Abstract

We applied a finite-difference time domain algorithm to the study of field and intensity correlations in random media. Close to the onset of Anderson localization, we observe deviations of the correlation functions, in both shape and magnitude, from those predicted by the diffusion theory. Physical implications of the observed phenomena are discussed.

© 2004 Optical Society of America

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  1. P. Sebbah, ed., Waves and Imaging Through Complex Media (Kluwer Academic, Dordrecht, The Netherlands, 2001).
    [CrossRef]
  2. B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
    [CrossRef] [PubMed]
  3. S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
    [CrossRef] [PubMed]
  4. P. A. Mello, E. Akkermans, and B. Shapiro, Phys. Rev. Lett. 61, 459 (1988).
    [CrossRef] [PubMed]
  5. C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
    [CrossRef]
  6. P. Sheng, ed., The Scattering and Localization of Classical Waves (World Scientific, Singapore, 1990).
  7. R. Berkovits and S. Feng, Phys. Rep. 238, 136 (1994).
    [CrossRef]
  8. M. C. W. van Rossum and Th. M. Nieuwenhuizen, Rev. Mod. Phys. 71, 313 (1999).
    [CrossRef]
  9. P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
    [CrossRef]
  10. A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
    [CrossRef]
  11. A. D. Mirlin, A. Müller-Groeling, and M. R. Zirnbauer, Ann. Phys. 236, 325 (1994).
    [CrossRef]
  12. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, Norwood, Mass., 2000).
  13. P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
    [CrossRef]
  14. A. Lagendijk, R. Vreeker, and P. de Vries, Phys. Lett. A 136, 81 (1989).
    [CrossRef]
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    [CrossRef] [PubMed]
  16. A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
    [CrossRef] [PubMed]
  17. I. Freund and D. Eliyahu, Phys. Rev. A 45, 6133 (1992).
    [CrossRef] [PubMed]
  18. N. Garcia and A. Z. Genack, Phys. Rev. Lett. 63, 1678 (1989).
    [CrossRef] [PubMed]
  19. M. C. W. van Rossum and Th. M. Nieuwenhuizen, Phys. Lett. A 177, 452 (1993).
    [CrossRef]

2003 (1)

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef]

2002 (1)

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef]

2000 (2)

P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
[CrossRef]

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef] [PubMed]

1999 (1)

M. C. W. van Rossum and Th. M. Nieuwenhuizen, Rev. Mod. Phys. 71, 313 (1999).
[CrossRef]

1997 (1)

C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
[CrossRef]

1994 (2)

R. Berkovits and S. Feng, Phys. Rep. 238, 136 (1994).
[CrossRef]

A. D. Mirlin, A. Müller-Groeling, and M. R. Zirnbauer, Ann. Phys. 236, 325 (1994).
[CrossRef]

1993 (1)

M. C. W. van Rossum and Th. M. Nieuwenhuizen, Phys. Lett. A 177, 452 (1993).
[CrossRef]

1992 (1)

I. Freund and D. Eliyahu, Phys. Rev. A 45, 6133 (1992).
[CrossRef] [PubMed]

1991 (1)

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, Phys. Rev. Lett. 66, 3132 (1991).
[CrossRef] [PubMed]

1989 (2)

A. Lagendijk, R. Vreeker, and P. de Vries, Phys. Lett. A 136, 81 (1989).
[CrossRef]

N. Garcia and A. Z. Genack, Phys. Rev. Lett. 63, 1678 (1989).
[CrossRef] [PubMed]

1988 (2)

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

P. A. Mello, E. Akkermans, and B. Shapiro, Phys. Rev. Lett. 61, 459 (1988).
[CrossRef] [PubMed]

1986 (1)

B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
[CrossRef] [PubMed]

Akkermans, E.

P. A. Mello, E. Akkermans, and B. Shapiro, Phys. Rev. Lett. 61, 459 (1988).
[CrossRef] [PubMed]

Apostol, A.

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef]

Beenakker, C. W. J.

C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
[CrossRef]

Berkovits, R.

