Abstract

Recently, the backscattering enhancement by densely distributed particles of a size comparable to the wavelength was reported. It has been explained as the constructive interference of two waves traveling in opposite directions. This enhancement was observed only in densely distributed particles, and its existence in sparsely distributed media has not been verified yet. In this paper we present the experimental evidence of backscattering enhancement by sparsely distributed very large particles. Experiments are conducted using 45-μm latex particles which are approximately 100 times the wavelength. Both copolarized and cross-polarized components are measured for different particle concentrations. Unlike for small particles, back-scattering enhancement is most noticeable when the particle concentration is low. The angular width of the peak is comparable to the ratio (wavelength)/(particle size) and is independent of the optical distance.

© 1989 Optical Society of America

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References

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  1. Y. Kuga, A. Ishimaru, “Retroreflectance from a Dense Distribution of Spherical Particles,” J. Opt. Soc. Am. A 1, 831–835 (1984).
    [CrossRef]
  2. Y. Kuga, A. Ishimaru, “Depolarization Effects of the Enhanced Retroreflectance from a Dense Distribution of Spherical Particles,” J. Opt. Soc. Am. A 2, 616–618 (1985).
    [CrossRef]
  3. M. van Albada, A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
    [CrossRef] [PubMed]
  4. P. E. Wolf, G. Maret, “Weak Localization and Coherent Backscattering of Photon in Disordered Media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
    [CrossRef] [PubMed]
  5. L. Tsang, A. Ishimaru, “Backscattering Enhancement of Random Discrete Scatterers,” J. Opt. Soc. Am. A 1, 836–839 (1984).
    [CrossRef]
  6. A. Ishimaru, L. Tsang, “Backscattering Enhancement of Random Discrete Scatterers of Moderate Sizes,” J. Opt. Soc. Am. A 5, 228–236 (1988).
    [CrossRef]
  7. Y. Kuga, A. Ishimaru, “Backscattering Enhancement by Randomly Distributed Particles of Different Sizes,” Proc. Soc. Photo-Opt. Instrum. Eng.927, 33–37 (1988), to be published.
  8. Y. A. Kravtsov, A. I. Saichev, “Effects of Double Passage of Waves in Randomly Inhomogeneous Media,” Sov. Phys. Usp. 25, 494–508 (1983).
    [CrossRef]
  9. V. I. Tatarskii, “Some New Aspects in the Problem of Waves and Turbulence,” Radio Sci. 22, 859–865 (1987).
    [CrossRef]
  10. Y. Kuga, A. Ishimaru, Q. Ma, “The Second-Order Multiple Scattering Theory for the Vector Radiative Transfer Equation,” Radio Sci. accepted for publication.
  11. D. A. De Wolf, “Electromagnetic Reflection from an Extended Turbulent Medium: Cumulative Forward-Scatter Single-Backscatter Approximation,” IEEE Trans. Antennas Propag. AP-19, 254–262 (1971).
    [CrossRef]

1988

1987

V. I. Tatarskii, “Some New Aspects in the Problem of Waves and Turbulence,” Radio Sci. 22, 859–865 (1987).
[CrossRef]

1985

M. van Albada, A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

P. E. Wolf, G. Maret, “Weak Localization and Coherent Backscattering of Photon in Disordered Media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Y. Kuga, A. Ishimaru, “Depolarization Effects of the Enhanced Retroreflectance from a Dense Distribution of Spherical Particles,” J. Opt. Soc. Am. A 2, 616–618 (1985).
[CrossRef]

1984

1983

Y. A. Kravtsov, A. I. Saichev, “Effects of Double Passage of Waves in Randomly Inhomogeneous Media,” Sov. Phys. Usp. 25, 494–508 (1983).
[CrossRef]

1971

D. A. De Wolf, “Electromagnetic Reflection from an Extended Turbulent Medium: Cumulative Forward-Scatter Single-Backscatter Approximation,” IEEE Trans. Antennas Propag. AP-19, 254–262 (1971).
[CrossRef]

De Wolf, D. A.

D. A. De Wolf, “Electromagnetic Reflection from an Extended Turbulent Medium: Cumulative Forward-Scatter Single-Backscatter Approximation,” IEEE Trans. Antennas Propag. AP-19, 254–262 (1971).
[CrossRef]

Ishimaru, A.

Kravtsov, Y. A.

Y. A. Kravtsov, A. I. Saichev, “Effects of Double Passage of Waves in Randomly Inhomogeneous Media,” Sov. Phys. Usp. 25, 494–508 (1983).
[CrossRef]

Kuga, Y.

Y. Kuga, A. Ishimaru, “Depolarization Effects of the Enhanced Retroreflectance from a Dense Distribution of Spherical Particles,” J. Opt. Soc. Am. A 2, 616–618 (1985).
[CrossRef]

Y. Kuga, A. Ishimaru, “Retroreflectance from a Dense Distribution of Spherical Particles,” J. Opt. Soc. Am. A 1, 831–835 (1984).
[CrossRef]

Y. Kuga, A. Ishimaru, Q. Ma, “The Second-Order Multiple Scattering Theory for the Vector Radiative Transfer Equation,” Radio Sci. accepted for publication.

