Abstract

We report an exceptional enhancement of photon localization effect in a certain one-dimensional random multilayer system. Our simulation with the transfer matrix method predicts and demonstrates that the photon localization effect in a system with weak disorder strength but in a destructive interference resonance region is stronger than that in a completely disordered system. The only reason for this peculiar phenomenon is that the certain weak disorder system confines the resonances between the wave and layers in the destructive interference resonance region.

© 2011 Optical Society of America

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Errata

Junying Huang and Luwei Zhou, "Exceptional enhancement of localization effect in a one-dimensional multilayer system with destructive weak disorder strength: erratum," Opt. Lett. 39, 2390-2390 (2014)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-39-8-2390

References

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  1. P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic, 1995).
  2. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
    [CrossRef]
  3. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
    [CrossRef]
  4. M. Stőrzer, P. Gross, C. M. Aegerter, and G. Maret, Phys. Rev. Lett. 96, 063904 (2006).
    [CrossRef] [PubMed]
  5. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
    [CrossRef] [PubMed]
  6. J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, Phys. Rev. Lett. 94, 113903 (2005).
    [CrossRef] [PubMed]
  7. C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, Phys. Rev. Lett. 101, 123901 (2008).
    [CrossRef] [PubMed]
  8. S. John, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  9. A. F. Koenderink and W. L. Vos, Phys. Rev. Lett. 91, 213902 (2003).
    [CrossRef] [PubMed]
  10. J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
    [CrossRef]
  11. J. Huang, N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, Phys. Rev. Lett. 86, 4815(2001).
    [CrossRef] [PubMed]
  12. D. J. Thouless, Phys. Rev. Lett. 39, 1167 (1977).
    [CrossRef]
  13. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
    [PubMed]
  14. M. V. Berry and S. Klein, Eur. J. Phys. 18, 222 (1997).
    [CrossRef]
  15. J. Y. Huang, B. Q. Dong, J. Zi, and L. W. Zhou, “Transmission terrace for light in 1D random multilayer system,” Euro. Phys. Lett., submitted for publication.
  16. S. Zhang, J. Park, V. Milner, and A. Z. Genack, Phys. Rev. Lett. 101, 183901 (2008).
    [CrossRef] [PubMed]
  17. J. B. Pendry, J. Phys. C 20, 733 (1987).
    [CrossRef]
  18. A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, Sov. Phys. Semicond. 21, 370 (1987).

2008

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, Phys. Rev. Lett. 101, 123901 (2008).
[CrossRef] [PubMed]

S. Zhang, J. Park, V. Milner, and A. Z. Genack, Phys. Rev. Lett. 101, 183901 (2008).
[CrossRef] [PubMed]

2007

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef] [PubMed]

2006

M. Stőrzer, P. Gross, C. M. Aegerter, and G. Maret, Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef] [PubMed]

2005

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, Phys. Rev. Lett. 94, 113903 (2005).
[CrossRef] [PubMed]

2003

A. F. Koenderink and W. L. Vos, Phys. Rev. Lett. 91, 213902 (2003).
[CrossRef] [PubMed]

2001

J. Huang, N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, Phys. Rev. Lett. 86, 4815(2001).
[CrossRef] [PubMed]

1997

M. V. Berry and S. Klein, Eur. J. Phys. 18, 222 (1997).
[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

1987

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

J. B. Pendry, J. Phys. C 20, 733 (1987).
[CrossRef]

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, Sov. Phys. Semicond. 21, 370 (1987).

1977

D. J. Thouless, Phys. Rev. Lett. 39, 1167 (1977).
[CrossRef]

1958

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Aegerter, C. M.

M. Stőrzer, P. Gross, C. M. Aegerter, and G. Maret, Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef] [PubMed]

Anderson, P. W.

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef] [PubMed]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

Baughman, R. H.

J. Huang, N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, Phys. Rev. Lett. 86, 4815(2001).
[CrossRef] [PubMed]

Berry, M. V.

M. V. Berry and S. Klein, Eur. J. Phys. 18, 222 (1997).
[CrossRef]

Bertolotti, J.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, Phys. Rev. Lett. 94, 113903 (2005).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
[PubMed]

Dong, B. Q.

