Abstract

We present a broadband technique for the measurement of diffuse light transport through opaque scattering media. Using the spectral correlations introduced by a scattering medium onto a white-light supercontinuum spectrum, the diffusion constant of light is determined over a wide spectral range in the visible and the near IR. Independent broadband measurements of both the transport mean free path and the diffusion constant are used to calculate the spectral dependence of the energy velocity in a porous GaP slab. Broadband correlation spectroscopy is found to be an excellent tool for the characterization of random scattering media.

© 2009 Optical Society of America

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  1. A. F. Fercher, W. Drexter, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
    [CrossRef]
  2. F. Scheffold and R. Cerbino, Curr. Opin. Colloid Interface Sci. 12, 50 (2007).
    [CrossRef]
  3. C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, Phys. Rev. Lett. 101, 123901 (2008).
    [CrossRef] [PubMed]
  4. J. Topolancik, B. Ilic, and F. Vollmer, Phys. Rev. Lett. 99, 253901 (2007).
    [CrossRef]
  5. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
    [CrossRef] [PubMed]
  6. R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
    [CrossRef]
  7. A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
    [CrossRef] [PubMed]
  8. O. L. Muskens and A. Lagendijk, Opt. Express 16, 1222 (2008).
    [CrossRef] [PubMed]
  9. W. H. Peeters, I. M. Vellekoop, A. P. Mosk, and A. Lagendijk, Phys. Rev. A 77, 035803 (2008).
    [CrossRef]
  10. P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, and A. Lagendijk, Phys. Rev. E 68, 016604 (2003).
    [CrossRef]
  11. A. Z. Genack, Phys. Rev. Lett. 58, 2043 (1987).
    [CrossRef] [PubMed]
  12. A. Z. Genack and J. M. Drake, Europhys. Lett. 11, 331 (1990).
    [CrossRef]
  13. M. P. van Albada, J. F. de Boer, and A. Lagendijk, Phys. Rev. Lett. 64, 2787 (1990).
    [CrossRef] [PubMed]
  14. J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
    [CrossRef]
  15. R. Berkovits and S. Feng, Phys. Rep. 238, 135 (1994) and references therein.
    [CrossRef]
  16. F. J. P. Schuurmans, D. Vanmaekelbergh, J. van de Lagemaat, and A. Lagendijk, Science 284, 141 (1999).
    [CrossRef] [PubMed]
  17. J. W. Goodman, in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975), p. 9.
    [CrossRef]
  18. J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
    [CrossRef]

2008 (4)

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

O. L. Muskens and A. Lagendijk, Opt. Express 16, 1222 (2008).
[CrossRef] [PubMed]

W. H. Peeters, I. M. Vellekoop, A. P. Mosk, and A. Lagendijk, Phys. Rev. A 77, 035803 (2008).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

2007 (3)

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

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

F. Scheffold and R. Cerbino, Curr. Opin. Colloid Interface Sci. 12, 50 (2007).
[CrossRef]

2003 (3)

A. F. Fercher, W. Drexter, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, and A. Lagendijk, Phys. Rev. E 68, 016604 (2003).
[CrossRef]

J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
[CrossRef]

2000 (1)

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

1999 (1)

F. J. P. Schuurmans, D. Vanmaekelbergh, J. van de Lagemaat, and A. Lagendijk, Science 284, 141 (1999).
[CrossRef] [PubMed]

1994 (1)

R. Berkovits and S. Feng, Phys. Rep. 238, 135 (1994) and references therein.
[CrossRef]

1992 (1)

J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
[CrossRef]

1990 (2)

A. Z. Genack and J. M. Drake, Europhys. Lett. 11, 331 (1990).
[CrossRef]

M. P. van Albada, J. F. de Boer, and A. Lagendijk, Phys. Rev. Lett. 64, 2787 (1990).
[CrossRef] [PubMed]

1987 (1)

A. Z. Genack, Phys. Rev. Lett. 58, 2043 (1987).
[CrossRef] [PubMed]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Berkovits, R.

R. Berkovits and S. Feng, Phys. Rep. 238, 135 (1994) and references therein.
[CrossRef]

Bertolotti, J.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Blanco, A.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Bret, B. P. J.