R. Berkovits and S. Feng, Phys. Rep. 238, 136 (1994).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef] [PubMed]

de Vries, P.

A. Lagendijk, R. Vreeker, and P. de Vries, Phys. Lett. A 136, 81 (1989).
[CrossRef]

Dogariu, A.

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef]

Eliyahu, D.

I. Freund and D. Eliyahu, Phys. Rev. A 45, 6133 (1992).
[CrossRef] [PubMed]

Feng, S.

R. Berkovits and S. Feng, Phys. Rep. 238, 136 (1994).
[CrossRef]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

Freund, I.

I. Freund and D. Eliyahu, Phys. Rev. A 45, 6133 (1992).
[CrossRef] [PubMed]

Garcia, N.

N. Garcia and A. Z. Genack, Phys. Rev. Lett. 63, 1678 (1989).
[CrossRef] [PubMed]

Genack, A. Z.

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef]

P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
[CrossRef]

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef] [PubMed]

N. Garcia and A. Z. Genack, Phys. Rev. Lett. 63, 1678 (1989).
[CrossRef] [PubMed]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, Norwood, Mass., 2000).

Hu, B.

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef]

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

Lagendijk, A.

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, Phys. Rev. Lett. 66, 3132 (1991).
[CrossRef] [PubMed]

A. Lagendijk, R. Vreeker, and P. de Vries, Phys. Lett. A 136, 81 (1989).
[CrossRef]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

Mello, P. A.

P. A. Mello, E. Akkermans, and B. Shapiro, Phys. Rev. Lett. 61, 459 (1988).
[CrossRef] [PubMed]

Mirlin, A. D.

A. D. Mirlin, A. Müller-Groeling, and M. R. Zirnbauer, Ann. Phys. 236, 325 (1994).
[CrossRef]

Müller-Groeling, A.

A. D. Mirlin, A. Müller-Groeling, and M. R. Zirnbauer, Ann. Phys. 236, 325 (1994).
[CrossRef]

Nieuwenhuizen, Th. M.

M. C. W. van Rossum and Th. M. Nieuwenhuizen, Rev. Mod. Phys. 71, 313 (1999).
[CrossRef]

M. C. W. van Rossum and Th. M. Nieuwenhuizen, Phys. Lett. A 177, 452 (1993).
[CrossRef]

Pnini, R.

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef]

P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
[CrossRef]

Sebbah, P.

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef]

P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
[CrossRef]

Shapiro, B.

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef]

P. A. Mello, E. Akkermans, and B. Shapiro, Phys. Rev. Lett. 61, 459 (1988).
[CrossRef] [PubMed]

B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
[CrossRef] [PubMed]

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

Stoytchev, M.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, Norwood, Mass., 2000).

Tip, A.

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, Phys. Rev. Lett. 66, 3132 (1991).
[CrossRef] [PubMed]

van Albada, M. P.

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, Phys. Rev. Lett. 66, 3132 (1991).
[CrossRef] [PubMed]

van Rossum, M. C. W.

M. C. W. van Rossum and Th. M. Nieuwenhuizen, Rev. Mod. Phys. 71, 313 (1999).
[CrossRef]

M. C. W. van Rossum and Th. M. Nieuwenhuizen, Phys. Lett. A 177, 452 (1993).
[CrossRef]

van Tiggelen, B. A.

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, Phys. Rev. Lett. 66, 3132 (1991).
[CrossRef] [PubMed]

Vreeker, R.

A. Lagendijk, R. Vreeker, and P. de Vries, Phys. Lett. A 136, 81 (1989).
[CrossRef]

Zirnbauer, M. R.