J. Y. Huang, B. Q. Dong, J. Zi, and L. W. Zhou, “Transmission terrace for light in 1D random multilayer system,” Euro. Phys. Lett., submitted for publication.

Eradat, N.

J. Huang, N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, Phys. Rev. Lett. 86, 4815(2001).
[CrossRef] [PubMed]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef] [PubMed]

Fistul, M. V.

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, Sov. Phys. Semicond. 21, 370 (1987).

Genack, A. Z.

S. Zhang, J. Park, V. Milner, and A. Z. Genack, Phys. Rev. Lett. 101, 183901 (2008).
[CrossRef] [PubMed]

Ghulinyan, M.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, Phys. Rev. Lett. 94, 113903 (2005).
[CrossRef] [PubMed]

Gottardo, S.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, Phys. Rev. Lett. 94, 113903 (2005).
[CrossRef] [PubMed]

Gross, P.

M. Stőrzer, P. Gross, C. M. Aegerter, and G. Maret, Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef] [PubMed]

Huang, J.

J. Huang, N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, Phys. Rev. Lett. 86, 4815(2001).
[CrossRef] [PubMed]

Huang, J. Y.

J. Y. Huang, B. Q. Dong, J. Zi, and L. W. Zhou, “Transmission terrace for light in 1D random multilayer system,” Euro. Phys. Lett., submitted for publication.

Ilic, B.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

John, S.

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, Phys. Rev. Lett. 101, 123901 (2008).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Klein, S.

M. V. Berry and S. Klein, Eur. J. Phys. 18, 222 (1997).
[CrossRef]

Koenderink, A. F.

A. F. Koenderink and W. L. Vos, Phys. Rev. Lett. 91, 213902 (2003).
[CrossRef] [PubMed]

Lagendijk, A.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

Maret, G.

M. Stőrzer, P. Gross, C. M. Aegerter, and G. Maret, Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef] [PubMed]

Milner, V.

S. Zhang, J. Park, V. Milner, and A. Z. Genack, Phys. Rev. Lett. 101, 183901 (2008).
[CrossRef] [PubMed]

Ozin, G. A.

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, Phys. Rev. Lett. 101, 123901 (2008).
[CrossRef] [PubMed]

Park, J.

S. Zhang, J. Park, V. Milner, and A. Z. Genack, Phys. Rev. Lett. 101, 183901 (2008).
[CrossRef] [PubMed]

Pavesi, L.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, Phys. Rev. Lett. 94, 113903 (2005).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, J. Phys. C 20, 733 (1987).
[CrossRef]

Raikh, M. E.

J. Huang, N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, Phys. Rev. Lett. 86, 4815(2001).
[CrossRef] [PubMed]

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, Sov. Phys. Semicond. 21, 370 (1987).

Righini, R.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

Ruzin, I. M.

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, Sov. Phys. Semicond. 21, 370 (1987).

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef] [PubMed]

Segev, M.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef] [PubMed]

Sheng, P.

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

Storzer, M.

M. Stőrzer, P. Gross, C. M. Aegerter, and G. Maret, Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef] [PubMed]

Tartakovskii, A. V.

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, Sov. Phys. Semicond. 21, 370 (1987).

Thouless, D. J.

D. J. Thouless, Phys. Rev. Lett. 39, 1167 (1977).
[CrossRef]

Toninelli, C.

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, Phys. Rev. Lett. 101, 123901 (2008).
[CrossRef] [PubMed]

Topolancik, J.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Vardeny, Z. V.

J. Huang, N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, Phys. Rev. Lett. 86, 4815(2001).
[CrossRef] [PubMed]

Vekris, E.

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, Phys. Rev. Lett. 101, 123901 (2008).
[CrossRef] [PubMed]

Vollmer, F.

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

Vos, W. L.

A. F. Koenderink and W. L. Vos, Phys. Rev. Lett. 91, 213902 (2003).
[CrossRef] [PubMed]

Wiersma, D. S.

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, Phys. Rev. Lett. 101, 123901 (2008).
[CrossRef] [PubMed]

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, Phys. Rev. Lett. 94, 113903 (2005).
[CrossRef] [PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
[PubMed]

Zakhidov, A. A.

