Abstract

The transmission spectra perform huge fluctuations even in the mostly suitable one-dimensional localized multilayer system. Fluctuations of layer thicknesses will cause random resonances between light waves and layers. We reveal that the nonuniform ensembles of the resonances are the key for the fluctuations of transmission spectra. The transmission spectra of each stack of layers are numerically calculated through the transfer-matrix method.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. W. Anderson, Rev. Mod. Phys. 50, 191 (1978).
    [CrossRef]
  2. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
    [CrossRef]
  3. J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
    [CrossRef] [PubMed]
  4. E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2006).
  5. R. L. Weaver, Wave Motion 12, 129 (1990).
    [CrossRef]
  6. R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Nature 354, 53 (1991).
    [CrossRef]
  7. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
    [CrossRef]
  8. M. Stőrzer, P. Gross, C. M. Aegerter, and G. Maret, Phys. Rev. Lett. 96, 063904 (2006).
    [CrossRef] [PubMed]
  9. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
    [CrossRef] [PubMed]
  10. J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, Phys. Rev. Lett. 94, 113903 (2005).
    [CrossRef] [PubMed]
  11. M. Ya. Azbel, Phys. Rev. B 28, 4106 (1983).
    [CrossRef]
  12. K. Yu. Bliokh, Yu. P. Bliokh, and V. Freilikher, J. Opt. Soc. Am. B 21, 113 (2004).
    [CrossRef]
  13. N. F. Mott and W. D. Twose, Adv. Phys. 10, 107 (1961).
    [CrossRef]
  14. D. J. Thouless, Phys. Rev. Lett. 39, 1167 (1977).
    [CrossRef]
  15. J. B. Pendry, J. Phys. C 20, 733 (1987).
    [CrossRef]
  16. A. V. Tartakovskii, M. V. Fistul’, M. E. Raikh, and I. M. Ruzin, Sov. Phys. Semicond. 21, 370 (1987).
  17. J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
    [CrossRef]
  18. P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
    [CrossRef] [PubMed]
  19. M. Ghulinyan, Phys. Rev. Lett. 99, 063905 (2007).
    [CrossRef] [PubMed]
  20. J. Y. Huang and L. W. Zhou, Opt. Lett. 36, 1305 (2011).
    [CrossRef] [PubMed]
  21. S. Zhang, J. Park, V. Milner, and A. Z. Genack, Phys. Rev. Lett. 101, 183901 (2008).
    [CrossRef] [PubMed]
  22. M. V. Berry and S. Klein, Eur. J. Phys. 18, 222 (1997).
    [CrossRef]
  23. J. B. Pendry, Adv. Phys. 43, 461 (1994).
    [CrossRef]
  24. F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice-Hall, Englewood, Cliffs, New Jersey, 1992).

2011 (1)

2008 (2)

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

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

2007 (2)

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

M. Ghulinyan, Phys. Rev. Lett. 99, 063905 (2007).
[CrossRef] [PubMed]

2006 (4)

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2006).

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

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
[CrossRef]

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[CrossRef] [PubMed]

2005 (1)

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

2004 (1)

1997 (2)

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]

1994 (1)

J. B. Pendry, Adv. Phys. 43, 461 (1994).
[CrossRef]

1992 (1)

F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice-Hall, Englewood, Cliffs, New Jersey, 1992).

1991 (1)

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Nature 354, 53 (1991).
[CrossRef]

1990 (1)

R. L. Weaver, Wave Motion 12, 129 (1990).
[CrossRef]

1987 (2)

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).

1983 (1)

M. Ya. Azbel, Phys. Rev. B 28, 4106 (1983).
[CrossRef]

1978 (1)

P. W. Anderson, Rev. Mod. Phys. 50, 191 (1978).
[CrossRef]

1977 (1)

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

1961 (1)

N. F. Mott and W. D. Twose, Adv. Phys. 10, 107 (1961).
[CrossRef]

1958 (1)

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]

Akkermans, E.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2006).

Anderson, P. W.

P. W. Anderson, Rev. Mod. Phys. 50, 191 (1978).
[CrossRef]

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

Andreani, L. C.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
[CrossRef]

Armstrong, J. P.

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Nature 354, 53 (1991).
[CrossRef]

Aspect, A.

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

Azbel, M. Ya.

M. Ya. Azbel, Phys. Rev. B 28, 4106 (1983).
[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]

Bernard, A.

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

Berry, M. V.

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

Bertolotti, J.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
[CrossRef]

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

Billy, J.

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

Bliokh, K. Yu.

Bliokh, Yu. P.

Bouyer, P.

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

Clment, D.

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

Dalichaouch, R.

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Nature 354, 53 (1991).
[CrossRef]

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).

Freilikher, V.

Galli, M.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
[CrossRef]

Genack, A. Z.

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

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[CrossRef] [PubMed]

Ghulinyan, M.

M. Ghulinyan, Phys. Rev. Lett. 99, 063905 (2007).
[CrossRef] [PubMed]

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
[CrossRef]

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

Gottardo, S.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
[CrossRef]

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]

Hambrecht, B.

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

Hu, B.

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[CrossRef] [PubMed]

Huang, J. Y.

Josse, V.

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

Klein, S.

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

Klosner, J. M.

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[CrossRef] [PubMed]

Lagendijk, A.