A. D. Mirlin, A. Müller-Groeling, and M. R. Zirnbauer, Ann. Phys. 236, 325 (1994).
[CrossRef]

Ann. Phys. (1)

A. D. Mirlin, A. Müller-Groeling, and M. R. Zirnbauer, Ann. Phys. 236, 325 (1994).
[CrossRef]

Nature (1)

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef] [PubMed]

Phys. Lett. A (2)

A. Lagendijk, R. Vreeker, and P. de Vries, Phys. Lett. A 136, 81 (1989).
[CrossRef]

M. C. W. van Rossum and Th. M. Nieuwenhuizen, Phys. Lett. A 177, 452 (1993).
[CrossRef]

Phys. Rep. (1)

R. Berkovits and S. Feng, Phys. Rep. 238, 136 (1994).
[CrossRef]

Phys. Rev. A (1)

I. Freund and D. Eliyahu, Phys. Rev. A 45, 6133 (1992).
[CrossRef] [PubMed]

Phys. Rev. E (1)

P. Sebbah, R. Pnini, and A. Z. Genack, Phys. Rev. E 62, 7348 (2000).
[CrossRef]

Phys. Rev. Lett. (7)

A. Apostol and A. Dogariu, Phys. Rev. Lett. 91, 093901 (2003).
[CrossRef]

B. Shapiro, Phys. Rev. Lett. 57, 2168 (1986).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[CrossRef] [PubMed]

P. A. Mello, E. Akkermans, and B. Shapiro, Phys. Rev. Lett. 61, 459 (1988).
[CrossRef] [PubMed]

N. Garcia and A. Z. Genack, Phys. Rev. Lett. 63, 1678 (1989).
[CrossRef] [PubMed]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, and A. Tip, Phys. Rev. Lett. 66, 3132 (1991).
[CrossRef] [PubMed]

P. Sebbah, B. Hu, A. Z. Genack, R. Pnini, and B. Shapiro, Phys. Rev. Lett. 88, 123901 (2002).
[CrossRef]

Rev. Mod. Phys. (2)

C. W. J. Beenakker, Rev. Mod. Phys. 69, 731 (1997).
[CrossRef]

M. C. W. van Rossum and Th. M. Nieuwenhuizen, Rev. Mod. Phys. 71, 313 (1999).
[CrossRef]

Other (3)

P. Sheng, ed., The Scattering and Localization of Classical Waves (World Scientific, Singapore, 1990).

P. Sebbah, ed., Waves and Imaging Through Complex Media (Kluwer Academic, Dordrecht, The Netherlands, 2001).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, Norwood, Mass., 2000).

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Figures (4)

Fig. 1
Fig. 1

Real part of spatial FCF. Squares, circles, and triangles correspond to the systems with g of 4.4, 2.2, and 1.1, respectively. The solid curve represents the fit of Eq. (3) with zb/l=0.8. The inset shows the geometry of our system.

Fig. 2
Fig. 2

Real (empty symbols) and imaginary (filled symbols) parts of the frequency FCF. Solid and dashed curves represent the real and imaginary parts, respectively, of CE given by Eq. (4) with l=1.8 cm. The inset compares δν found with a HWHM of CEΔν2 to D/L2. Both quantities are normalized to average mode spacing. Symbol notations are the same as in Fig. 1.

Fig. 3
Fig. 3

Magnitude of long-range contribution to ICF versus dimensionless conductance g. Symbol notations are the same as in Fig. 1. Solid line represents diffusion expansion formula Eq. (5) at Δr=0. The inset shows the long-range contribution to the ICF normalized to 1 at Δr=0. Solid, dashed, and dotted–dashed curves correspond to samples with g of 4.4, 2.2, and 1.1, respectively. Thick solid curve plots Eq. (5).

Fig. 4
Fig. 4

Frequency dependence of the long-range contribution to the ICF normalized to value at Δν=0. Symbol notations are the same as in Fig. 1.

Equations (5)

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

CΔr,Δν=Ir+Δr,ν+ΔνIr,νIr+Δr,ν+ΔνIr,ν-1,
CEΔr,Δν=Er+Δr,ν+ΔνE*r,νIr+Δr,ν+Δν1/2Ir,ν1/2
CEΔr=πzb/lJ0kΔr+2 sinkΔr/kΔrπzb/l+2,
CEΔν=qL/sinhqL,
CΔr-CEΔr2=43g+815g21+CEΔr22.

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