Abstract

The zero-mean circular complex Gaussian field statistics of a random medium are experimentally demonstrated in the optical domain, thus verifying this key assumption of statistical optics. Using a frequency-tunable laser source in a fixed-path-length interferometer, we obtain optical field fluctuations in the time and frequency domains that clearly show that the ensemble-averaged temporal intensity converges to the photon transit time distribution, which for the samples used is in excellent agreement with a diffusion model.

© 2004 Optical Society of America

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References

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  1. J. Goodman, in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.
  2. G. Parry, Opt. Acta 21, 763 (1974).
    [CrossRef]
  3. A. Z. Genack and J. M. Drake, Europhys. Lett. 11, 331 (1990).
    [CrossRef]
  4. J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, Opt. Lett. 25, 4 (2000).
    [CrossRef]
  5. M. A. Webster, K. J. Webb, and A. M. Weiner, Phys. Rev. Lett. 88, 033901 (2002).
    [CrossRef]
  6. M. Tomita and M. Matsuoka, Phys. Rev. B 43, 13579 (1991).
    [CrossRef]
  7. A. A. Chabanov and A. Z. Genack, Phys. Rev. E 56, R1338 (1997).
    [CrossRef]
  8. J. Pearce, Z. Jain, and D. M. Mittleman, Phys. Rev. Lett. 91, 043903 (2003).
    [CrossRef]
  9. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  10. H. T. Shang, Electron. Lett. 17, 603 (1981).
    [CrossRef]
  11. J. M. Tualle, E. Tinet, and S. Avrillier, Opt. Commun. 189, 211 (2001).
    [CrossRef]
  12. M. S. Patterson, B. Chance, and B. C. Wilson, Appl. Opt. 28, 2331 (1989).
    [CrossRef] [PubMed]
  13. K. M. Yoo and R. R. Alfano, Opt. Lett. 15, 320 (1990).
    [CrossRef]

2003 (1)

J. Pearce, Z. Jain, and D. M. Mittleman, Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef]

2002 (1)

M. A. Webster, K. J. Webb, and A. M. Weiner, Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef]

2001 (1)

J. M. Tualle, E. Tinet, and S. Avrillier, Opt. Commun. 189, 211 (2001).
[CrossRef]

2000 (1)

1997 (1)

A. A. Chabanov and A. Z. Genack, Phys. Rev. E 56, R1338 (1997).
[CrossRef]

1991 (1)

M. Tomita and M. Matsuoka, Phys. Rev. B 43, 13579 (1991).
[CrossRef]

1990 (2)

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

K. M. Yoo and R. R. Alfano, Opt. Lett. 15, 320 (1990).
[CrossRef]

1989 (1)

1981 (1)

H. T. Shang, Electron. Lett. 17, 603 (1981).
[CrossRef]

1974 (1)

G. Parry, Opt. Acta 21, 763 (1974).
[CrossRef]

Alfano, R. R.

Avrillier, S.

J. M. Tualle, E. Tinet, and S. Avrillier, Opt. Commun. 189, 211 (2001).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov and A. Z. Genack, Phys. Rev. E 56, R1338 (1997).
[CrossRef]

Chance, B.

Drake, J. M.

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

Genack, A. Z.

A. A. Chabanov and A. Z. Genack, Phys. Rev. E 56, R1338 (1997).
[CrossRef]

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

Goodman, J.

J. Goodman, in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Jain, Z.

J. Pearce, Z. Jain, and D. M. Mittleman, Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef]

Matsuoka, M.

M. Tomita and M. Matsuoka, Phys. Rev. B 43, 13579 (1991).
[CrossRef]

McKinney, J. D.

Mittleman, D. M.

J. Pearce, Z. Jain, and D. M. Mittleman, Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef]

Parry, G.

G. Parry, Opt. Acta 21, 763 (1974).
[CrossRef]

Patterson, M. S.

Pearce, J.

J. Pearce, Z. Jain, and D. M. Mittleman, Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef]

Shang, H. T.

H. T. Shang, Electron. Lett. 17, 603 (1981).
[CrossRef]

Tinet, E.

J. M. Tualle, E. Tinet, and S. Avrillier, Opt. Commun. 189, 211 (2001).
[CrossRef]

Tomita, M.

M. Tomita and M. Matsuoka, Phys. Rev. B 43, 13579 (1991).
[CrossRef]

Tualle, J. M.

J. M. Tualle, E. Tinet, and S. Avrillier, Opt. Commun. 189, 211 (2001).
[CrossRef]

Webb, K. J.

M. A. Webster, K. J. Webb, and A. M. Weiner, Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef]

J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, Opt. Lett. 25, 4 (2000).
[CrossRef]

Webster, M. A.

M. A. Webster, K. J. Webb, and A. M. Weiner, Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef]

J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, Opt. Lett. 25, 4 (2000).
[CrossRef]

Weiner, A. M.

M. A. Webster, K. J. Webb, and A. M. Weiner, Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef]

J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, Opt. Lett. 25, 4 (2000).
[CrossRef]

Wilson, B. C.

Yoo, K. M.

Appl. Opt. (1)

Electron. Lett. (1)

H. T. Shang, Electron. Lett. 17, 603 (1981).
[CrossRef]

Europhys. Lett. (1)

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

Opt. Acta (1)

G. Parry, Opt. Acta 21, 763 (1974).
[CrossRef]

Opt. Commun. (1)

J. M. Tualle, E. Tinet, and S. Avrillier, Opt. Commun. 189, 211 (2001).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (1)

M. Tomita and M. Matsuoka, Phys. Rev. B 43, 13579 (1991).
[CrossRef]

Phys. Rev. E (1)

A. A. Chabanov and A. Z. Genack, Phys. Rev. E 56, R1338 (1997).
[CrossRef]

Phys. Rev. Lett. (2)

J. Pearce, Z. Jain, and D. M. Mittleman, Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef]

M. A. Webster, K. J. Webb, and A. M. Weiner, Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef]

Other (2)

J. Goodman, in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 9–75.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for characterizing a random medium by use of frequency-resolved interferometer measurements.

Fig. 2
Fig. 2

(a) Real component of the complex electric field amplitude Aoν˜ from four independent measurements of the d=6 mm sample (offset for clarity). (b) Histogram of the real and the imaginary components of the field averaged over 100 measurements, plotted on a semi-log scale.

Fig. 3
Fig. 3

(a) Typical intensity temporal responses obtained from inverse Fourier transforms of the data in Fig. 2(a) (offset for clarity). (b) Estimate of the ensemble-average intensity temporal response obtained by averaging 100 measurements (solid curves). Excellent agreement with a diffusion model for each sample thickness is shown (dashed curves).

Equations (2)

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Adetν˜2Hνexp-j2πντ+H*ν×expj2πντ+Hν2+1Aiν˜2.
pt=aot20dtaot2,

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