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

Lugan, P.

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

Maret, G.

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

McCall, S. L.

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Nature 354, 53 (1991).
[CrossRef]

Milner, V.

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

Montambaux, G.

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2006).

Mott, N. F.

N. F. Mott and W. D. Twose, Adv. Phys. 10, 107 (1961).
[CrossRef]

Park, J.

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

Pavesi, L.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
[CrossRef]

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

Pedrotti, F. J.

F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice-Hall, Englewood, Cliffs, New Jersey, 1992).

Pedrotti, L. S.

F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice-Hall, Englewood, Cliffs, New Jersey, 1992).

Pendry, J. B.

J. B. Pendry, Adv. Phys. 43, 461 (1994).
[CrossRef]

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

Platzman, P. M.

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Nature 354, 53 (1991).
[CrossRef]

Raikh, M. E.

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).

Sanchez-Palencia, L.

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

Sapienza, R.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
[CrossRef]

Schultz, S.

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Nature 354, 53 (1991).
[CrossRef]

Schwartz, T.

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

Sebbah, P.

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[CrossRef] [PubMed]

Segev, M.

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

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]

Twose, W. D.

N. F. Mott and W. D. Twose, Adv. Phys. 10, 107 (1961).
[CrossRef]

Weaver, R. L.

R. L. Weaver, Wave Motion 12, 129 (1990).
[CrossRef]

Wiersma, D. S.

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
[CrossRef]

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]

Zhang, S.

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

Zhou, L. W.

Zou, Z.

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

Adv. Phys. (2)

N. F. Mott and W. D. Twose, Adv. Phys. 10, 107 (1961).
[CrossRef]

J. B. Pendry, Adv. Phys. 43, 461 (1994).
[CrossRef]

Eur. J. Phys. (1)

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

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

J. Phys. C (1)

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

Nature (4)

J. Billy, V. Josse, Z. Zou, A. Bernard, B. Hambrecht, P. Lugan, D. Clment, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Nature 453, 891 (2008).
[CrossRef] [PubMed]

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, and S. L. McCall, Nature 354, 53 (1991).
[CrossRef]

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]

Opt. Lett. (1)

Phys. Rev. (1)

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

Phys. Rev. B (1)

M. Ya. Azbel, Phys. Rev. B 28, 4106 (1983).
[CrossRef]

Phys. Rev. E (1)

J. Bertolotti, M. Galli, R. Sapienza, M. Ghulinyan, S. Gottardo, L. C. Andreani, L. Pavesi, and D. S. Wiersma, Phys. Rev. E 74, 035602(R) (2006).
[CrossRef]

Phys. Rev. Lett. (6)

P. Sebbah, B. Hu, J. M. Klosner, and A. Z. Genack, Phys. Rev. Lett. 96, 183902 (2006).
[CrossRef] [PubMed]

M. Ghulinyan, Phys. Rev. Lett. 99, 063905 (2007).
[CrossRef] [PubMed]

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

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

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

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

Rev. Mod. Phys. (1)

P. W. Anderson, Rev. Mod. Phys. 50, 191 (1978).
[CrossRef]

Sov. Phys. Semicond. (1)

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

Wave Motion (1)

R. L. Weaver, Wave Motion 12, 129 (1990).
[CrossRef]

Other (2)

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2006).

F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics(Prentice-Hall, Englewood, Cliffs, New Jersey, 1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Experimentally observed (a) and numerically calculated (b) transmission spectra of samples consisting of 100 glass layers. Red dashed line shows the transmission eigenstate of the system. The average distances between two neighboring high (low) transmission regions are nearly the same between (a) experimental and (b) simulated spectra. The average transmittances are ( 1.8 ± 0.1 ) × 10 4 and ( 1.86 ± 0.06 ) × 10 4 for (a) experiment and (b) simulation, respectively.

Fig. 2
Fig. 2

Distribution of average phase factors (Av. PF) of the sample consisting of 100 layers, whose transmission spectrum is shown in Fig. 1b. Red dashed line shows the phase factor corresponding to the transmission eigenstate of the system. Compared with Fig. 1, the transmittances are higher than the transmission eigenstate when Δ δ < π / 2 , while they are lower than the transmission eigenstate when Δ δ > π / 2 .

Fig. 3
Fig. 3

Distribution of ensemble deviation ratios (En. DR) for the sample consisting of 100 layers we discussed above. Compared with Fig. 1b, the transmittance is high with respect to the transmission eigenstate of the system, when χ en > 0 . On the contrary, the transmittance is lower than the transmission eigenstate of the system, when χ en < 0 .

Equations (7)

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

m A = 1 t A * r A * t A * r A t A 1 t A ,
t A = 1 cos δ A I n A 2 + n B 2 2 n A n B sin δ A ,
r A = I n B 2 n A 2 2 n A n B sin δ A cos δ A I n A 2 + n B 2 2 n A n B sin δ A ,
M 2 N = 1 t 12 2 N * r 12 2 N * t 12 2 N * r 12 2 N t 12 2 N 1 t 12 2 N = m 1 m 2 m 2 N ,
T 12 2 N = 1 | [ M 2 N ] 22 | 2 = | t 12 2 N | 2 .
χ = T T T ,
χ en = i = 1 2 N T i T T .

Metrics