Abstract

Two different transport regimes of light are observed in reflection from the same disordered photonic crystal. A model based on the scaling theory of localization explains the behavior of the path length-resolved reflection at two different probing wavelengths. Our results demonstrate the continuous renormalization of the photon diffusion coefficient measured in reflection from random media.

© 2011 OSA

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  2. M. C. W. van Rossum and T. M. N. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
    [CrossRef]
  3. Y. Kuga and A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 1(8), 831–835 (1984).
    [CrossRef]
  4. A. Z. Genack and A. A. Chabanov, “Signatures of photon localization,” J. Phys. Math. Gen. 38(49), 10465–10488 (2005).
    [CrossRef]
  5. F. Scheffold and G. Maret, “Universal conductance fluctuations of light,” Phys. Rev. Lett. 81(26), 5800–5803 (1998).
    [CrossRef]
  6. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
    [CrossRef]
  7. S. John and M. J. Stephen, “Wave propagation and localization in a long-range correlated random potential,” Phys. Rev. B 28(11), 6358–6368 (1983).
    [CrossRef]
  8. S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53(22), 2169–2172 (1984).
    [CrossRef]
  9. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
    [CrossRef] [PubMed]
  10. S. John and R. Rangarajan, “Optimal structures for classical wave localization: An alternative to the Ioffe-Regel criterion,” Phys. Rev. B Condens. Matter 38(14), 10101–10104 (1988).
    [CrossRef] [PubMed]
  11. M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96(6), 063904–063907 (2006).
    [CrossRef] [PubMed]
  12. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
    [CrossRef]
  13. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
    [CrossRef] [PubMed]
  14. 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]
  15. C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, “Exceptional reduction of the diffusion constant in partially disordered photonic crystals,” Phys. Rev. Lett. 101(12), 123901 (2008).
    [CrossRef] [PubMed]
  16. P. W. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52(3), 505–509 (1985).
    [CrossRef]
  17. M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28(12), 2331–2336 (1989).
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    [CrossRef] [PubMed]
  19. A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
    [CrossRef] [PubMed]
  20. C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4(10), 794–798 (2008).
    [CrossRef]
  21. P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
    [CrossRef] [PubMed]
  22. J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44(6), 3948–3959 (1991).
    [CrossRef] [PubMed]

2008

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, “Exceptional reduction of the diffusion constant in partially disordered photonic crystals,” Phys. Rev. Lett. 101(12), 123901 (2008).
[CrossRef] [PubMed]

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4(10), 794–798 (2008).
[CrossRef]

2007

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

2006

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96(6), 063904–063907 (2006).
[CrossRef] [PubMed]

2005

A. Z. Genack and A. A. Chabanov, “Signatures of photon localization,” J. Phys. Math. Gen. 38(49), 10465–10488 (2005).
[CrossRef]

2003

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[CrossRef] [PubMed]

2000

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

1999

M. C. W. van Rossum and T. M. N. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[CrossRef]

G. Popescu and A. Dogariu, “Optical path-length spectroscopy of wave propagation in random media,” Opt. Lett. 24(7), 442–444 (1999).
[CrossRef] [PubMed]

1998

F. Scheffold and G. Maret, “Universal conductance fluctuations of light,” Phys. Rev. Lett. 81(26), 5800–5803 (1998).
[CrossRef]

1997

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

1991

J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44(6), 3948–3959 (1991).
[CrossRef] [PubMed]

1989

1988

S. John and R. Rangarajan, “Optimal structures for classical wave localization: An alternative to the Ioffe-Regel criterion,” Phys. Rev. B Condens. Matter 38(14), 10101–10104 (1988).
[CrossRef] [PubMed]

1987

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

1985

P. W. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52(3), 505–509 (1985).
[CrossRef]

1984

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

Y. Kuga and A. Ishimaru, “Retroreflectance from a dense distribution of spherical particles,” J. Opt. Soc. Am. A 1(8), 831–835 (1984).
[CrossRef]

1983

S. John and M. J. Stephen, “Wave propagation and localization in a long-range correlated random potential,” Phys. Rev. B 28(11), 6358–6368 (1983).
[CrossRef]

1979

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]

1958

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]

Aegerter, C. M.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96(6), 063904–063907 (2006).
[CrossRef] [PubMed]

Anderson, P. W.

P. W. Anderson, “The question of classical localization: a theory of white paint?” Philos. Mag. B 52(3), 505–509 (1985).
[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]

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

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

Blanco, A.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

Bret, B. P. J.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[CrossRef] [PubMed]

Chabanov, A. A.

A. Z. Genack and A. A. Chabanov, “Signatures of photon localization,” J. Phys. Math. Gen. 38(49), 10465–10488 (2005).
[CrossRef]

Chance, B.

Chomski, E.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

Conti, C.

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4(10), 794–798 (2008).
[CrossRef]

Dogariu, A.

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Fratalocchi, A.

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4(10), 794–798 (2008).
[CrossRef]

Genack, A. Z.

A. Z. Genack and A. A. Chabanov, “Signatures of photon localization,” J. Phys. Math. Gen. 38(49), 10465–10488 (2005).
[CrossRef]

Grabtchak, S.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

Gross, P.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96(6), 063904–063907 (2006).
[CrossRef] [PubMed]

Ibisate, M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

Imhof, A.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[CrossRef] [PubMed]

Ishimaru, A.

John, S.