J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
[CrossRef]

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, and A. Lagendijk, Phys. Rev. E 68, 016604 (2003).
[CrossRef]

Cerbino, R.

F. Scheffold and R. Cerbino, Curr. Opin. Colloid Interface Sci. 12, 50 (2007).
[CrossRef]

Chabanov, A. A.

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

Dau, D. H.

J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
[CrossRef]

de Boer, J. F.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
[CrossRef]

M. P. van Albada, J. F. de Boer, and A. Lagendijk, Phys. Rev. Lett. 64, 2787 (1990).
[CrossRef] [PubMed]

Drake, J. M.

A. Z. Genack and J. M. Drake, Europhys. Lett. 11, 331 (1990).
[CrossRef]

Drexter, W.

A. F. Fercher, W. Drexter, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Feng, S.

R. Berkovits and S. Feng, Phys. Rep. 238, 135 (1994) and references therein.
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexter, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

García, P. D.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Genack, A. Z.

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

A. Z. Genack and J. M. Drake, Europhys. Lett. 11, 331 (1990).
[CrossRef]

A. Z. Genack, Phys. Rev. Lett. 58, 2043 (1987).
[CrossRef] [PubMed]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Gomez Rivas, J.

J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
[CrossRef]

Gómez Rivas, J.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, and A. Lagendijk, Phys. Rev. E 68, 016604 (2003).
[CrossRef]

Goodman, J. W.

J. W. Goodman, in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975), p. 9.
[CrossRef]

Hijmans, T. W.

J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
[CrossRef]

Hitzenberger, C. K.

A. F. Fercher, W. Drexter, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Ilic, B.

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

Imhof, A.

J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
[CrossRef]

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, and A. Lagendijk, Phys. Rev. E 68, 016604 (2003).
[CrossRef]

John, S.

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

Johnson, P. M.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, and A. Lagendijk, Phys. Rev. E 68, 016604 (2003).
[CrossRef]

J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
[CrossRef]

Lagendijk, A.

O. L. Muskens and A. Lagendijk, Opt. Express 16, 1222 (2008).
[CrossRef] [PubMed]

W. H. Peeters, I. M. Vellekoop, A. P. Mosk, and A. Lagendijk, Phys. Rev. A 77, 035803 (2008).
[CrossRef]

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, and A. Lagendijk, Phys. Rev. E 68, 016604 (2003).
[CrossRef]

J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
[CrossRef]

F. J. P. Schuurmans, D. Vanmaekelbergh, J. van de Lagemaat, and A. Lagendijk, Science 284, 141 (1999).
[CrossRef] [PubMed]

J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
[CrossRef]

M. P. van Albada, J. F. de Boer, and A. Lagendijk, Phys. Rev. Lett. 64, 2787 (1990).
[CrossRef] [PubMed]

Lasser, T.

A. F. Fercher, W. Drexter, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

López, C.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Martín, M. D.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Mosk, A. P.

W. H. Peeters, I. M. Vellekoop, A. P. Mosk, and A. Lagendijk, Phys. Rev. A 77, 035803 (2008).
[CrossRef]

Muskens, O. L.

Ozin, G. A.

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

Peeters, W. H.

W. H. Peeters, I. M. Vellekoop, A. P. Mosk, and A. Lagendijk, Phys. Rev. A 77, 035803 (2008).
[CrossRef]

Sapienza, R.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Scheffold, F.

F. Scheffold and R. Cerbino, Curr. Opin. Colloid Interface Sci. 12, 50 (2007).
[CrossRef]

Schuurmans, F. J. P.

F. J. P. Schuurmans, D. Vanmaekelbergh, J. van de Lagemaat, and A. Lagendijk, Science 284, 141 (1999).
[CrossRef] [PubMed]

Sprik, R.

J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
[CrossRef]

Stoytchev, M.

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

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]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

van Albada, M. P.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
[CrossRef]

M. P. van Albada, J. F. de Boer, and A. Lagendijk, Phys. Rev. Lett. 64, 2787 (1990).
[CrossRef] [PubMed]

van de Lagemaat, J.

F. J. P. Schuurmans, D. Vanmaekelbergh, J. van de Lagemaat, and A. Lagendijk, Science 284, 141 (1999).
[CrossRef] [PubMed]

Vanmaekelbergh, D.

