Abstract

The backscattering enhancement of light from random media is analyzed for situations in which the scatterers are illuminated with spatially partially coherent light. The effect of coherence is incorporated into the existing theories by use of the angular correlation description for the illuminating light field. When the area of illumination is infinite, an analogy to the van Cittert–Zernike theorem leads to the expression for the intensity distribution that is given by the sum of backscattered intensities, each of which would arise from each incident plane-wave component of the angular spectrum. It is shown that the backscattering cone is partially suppressed and deformed owing to breaking of the time-reversal symmetry of mutiple-scattering paths.

© 1996 Optical Society of America

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References

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  1. M. P. V. Albada, A. Lagendijk, Phys. Rev. Lett. 55, 2692 (1985).
    [CrossRef] [PubMed]
  2. P. E. Wolf, G. Maret, Phys. Rev. Lett. 55, 2696 (1985).
    [CrossRef] [PubMed]
  3. M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
    [CrossRef] [PubMed]
  4. S. Etemad, R. Thompson, M. J. Andrejco, Phys. Rev. Lett. 57, 575 (1986).
    [CrossRef] [PubMed]
  5. M. Tomita, H. Ikari, Phys. Rev. B 43, 3716 (1991).
    [CrossRef]
  6. E. W. Marchand, E. Wolf, J. Opt. Soc. Am. 62, 379 (1972).
    [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 48.
  8. E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, J. Phys. (Paris) 49, 77 (1988).
    [CrossRef]
  9. A. Z. Genack, in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), p. 260.
  10. E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).
    [CrossRef]
  11. See, for example, E. Wolf, Opt. Lett. 19, 2024 (1994).
    [CrossRef] [PubMed]
  12. F. A. Erbacher, R. Lenke, G. Maret, Europhys. Lett. 21, 551 (1993).
    [CrossRef]

1994

1993

F. A. Erbacher, R. Lenke, G. Maret, Europhys. Lett. 21, 551 (1993).
[CrossRef]

1991

M. Tomita, H. Ikari, Phys. Rev. B 43, 3716 (1991).
[CrossRef]

1988

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

1986

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[CrossRef] [PubMed]

S. Etemad, R. Thompson, M. J. Andrejco, Phys. Rev. Lett. 57, 575 (1986).
[CrossRef] [PubMed]

1985

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

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

1982

1972

Akkermans, E.

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

Albada, M. P. V.

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

Andrejco, M. J.

S. Etemad, R. Thompson, M. J. Andrejco, Phys. Rev. Lett. 57, 575 (1986).
[CrossRef] [PubMed]

Edrei, I.

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[CrossRef] [PubMed]

Erbacher, F. A.

F. A. Erbacher, R. Lenke, G. Maret, Europhys. Lett. 21, 551 (1993).
[CrossRef]

Etemad, S.

S. Etemad, R. Thompson, M. J. Andrejco, Phys. Rev. Lett. 57, 575 (1986).
[CrossRef] [PubMed]

Freund, I.

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[CrossRef] [PubMed]

Genack, A. Z.

A. Z. Genack, in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), p. 260.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 48.

Ikari, H.

M. Tomita, H. Ikari, Phys. Rev. B 43, 3716 (1991).
[CrossRef]

Kaveh, M.

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[CrossRef] [PubMed]

Lagendijk, A.

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

Lenke, R.

F. A. Erbacher, R. Lenke, G. Maret, Europhys. Lett. 21, 551 (1993).
[CrossRef]

Marchand, E. W.

Maret, G.

F. A. Erbacher, R. Lenke, G. Maret, Europhys. Lett. 21, 551 (1993).
[CrossRef]

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

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

Maynard, R.

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

Rosenbluh, M.

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[CrossRef] [PubMed]

Thompson, R.

S. Etemad, R. Thompson, M. J. Andrejco, Phys. Rev. Lett. 57, 575 (1986).
[CrossRef] [PubMed]

Tomita, M.

M. Tomita, H. Ikari, Phys. Rev. B 43, 3716 (1991).
[CrossRef]

Wolf, E.

Wolf, P. E.

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

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

Europhys. Lett.

F. A. Erbacher, R. Lenke, G. Maret, Europhys. Lett. 21, 551 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Phys.

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

Opt. Lett.

Phys. Rev. B

M. Tomita, H. Ikari, Phys. Rev. B 43, 3716 (1991).
[CrossRef]

Phys. Rev. Lett.

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

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

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, Phys. Rev. Lett. 57, 2049 (1986).
[CrossRef] [PubMed]

S. Etemad, R. Thompson, M. J. Andrejco, Phys. Rev. Lett. 57, 575 (1986).
[CrossRef] [PubMed]

Other

A. Z. Genack, in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), p. 260.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 48.

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Figures (3)

Fig. 1
Fig. 1

Geometry used for calculation of the backscattered intensity.

Fig. 2
Fig. 2

Normalized intensity distribution of the backscattered light plotted against the scattering angle for various values of the coherence interval. The value of the transport mean free path is 10λ.

Fig. 3
Fig. 3

Enhancement factor of the backscattered intensity as a function of the normalized coherence interval. The value of the transport mean free path is the same as in Fig. 2.

Equations (13)

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U i j ( k s 0 , k s f , ν ) = α a ( s 0 , ν ) p i j ( α , ν ) × exp [ i k ( s 0 · r i - s f · r j + s f · r d ) ] ,
U ( k s f , ν ) = s 0 2 1 d 2 s 0 i , j U i j ( k s 0 , k s f , ν ) .
I ( k s f , ν ) = Re [ S 1 2 1 d 2 s 1 S 2 2 1 d 2 s 2 × A ( s 1 , s 2 , ν ) i , j α p i , j ( α , ν ) 2 × ( exp [ i k ( s 2 - s 1 ) · r i ] + exp { i k [ s 2 + s f ) · r j - ( s 1 + s f ) · r i ] } ) ] ,
i , j α p i j ( α , ν ) 2 = P ( r , ν ) d 2 r i d 2 r j ,
I ( k s f , ν ) = Re ( S 2 1 d 2 s s 2 4 d 2 s A ( s - s / 2 , s + s / 2 , ν ) × S exp ( i k s · r ) d 2 r S P ( r , ν ) { exp ( i k s · r / 2 ) + exp [ i k ( s + s f ) · r ] } d 2 r ) ,
A ( s 1 , s 2 , ν ) = ( k / 2 π ) 4 d 2 r 1 d 2 r 2 W ( r 1 , r 2 , ν ) × exp [ - i k ( s 2 · r 2 - s 1 · r 1 ) ] .
W ( r 1 , r 2 , ν ) = I ( r 1 + r 2 2 , ν ) μ ( r 2 - r 1 , ν ) ,
A ( s - s / 2 , s + s / 2 , ν ) = I A ( k s , ν ) μ A ( k s , ν ) ,
I A ( k s , ν ) = ( k / 2 π ) 2 μ ( r , ν ) exp ( - i k s · r ) d 2 r ,
μ A ( k s , ν ) = ( k / 2 π ) 2 I ( r , ν ) exp ( - i k s · r ) d 2 r .
I N ( k s f , ν ) = C - 1 S 2 1 d 2 s I A ( k s , ν ) I 0 ( k s , k s f , ν ) ,
I 0 ( k s , k s f , ν ) = d 2 r P ( r , ν ) { 1 + exp [ i k ( s + s f ) · r ] }
I 0 ( k s , k s f , ν ) = 1 + ( 1 1 + 2 Δ 0 ) 1 ( 1 + k l * ) 2 × [ 1 + 1 - exp ( - 2 Δ 0 k l * ) k l * ] ,

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