J. Huang, N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, Phys. Rev. Lett. 86, 4815(2001).
[CrossRef] [PubMed]

Zhang, S.

S. Zhang, J. Park, V. Milner, and A. Z. Genack, Phys. Rev. Lett. 101, 183901 (2008).
[CrossRef] [PubMed]

Zhou, L. W.

J. Y. Huang, B. Q. Dong, J. Zi, and L. W. Zhou, “Transmission terrace for light in 1D random multilayer system,” Euro. Phys. Lett., submitted for publication.

Zi, J.

J. Y. Huang, B. Q. Dong, J. Zi, and L. W. Zhou, “Transmission terrace for light in 1D random multilayer system,” Euro. Phys. Lett., submitted for publication.

Eur. J. Phys.

M. V. Berry and S. Klein, Eur. J. Phys. 18, 222 (1997).
[CrossRef]

J. Phys. C

J. B. Pendry, J. Phys. C 20, 733 (1987).
[CrossRef]

Nature

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef] [PubMed]

Phys. Rev.

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Phys. Rev. Lett.

M. Stőrzer, P. Gross, C. M. Aegerter, and G. Maret, Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef] [PubMed]

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, Phys. Rev. Lett. 94, 113903 (2005).
[CrossRef] [PubMed]

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, Phys. Rev. Lett. 101, 123901 (2008).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

A. F. Koenderink and W. L. Vos, Phys. Rev. Lett. 91, 213902 (2003).
[CrossRef] [PubMed]

J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
[CrossRef]

J. Huang, N. Eradat, M. E. Raikh, Z. V. Vardeny, A. A. Zakhidov, and R. H. Baughman, Phys. Rev. Lett. 86, 4815(2001).
[CrossRef] [PubMed]

D. J. Thouless, Phys. Rev. Lett. 39, 1167 (1977).
[CrossRef]

S. Zhang, J. Park, V. Milner, and A. Z. Genack, Phys. Rev. Lett. 101, 183901 (2008).
[CrossRef] [PubMed]

Sov. Phys. Semicond.

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, Sov. Phys. Semicond. 21, 370 (1987).

Other

J. Y. Huang, B. Q. Dong, J. Zi, and L. W. Zhou, “Transmission terrace for light in 1D random multilayer system,” Euro. Phys. Lett., submitted for publication.

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

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
[PubMed]

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram showing multiple scatterings of the wave propagation in a single layer. Solid lines, wave propagation without multiple scattering effects; dashed lines, multiple scatterings introduced by the boundary surfaces.

Fig. 2
Fig. 2

Three-dimensional plot of the localization strength 1 / T as a function of phase difference δ and relative refractive index n = n A / n B . The maximum and minimum localization strengths in a period of 2 π with the same n are located at the peak and the valley, respectively. The periodicity of localization strength is merely determined by the phase difference.

Fig. 3
Fig. 3

Simulation results for transmission states of multilayer systems with different types of disorder strength. The necklace (open diamonds), classical reflection (open circles), and strongest localization (open squares) states correspond to Δ δ = 0 , π / 2 , π when κ = 0 , respectively. The eigenstate of a completely disordered system (crosses) is the same as the classical reflection state of a completely ordered system. Full triangles and full inverse triangles show examples of wave propagation in systems with constructive and destructive weak disorder strength, respectively. The simulation is under the condition n A = 1.523 and n B = 1 .

Fig. 4
Fig. 4

Three-dimensional plot of the localization strength 1 / ξ as a function of disorder strength κ and average phase factor Δ δ . The curved surface depicts that a weaker disordered system in a destructive interference resonance region ( π / 2 < Δ δ < π ) corresponds to stronger localizations, while a stronger disordered system in constructive interference resonance region ( 0 < Δ δ < π / 2 ) corresponds to weaker localizations. The number of localization states of a system reduces to 1 when κ increases to 1.

Equations (3)

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

t e = 1 γ 2 1 γ 2 exp ( I δ ) ,
r e = γ [ 1 exp ( I δ ) ] 1 γ 2 exp ( I δ ) ,
T = t e t e * = ( 1 γ 2 ) 2 1 + γ 4 2 γ 2 cos δ .

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