F. J. P. Schuurmans, D. Vanmaekelbergh, J. van de Lagemaat, and A. Lagendijk, Science 284, 141 (1999).
[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]

Vellekoop, I. M.

W. H. Peeters, I. M. Vellekoop, A. P. Mosk, and A. Lagendijk, Phys. Rev. A 77, 035803 (2008).
[CrossRef]

Viña, L.

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Vollmer, F.

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

Wiersma, D. S.

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

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Curr. Opin. Colloid Interface Sci. (1)

F. Scheffold and R. Cerbino, Curr. Opin. Colloid Interface Sci. 12, 50 (2007).
[CrossRef]

Europhys. Lett. (1)

A. Z. Genack and J. M. Drake, Europhys. Lett. 11, 331 (1990).
[CrossRef]

Nature (2)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

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

Opt. Commun. (1)

J. Gomez Rivas, D. H. Dau, A. Imhof, R. Sprik, B. P. J. Bret, P. M. Johnson, T. W. Hijmans, and A. Lagendijk, Opt. Commun. 220, 17 (2003).
[CrossRef]

Opt. Express (1)

Phys. Rep. (1)

R. Berkovits and S. Feng, Phys. Rep. 238, 135 (1994) and references therein.
[CrossRef]

Phys. Rev. A (1)

W. H. Peeters, I. M. Vellekoop, A. P. Mosk, and A. Lagendijk, Phys. Rev. A 77, 035803 (2008).
[CrossRef]

Phys. Rev. B (1)

J. F. de Boer, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 45, 658 (1992).
[CrossRef]

Phys. Rev. E (1)

P. M. Johnson, A. Imhof, B. P. J. Bret, J. Gómez Rivas, and A. Lagendijk, Phys. Rev. E 68, 016604 (2003).
[CrossRef]

Phys. Rev. Lett. (5)

A. Z. Genack, Phys. Rev. Lett. 58, 2043 (1987).
[CrossRef] [PubMed]

R. Sapienza, P. D. García, J. Bertolotti, M. D. Martín, A. Blanco, L. Viña, C. López, and D. S. Wiersma, Phys. Rev. Lett. 99, 233902 (2007).
[CrossRef]

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

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

M. P. van Albada, J. F. de Boer, and A. Lagendijk, Phys. Rev. Lett. 64, 2787 (1990).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexter, C. K. Hitzenberger, and T. Lasser, Rep. Prog. Phys. 66, 239 (2003).
[CrossRef]

Science (1)

F. J. P. Schuurmans, D. Vanmaekelbergh, J. van de Lagemaat, and A. Lagendijk, Science 284, 141 (1999).
[CrossRef] [PubMed]

Other (1)

J. W. Goodman, in Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer-Verlag, 1975), p. 9.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Transmission spectrum through a 10.2 - μ m -thick porous GaP slab normalized to the spectrum averaged over 30 different sample positions. Inset, detail of the spectrum showing individual speckle.

Fig. 3
Fig. 3

Spectral correlation function C 1 ( Δ ν ) obtained from experimental speckle spectra over a bandwidth of 1000 cm 1 around center frequencies of 11,000 cm 1 (circles), 13,000 cm 1 (diamonds), and 16,000 cm 1 (triangles). Curves denote fits using Eq. (2).

Fig. 4
Fig. 4

Experimental values over a wide spectral range of (a) transport mean free path l (cf. [8]) and (b) diffusion constant D obtained from the C ( 1 ) frequency correlation function for a 10.2 μ m porous GaP slab. (c) Calculated energy velocity v E using D = v E l 3 . Error bars denote a fitting error at a fixed extrapolation length z 1 + z 2 = 4.3 , while the shaded areas represent a confidence interval (including fitting error) for z 1 + z 2 = 3.8 (solid curves) and 4.8 (dashed curves).

Equations (2)

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

C ( 1 ) ( Δ ν ) ν min ν max d ν δ I a b ( ν ) δ I a b ( ν + Δ ν ) σ a b ( ν ) σ a b ( ν + Δ ν ) ,
C ( 1 ) ( Δ ν ) = L 2 l 2 cosh l η cos l η cosh L η cos L η ,

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