Abstract

Angle- and time-resolved studies are presented for an ultrafast laser pulse propagating through a slab of random media in the intermediate scattering regime, where a coherent (ballistic) component coexists with a incoherent (diffusive) component in the forward-scattered light. The incoherent component can be approximated by diffusion theory when the thickness of the slab is greater than 10 transport mean free paths. The theoretical results from the two-frequency coherence function in the Rytov approximation are in qualitative but not quantitative agreement with the experimental results.

© 1990 Optical Society of America

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References

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  1. M. Lax, V. Nayaramamurti, R. C. Fulton, in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), p. 229.
  2. G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
    [CrossRef] [PubMed]
  3. A. Ishimaru, S. T. Hong, Radio Sci. 10, 637 (1975).
    [CrossRef]
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, pp. 318–324.

1987

G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
[CrossRef] [PubMed]

1975

A. Ishimaru, S. T. Hong, Radio Sci. 10, 637 (1975).
[CrossRef]

Fleury, P. A.

G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
[CrossRef] [PubMed]

Fulton, R. C.

M. Lax, V. Nayaramamurti, R. C. Fulton, in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), p. 229.

Hong, S. T.

A. Ishimaru, S. T. Hong, Radio Sci. 10, 637 (1975).
[CrossRef]

Ishimaru, A.

A. Ishimaru, S. T. Hong, Radio Sci. 10, 637 (1975).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, pp. 318–324.

Lax, M.

M. Lax, V. Nayaramamurti, R. C. Fulton, in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), p. 229.

McCall, S. L.

G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
[CrossRef] [PubMed]

Nayaramamurti, V.

M. Lax, V. Nayaramamurti, R. C. Fulton, in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), p. 229.

Watson, G. H.

G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett.

G. H. Watson, P. A. Fleury, S. L. McCall, Phys. Rev. Lett. 58, 945 (1987).
[CrossRef] [PubMed]

Radio Sci.

A. Ishimaru, S. T. Hong, Radio Sci. 10, 637 (1975).
[CrossRef]

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 2, pp. 318–324.

M. Lax, V. Nayaramamurti, R. C. Fulton, in Laser Optics of Condensed Matter, J. L. Birman, H. Z. Cummins, A. A. Kaplyanskii, eds. (Plenum, New York, 1987), p. 229.

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Figures (4)

Fig. 1
Fig. 1

Photographs taken by a streak camera showing the angular and temporal behavior of a light pulse propagating through a 10-mm slab of random media. The first white spot is the reference pulse, the second spot is the coherent pulse, and the incoherent pulse is spread over a wide angular and temporal region. The curves trace the intensity versus time for waves scattered in the forward direction ±4 mrad. The series of photographs are for an increasing number particle density for latex beads of 0.33-μm diameter: (a) n = 7.0 × 1016 m−3, (b) 7.9 × 1016 m−3, (c) 8.9 × 1016 m−3, (d) 9.5 × 1016 m−3, (e) 10.4 × 1016 m−3, and (f) 17.3 × 1016 m−3.

Fig. 2
Fig. 2

Photographs for scattered light through 10 mm of random media in the intermediate scattering regime: (a) d = 15.8 μm, nσsz = 19.8, (b) d = 3.134 μm, nσsz = 12.9.

Fig. 3
Fig. 3

Plots of the ratio of coherent (Ic) to total (It) intensity of scattered light in the forward direction versus nσsz for four different scatterer diameters. The solid curve is plotted from Eq. (1) for a bead diameter of 0.46 μm, where σs = 0.109 × 10−12 m2, σm = 0.11σm, and f = 10−7.

Fig. 4
Fig. 4

Normalized intensity of forward-scattered light as a function of arrival time: (a) d = 3.134 μm, nσsz = 42.6, and lt = 1.52 mm; (b) d = 0.296 μm, nσsz = 33.5, and lt = 1.1 mm. Dotted curves, experimental results; solid curves, Eq. (2); dashed curves, Eq. (3); dashed–dotted curves, Eq. (6).

Equations (6)

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I c I t = 1 1 + f [ exp ( n σ s z ) 1 ] / ( 1 + n σ m w ) ,
I z ( t ) = D π z 2 m = 1 m ( π z / d ) 2 sin ( m π z / d ) × exp [− D t ( m π / d ) 2 ] ,
I ( t ) = T ω r 2 π 0 exp [− ( T w r x ) 2 / 8 ] A ( x ) × cos [ ϕ ( x ) w r x t ] d x ,
A ( x ) = exp {− n σ t z [ 1 ( W 0 / x ) tan 1 x ] } ,
ϕ ( x ) = ( n σ t z / 2 ) [ ( W 0 / x ) ln ( 1 + x 2 ) ] , x = ω d / ω r , ω r = 2 α v / z , W 0 = σ s / σ t ,
I ( t ) = π ω c 4 m = 0 ( 2 m + 1 ) ( 1 ) m × exp { [ ( 2 m + 1 ) π 4 ] 2 ω c t } ,

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