Abstract

The origin of low-coherence enhanced backscattering (EBS) of light in random media when the spatial coherence length of illumination is much smaller than the transport mean free path has been poorly understood. We report that in weakly scattering discrete random media low-coherence EBS originates from time-reversed paths of double scattering. Low spatial coherence illumination dephases the time-reversed waves outside its finite coherence area, which isolates the minimal number of scattering events in EBS from higher-order scattering. Moreover, we show the first experimental evidence that the minimal number of scattering events in EBS is double scattering, which has been hypothesized since the first observation of EBS.

© 2006 Optical Society of America

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2005

2004

2003

G. Labeyrie, D. Delande, C. A. Muller, C. Miniatura, and R. Kaiser, Phys. Rev. A 67, 033814 (2003).
[CrossRef]

2000

R. Lenke, R. Lehner, and G. Maret, Europhys. Lett. 52, 620 (2000).
[CrossRef]

1996

1990

1988

R. Vreeker, M. P. van Albada, R. Sprik, and A. Lagendijk, Phys. Lett. A 132, 51 (1988).
[CrossRef]

M. B. van der Mark, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 37, 3575 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. (France) 49, 77 (1988).
[CrossRef]

1985

M. P. van 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]

1984

Akkermans, E.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. (France) 49, 77 (1988).
[CrossRef]

Alfano, R. R.

Asakura, T.

Backman, V.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), p. 572.

Delande, D.

G. Labeyrie, D. Delande, C. A. Muller, C. Miniatura, and R. Kaiser, Phys. Rev. A 67, 033814 (2003).
[CrossRef]

Dogariu, A.

Ishimaru, A.

Kaiser, R.

G. Labeyrie, D. Delande, C. A. Muller, C. Miniatura, and R. Kaiser, Phys. Rev. A 67, 033814 (2003).
[CrossRef]

Kim, Y. L.

Kuga, Y.

Labeyrie, G.

G. Labeyrie, D. Delande, C. A. Muller, C. Miniatura, and R. Kaiser, Phys. Rev. A 67, 033814 (2003).
[CrossRef]

Lagendijk, A.

R. Vreeker, M. P. van Albada, R. Sprik, and A. Lagendijk, Phys. Lett. A 132, 51 (1988).
[CrossRef]

M. B. van der Mark, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 37, 3575 (1988).
[CrossRef]

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

Lehner, R.

R. Lenke, R. Lehner, and G. Maret, Europhys. Lett. 52, 620 (2000).
[CrossRef]

Lenke, R.

R. Lenke, R. Lehner, and G. Maret, Europhys. Lett. 52, 620 (2000).
[CrossRef]

Liu, Y.

Maret, G.

R. Lenke, R. Lehner, and G. Maret, Europhys. Lett. 52, 620 (2000).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. (France) 49, 77 (1988).
[CrossRef]

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

Maynard, R.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. (France) 49, 77 (1988).
[CrossRef]

Miniatura, C.

G. Labeyrie, D. Delande, C. A. Muller, C. Miniatura, and R. Kaiser, Phys. Rev. A 67, 033814 (2003).
[CrossRef]

Muller, C. A.

G. Labeyrie, D. Delande, C. A. Muller, C. Miniatura, and R. Kaiser, Phys. Rev. A 67, 033814 (2003).
[CrossRef]

Okamoto, T.

Roy, H. K.

Schwartz, C.

Sprik, R.

R. Vreeker, M. P. van Albada, R. Sprik, and A. Lagendijk, Phys. Lett. A 132, 51 (1988).
[CrossRef]

Tang, G. C.

Turzhitsky, V. M.

van Albada, M. P.

M. B. van der Mark, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 37, 3575 (1988).
[CrossRef]

R. Vreeker, M. P. van Albada, R. Sprik, and A. Lagendijk, Phys. Lett. A 132, 51 (1988).
[CrossRef]

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

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1995).

van der Mark, M. B.

M. B. van der Mark, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 37, 3575 (1988).
[CrossRef]

Vreeker, R.

R. Vreeker, M. P. van Albada, R. Sprik, and A. Lagendijk, Phys. Lett. A 132, 51 (1988).
[CrossRef]

Wali, R. K.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), p. 572.

Wolf, P. E.

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. (France) 49, 77 (1988).
[CrossRef]

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

Yoo, K. M.

Appl. Opt.

Europhys. Lett.

R. Lenke, R. Lehner, and G. Maret, Europhys. Lett. 52, 620 (2000).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. (France)

E. Akkermans, P. E. Wolf, R. Maynard, and G. Maret, J. Phys. (France) 49, 77 (1988).
[CrossRef]

Opt. Lett.

Phys. Lett. A

R. Vreeker, M. P. van Albada, R. Sprik, and A. Lagendijk, Phys. Lett. A 132, 51 (1988).
[CrossRef]

Phys. Rev. A

G. Labeyrie, D. Delande, C. A. Muller, C. Miniatura, and R. Kaiser, Phys. Rev. A 67, 033814 (2003).
[CrossRef]

Phys. Rev. B

M. B. van der Mark, M. P. van Albada, and A. Lagendijk, Phys. Rev. B 37, 3575 (1988).
[CrossRef]

Phys. Rev. Lett.

M. P. van 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

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999), p. 572.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1995).

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Figures (3)

Fig. 1
Fig. 1

I EBS ( θ , λ ) obtained from the aqueous suspension of microspheres ( d = 1.5 μ m ) under low spatial coherence illumination ( L sc = 35 μ m ) for various mean free paths l s . For l s L sc , the spectral shape remains unchanged, indicating that it reaches the minimal number of scattering events in EBS (i.e., double scattering).

Fig. 2
Fig. 2

Accuracy analyses of the double-scattering model of LEBS. (a) Spectra of LEBS in the backward direction. (b) Correlation coefficient. (c) RMS error.

Fig. 3
Fig. 3

I EBS ( θ , λ ) obtained from the experiment of the aqueous suspension of microspheres ( d = 1.5 μ m ) and its simulation from the double-scattering model for L sc = 35 and 110 μ m with l s = 700 μ m . Bottom, angular profiles of the EBS peaks at λ = 532 nm .

Equations (2)

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P ( r , λ ) = 0 0 exp [ μ a ( r 2 + ( z z ) 2 + z + z ) ] [ r 2 + ( z z ) 2 ] ( z + d ) 2 μ s ( λ ) F ( Θ , λ ) μ s ( λ ) F ( π Θ , λ ) d z d z ,
I EBS ( θ ) 0 C ( r ) r P ( r ) exp ( i 2 π r θ λ ) d r ,

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