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, “Exceptional reduction of the diffusion constant in partially disordered photonic crystals,” Phys. Rev. Lett. 101(12), 123901 (2008).
[CrossRef] [PubMed]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

S. John and R. Rangarajan, “Optimal structures for classical wave localization: An alternative to the Ioffe-Regel criterion,” Phys. Rev. B Condens. Matter 38(14), 10101–10104 (1988).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

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

S. John and M. J. Stephen, “Wave propagation and localization in a long-range correlated random potential,” Phys. Rev. B 28(11), 6358–6368 (1983).
[CrossRef]

Johnson, P. M.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[CrossRef] [PubMed]

Kuga, Y.

Lagendijk, A.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[CrossRef] [PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

Leonard, S. W.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

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]

Lopez, C.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

Maret, G.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96(6), 063904–063907 (2006).
[CrossRef] [PubMed]

F. Scheffold and G. Maret, “Universal conductance fluctuations of light,” Phys. Rev. Lett. 81(26), 5800–5803 (1998).
[CrossRef]

Meseguer, F.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

Miguez, H.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

Mondia, J. P.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

Nieuwenhuizen, T. M. N.

M. C. W. van Rossum and T. M. N. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[CrossRef]

Ozin, G. A.

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, “Exceptional reduction of the diffusion constant in partially disordered photonic crystals,” Phys. Rev. Lett. 101(12), 123901 (2008).
[CrossRef] [PubMed]

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

Patterson, M. S.

Pine, D. J.

J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44(6), 3948–3959 (1991).
[CrossRef] [PubMed]

Popescu, G.

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]

Rangarajan, R.

S. John and R. Rangarajan, “Optimal structures for classical wave localization: An alternative to the Ioffe-Regel criterion,” Phys. Rev. B Condens. Matter 38(14), 10101–10104 (1988).
[CrossRef] [PubMed]

Righini, R.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

Rivas, J. G.

P. M. Johnson, A. Imhof, B. P. J. Bret, J. G. Rivas, and A. Lagendijk, “Time-resolved pulse propagation in a strongly scattering material,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(1), 016604 (2003).
[CrossRef] [PubMed]

Scheffold, F.

F. Scheffold and G. Maret, “Universal conductance fluctuations of light,” Phys. Rev. Lett. 81(26), 5800–5803 (1998).
[CrossRef]

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Segev, M.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Stephen, M. J.

S. John and M. J. Stephen, “Wave propagation and localization in a long-range correlated random potential,” Phys. Rev. B 28(11), 6358–6368 (1983).
[CrossRef]

Störzer, M.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96(6), 063904–063907 (2006).
[CrossRef] [PubMed]

Toader, O.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

Toninelli, C.

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, “Exceptional reduction of the diffusion constant in partially disordered photonic crystals,” Phys. Rev. Lett. 101(12), 123901 (2008).
[CrossRef] [PubMed]

van Driel, H. M.

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

van Rossum, M. C. W.

M. C. W. van Rossum and T. M. N. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71(1), 313–371 (1999).
[CrossRef]

Vekris, E.

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, “Exceptional reduction of the diffusion constant in partially disordered photonic crystals,” Phys. Rev. Lett. 101(12), 123901 (2008).
[CrossRef] [PubMed]

Weitz, D. A.

J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44(6), 3948–3959 (1991).
[CrossRef] [PubMed]

Wiersma, D. S.

C. Toninelli, E. Vekris, G. A. Ozin, S. John, and D. S. Wiersma, “Exceptional reduction of the diffusion constant in partially disordered photonic crystals,” Phys. Rev. Lett. 101(12), 123901 (2008).
[CrossRef] [PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

Wilson, B. C.

Zhu, J. X.

J. X. Zhu, D. J. Pine, and D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44(6), 3948–3959 (1991).
[CrossRef] [PubMed]

Appl. Opt.

J. Opt. Soc. Am. A

J. Phys. Math. Gen.

A. Z. Genack and A. A. Chabanov, “Signatures of photon localization,” J. Phys. Math. Gen. 38(49), 10465–10488 (2005).
[CrossRef]

Nat. Phys.

C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional Anderson localization and lasing in inverted opals,” Nat. Phys. 4(10), 794–798 (2008).
[CrossRef]

Nature

A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel; “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405(6785), 437–440 (2000).
[CrossRef] [PubMed]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390(6661), 671–673 (1997).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007).
[CrossRef] [PubMed]

Opt. Lett.

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Figures (5)

Fig. 1
Fig. 1

The RMS displacement of the diffuse light from a source determines the effective size L of the material seen by the light.

Fig. 2
Fig. 2

Path length distribution measured in reflection for a semi-infinite medium comprising a suspension of 0.43 μm diameter polystyrene spheres in water. The −5/2 slope on a log-log scale is indicative of normal diffusion.

Fig. 3
Fig. 3

Fiber-based Michelson interferometer used for collection of photon path length distributions from multiple scattering media. The single-mode fiber acts as both a source and detector.

Fig. 4
Fig. 4

(a) Path length distribution of reflected photon path lengths from the disordered photonic crystal. (b) Estimated density of states for the sample. Shaded bands indicate the spectral regions that were probed. The widths of the bands are related to the uncertainty in the lattice constant, a.

Fig. 5
Fig. 5

Time of flight distributions measured in transmission at the two different wavelengths. The linear dependence on a semilog scale indicates that the diffusion coefficient depends on the size of the system, not time.

Equations (5)

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D= v 3 ( ξ + L + L abs )
p( t )= ( 4πD ) 3/2 z 0 z e t 5/2 ×exp( μ abs vt )exp[ ( z 0 z e ) 2 4Dt ]
log[ p( t ) ]= 3 2 log( D ) 5 2 log( t )2 μ abs vt ( z 0 z e ) 2 4Dt +const.
D= D 0 ( 1 ξ + 1 6Dt ).
log[ p( t ) ]2log( t )+const.

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