Abstract

We extensively investigate in-plane light diffusion in systems with thicknesses larger than but comparable with the transport mean free path. By exploiting amplified spontaneous emission from dye molecules placed in the same holder of the sample, we obtain a directional probe beam precisely aligned to the sample plane. By comparing spatial intensity distribution of laterally leaking photons with predictions from random walk simulations, we extract accurate values of transport mean free path, opening the way to the investigation of a previously inaccessible kind of sample.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Tromberg, A. Yodh, E. Sevick, and D. Pine, Appl. Opt. 36, 9 (1997).
    [CrossRef] [PubMed]
  2. S. Chandrasekhar, Radiative Transfer (Dover, 1960).
  3. M. Leonetti, S. Capuani, M. Peccianti, G. Ruocco, and C. Conti, Appl. Phys. Lett. 94, 101101 (2009).
    [CrossRef]
  4. P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
    [CrossRef] [PubMed]
  5. M. P. V. Albada and A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985).
    [CrossRef] [PubMed]
  6. P.-E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
    [CrossRef] [PubMed]
  7. N. Garcia, A. Z. Genack, and A. A. Lisyansky, Phys. Rev. B 46, 14475 (1992).
    [CrossRef]
  8. P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
    [CrossRef]
  9. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic, 1995).
  10. J. Taniguchi, H. Murata, and Y. Okamura, Appl. Opt. 46, 2649 (2007).
    [CrossRef] [PubMed]
  11. P. M. Johnson, S. Faez, and A. Lagendijk, Opt. Express 16, 7435 (2008).
    [CrossRef] [PubMed]
  12. A. E. Siegman, Lasers (University Science Books, 1986).
  13. N. G. Chen and J. Bai, Phys. Rev. Lett. 80, 5321 (1998).
    [CrossRef]
  14. E. Akkermans, P. E. Wolf, and R. Maynard, Phys. Rev. Lett. 56, 1471 (1986).
    [CrossRef] [PubMed]
  15. J. X. Zhu, D. J. Pine, and D. A. Weitz, Phys. Rev. A 44, 3948 (1991).
    [CrossRef] [PubMed]
  16. S. Mitani, K. Sakai, and K. Takagi, Jpn. J. Appl. Phys. 39, 146 (2000).
    [CrossRef]
  17. K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
    [CrossRef] [PubMed]

2009

M. Leonetti, S. Capuani, M. Peccianti, G. Ruocco, and C. Conti, Appl. Phys. Lett. 94, 101101 (2009).
[CrossRef]

2008

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
[CrossRef] [PubMed]

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

P. M. Johnson, S. Faez, and A. Lagendijk, Opt. Express 16, 7435 (2008).
[CrossRef] [PubMed]

2007

2000

S. Mitani, K. Sakai, and K. Takagi, Jpn. J. Appl. Phys. 39, 146 (2000).
[CrossRef]

1998

N. G. Chen and J. Bai, Phys. Rev. Lett. 80, 5321 (1998).
[CrossRef]

1997

1992

N. Garcia, A. Z. Genack, and A. A. Lisyansky, Phys. Rev. B 46, 14475 (1992).
[CrossRef]

1991

J. X. Zhu, D. J. Pine, and D. A. Weitz, Phys. Rev. A 44, 3948 (1991).
[CrossRef] [PubMed]

1990

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef] [PubMed]

1986

E. Akkermans, P. E. Wolf, and R. Maynard, Phys. Rev. Lett. 56, 1471 (1986).
[CrossRef] [PubMed]

1985

M. P. V. Albada and A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985).
[CrossRef] [PubMed]

P.-E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
[CrossRef] [PubMed]

Akkermans, E.

E. Akkermans, P. E. Wolf, and R. Maynard, Phys. Rev. Lett. 56, 1471 (1986).
[CrossRef] [PubMed]

Albada, M. P. V.

M. P. V. Albada and A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985).
[CrossRef] [PubMed]

Alfano, R. R.

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef] [PubMed]

Altube, A.

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

Bai, J.

N. G. Chen and J. Bai, Phys. Rev. Lett. 80, 5321 (1998).
[CrossRef]

Barthelemy, P.

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
[CrossRef] [PubMed]

Bertolotti, J.

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
[CrossRef] [PubMed]

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

Blanco, A.

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

Capuani, S.

M. Leonetti, S. Capuani, M. Peccianti, G. Ruocco, and C. Conti, Appl. Phys. Lett. 94, 101101 (2009).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Chen, N. G.

N. G. Chen and J. Bai, Phys. Rev. Lett. 80, 5321 (1998).
[CrossRef]

Conti, C.

M. Leonetti, S. Capuani, M. Peccianti, G. Ruocco, and C. Conti, Appl. Phys. Lett. 94, 101101 (2009).
[CrossRef]

Faez, S.

Garcia, N.

N. Garcia, A. Z. Genack, and A. A. Lisyansky, Phys. Rev. B 46, 14475 (1992).
[CrossRef]

García, P. D.

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

Genack, A. Z.

N. Garcia, A. Z. Genack, and A. A. Lisyansky, Phys. Rev. B 46, 14475 (1992).
[CrossRef]

Johnson, P. M.

Lagendijk, A.

Leonetti, M.

M. Leonetti, S. Capuani, M. Peccianti, G. Ruocco, and C. Conti, Appl. Phys. Lett. 94, 101101 (2009).
[CrossRef]

Lisyansky, A. A.

N. Garcia, A. Z. Genack, and A. A. Lisyansky, Phys. Rev. B 46, 14475 (1992).
[CrossRef]

Liu, F.

