t d l = i k cos θ t ( l ) + i k 2 cos θ [ a + δ ˜ ( l ) ] [ 1 + r ( l ) ] t ( l ) ,
lim L ln T = L ξ .
1 k d d l ln T = g cos 2 θ Re [ ( i a cos θ + 2 g cos 2 θ ) Z 1 ( l ) + g cos 2 θ Z 2 ( l ) ] ,
1 k ξ = g cos 2 θ + Re [ ( i a cos θ + 2 g cos 2 θ ) Z 1 ( l ) + g cos 2 θ Z 2 ( l ) ] .
1 k d d l Z n = [ i ( 2 cos θ + a cos θ ) n 3 g cos 2 θ n 2 ] Z n + n [ i a 2 cos θ g cos 2 θ ( 2 n + 1 ) ] Z n + 1 + n [ i a 2 cos θ g cos 2 θ ( 2 n 1 ) ] Z n 1 g 2 cos 2 θ n ( n + 1 ) Z n + 2 g 2 cos 2 θ n ( n 1 ) Z n 2 ,
ln ( 1 k ξ c ) = 1 3 ln g + constant .
lim X F ( X ) = X 1 4 X + ,
1 k ξ = 2 ( sin 2 θ 1 ) 1 / 2 g sin 2 θ 1 + .

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