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef] [PubMed]

López, C.

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

Maret, G.

P.-E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
[CrossRef] [PubMed]

Martín, M. D.

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

Maynard, R.

E. Akkermans, P. E. Wolf, and R. Maynard, Phys. Rev. Lett. 56, 1471 (1986).
[CrossRef] [PubMed]

Mitani, S.

S. Mitani, K. Sakai, and K. Takagi, Jpn. J. Appl. Phys. 39, 146 (2000).
[CrossRef]

Murata, H.

Okamura, Y.

Peccianti, M.

M. Leonetti, S. Capuani, M. Peccianti, G. Ruocco, and C. Conti, Appl. Phys. Lett. 94, 101101 (2009).
[CrossRef]

Pine, D.

Pine, D. J.

J. X. Zhu, D. J. Pine, and D. A. Weitz, Phys. Rev. A 44, 3948 (1991).
[CrossRef] [PubMed]

Ruocco, G.

M. Leonetti, S. Capuani, M. Peccianti, G. Ruocco, and C. Conti, Appl. Phys. Lett. 94, 101101 (2009).
[CrossRef]

Sakai, K.

S. Mitani, K. Sakai, and K. Takagi, Jpn. J. Appl. Phys. 39, 146 (2000).
[CrossRef]

Sapienza, R.

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

Sevick, E.

Sheng, P.

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

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Takagi, K.

S. Mitani, K. Sakai, and K. Takagi, Jpn. J. Appl. Phys. 39, 146 (2000).
[CrossRef]

Taniguchi, J.

Tromberg, B.

Viña, L.

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

Weitz, D. A.

J. X. Zhu, D. J. Pine, and D. A. Weitz, Phys. Rev. A 44, 3948 (1991).
[CrossRef] [PubMed]

Wiersma, D. S.

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
[CrossRef] [PubMed]

Wolf, P. E.

E. Akkermans, P. E. Wolf, and R. Maynard, Phys. Rev. Lett. 56, 1471 (1986).
[CrossRef] [PubMed]

Wolf, P.-E.

P.-E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
[CrossRef] [PubMed]

Yodh, A.

Yoo, K. M.

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef] [PubMed]

Zhu, J. X.

J. X. Zhu, D. J. Pine, and D. A. Weitz, Phys. Rev. A 44, 3948 (1991).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

M. Leonetti, S. Capuani, M. Peccianti, G. Ruocco, and C. Conti, Appl. Phys. Lett. 94, 101101 (2009).
[CrossRef]

Jpn. J. Appl. Phys.

S. Mitani, K. Sakai, and K. Takagi, Jpn. J. Appl. Phys. 39, 146 (2000).
[CrossRef]

Nature

P. Barthelemy, J. Bertolotti, and D. S. Wiersma, Nature 453, 495 (2008).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. A

J. X. Zhu, D. J. Pine, and D. A. Weitz, Phys. Rev. A 44, 3948 (1991).
[CrossRef] [PubMed]

P. D. García, R. Sapienza, J. Bertolotti, M. D. Martín, A. Blanco, A. Altube, L. Viña, D. S. Wiersma, and C. López, Phys. Rev. A 78, 023823 (2008).
[CrossRef]

Phys. Rev. B

N. Garcia, A. Z. Genack, and A. A. Lisyansky, Phys. Rev. B 46, 14475 (1992).
[CrossRef]

Phys. Rev. Lett.

K. M. Yoo, F. Liu, and R. R. Alfano, Phys. Rev. Lett. 64, 2647 (1990).
[CrossRef] [PubMed]

N. G. Chen and J. Bai, Phys. Rev. Lett. 80, 5321 (1998).
[CrossRef]

E. Akkermans, P. E. Wolf, and R. Maynard, Phys. Rev. Lett. 56, 1471 (1986).
[CrossRef] [PubMed]

M. P. V. Albada and A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985).
[CrossRef] [PubMed]

P.-E. Wolf and G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
[CrossRef] [PubMed]

Other

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

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

A. E. Siegman, Lasers (University Science Books, 1986).

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 (4)

Fig. 1
Fig. 1

(a) Image of the light scattered by the ASE beam in the rhodamine solution. (b) Image of two drops inside the sample holder. The shaded rectangle indicates the pumping area and the white line is 870 μm long. (c) Setup of the experiment. A stripe-shaped beam from a nanosecond Nd:YAG pulsed laser (PL) shines on the rhodamine solution (DYE), producing a pencil of light emitted at the edges of the inverted area. The amplified spontaneous emitted light impinges on the diffusive sample (D). Light leaked from the sides of the sample is collected on the image plane of a 10 × enlarging telescope (ET) and collected by the CCD array of a camera.

Fig. 2
Fig. 2

(a) Color-coded image for the intensity of laterally escaping light. The graphs in (b) and (c) show I ( z ) relative, respectively, to the upper and lower shaded area of (a).

Fig. 3
Fig. 3

(a) Trajectory of a single photon particle with a random walk step of R = 3 μm . (b)  P ( z ) for different values of r is reported. Graphs are translated vertically an arbitrary amount for clarity.

Fig. 4
Fig. 4

(a) Measurements and best fits for (a) sample Latex 5% and (b) for sample PG. (c) Fit residuals as a function of the spacers size S for the sample Latex 10%.

Tables (1)

Tables Icon

Table 1 Measured Compared with Literature ( Are from Ref. [16], While # Is Relative to Ref. [8])

Metrics