Y. Kuga, A. Ishimaru, “Backscattering Enhancement by Randomly Distributed Particles of Different Sizes,” Proc. Soc. Photo-Opt. Instrum. Eng.927, 33–37 (1988), to be published.

Lagendijk, A.

M. van Albada, A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

Ma, Q.

Y. Kuga, A. Ishimaru, Q. Ma, “The Second-Order Multiple Scattering Theory for the Vector Radiative Transfer Equation,” Radio Sci. accepted for publication.

Maret, G.

P. E. Wolf, G. Maret, “Weak Localization and Coherent Backscattering of Photon in Disordered Media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Saichev, A. I.

Y. A. Kravtsov, A. I. Saichev, “Effects of Double Passage of Waves in Randomly Inhomogeneous Media,” Sov. Phys. Usp. 25, 494–508 (1983).
[CrossRef]

Tatarskii, V. I.

V. I. Tatarskii, “Some New Aspects in the Problem of Waves and Turbulence,” Radio Sci. 22, 859–865 (1987).
[CrossRef]

Tsang, L.

van Albada, M.

M. van Albada, A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

Wolf, P. E.

P. E. Wolf, G. Maret, “Weak Localization and Coherent Backscattering of Photon in Disordered Media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propag.

D. A. De Wolf, “Electromagnetic Reflection from an Extended Turbulent Medium: Cumulative Forward-Scatter Single-Backscatter Approximation,” IEEE Trans. Antennas Propag. AP-19, 254–262 (1971).
[CrossRef]

J. Opt. Soc. Am. A

Phys. Rev. Lett.

M. van Albada, A. Lagendijk, “Observation of Weak Localization of Light in a Random Medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

P. E. Wolf, G. Maret, “Weak Localization and Coherent Backscattering of Photon in Disordered Media,” Phys. Rev. Lett. 55, 2696–2699 (1985).
[CrossRef] [PubMed]

Radio Sci.

V. I. Tatarskii, “Some New Aspects in the Problem of Waves and Turbulence,” Radio Sci. 22, 859–865 (1987).
[CrossRef]

Sov. Phys. Usp.

Y. A. Kravtsov, A. I. Saichev, “Effects of Double Passage of Waves in Randomly Inhomogeneous Media,” Sov. Phys. Usp. 25, 494–508 (1983).
[CrossRef]

Other

Y. Kuga, A. Ishimaru, Q. Ma, “The Second-Order Multiple Scattering Theory for the Vector Radiative Transfer Equation,” Radio Sci. accepted for publication.

Y. Kuga, A. Ishimaru, “Backscattering Enhancement by Randomly Distributed Particles of Different Sizes,” Proc. Soc. Photo-Opt. Instrum. Eng.927, 33–37 (1988), to be published.

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Figures (10)

Fig. 1
Fig. 1

Experimental setup: SC, scattering cell; BS, beam splitter; P, polarizer; L, lens; FO, optical fiber cable; PMT, photomultiplier.

Fig. 2
Fig. 2

Copolarized intensity for different volume densities: A = 19.1% (τ = 253), B = 9.55% (τ = 126.5), C = 4.775% (τ = 63.3), D = 2.39% (τ = 31.6), E = 1.19% (τ = 15.8), F = 0.597% (τ = 7.9), G = 0.298% (τ = 3.95), H = 0.149% (τ = 1.98), I = 0.0745% (τ = 0.99).

Fig. 3
Fig. 3

Cross-polarized intensity for different volume densities: A = 19.1% (τ = 253), B = 9.55% (τ = 126.5), C = 4.775% (τ = 63.3), D = 2.39% (τ = 31.6), E = 1.19% (τ = 15.8), F = 0.597% (τ = 7.9), G = 0.298% (τ = 3.95), H = 0.149% (τ = 1.98).

Fig. 4
Fig. 4

SOMS theory for 45-μm particles. Standard deviation = 9.9 μm, ka = 298, ϕ = 90°, τ = 2, n = 1.186 + i10−5, and λ = 0.

Fig. 5
Fig. 5

Enhancement in the copolarized intensity for different volume densities: A = 0.0745% (factor = 0.6), B = 0.149% (factor = 0.6), C = 0.298% (factor = 0.6).

Fig. 6
Fig. 6

Enhancement in the copolarized intensity for different volume densities: A = 4.775% (factor = 0.15), B = 1.19% (factor = 0.3), C = 0.149% (factor = 0.6); 3 dB is shown by an arrow.

Fig. 7
Fig. 7

Enhancement in the cross-polarized intensity for volume densities: A = 0.597% (factor = 0.05) and B = 0.149% (factor = 0.15); 3 dB is shown by an arrow.

Fig. 8
Fig. 8

Height and angular width of the backscattering enhancement peak in the cross-polarized intensity.

Fig. 9
Fig. 9

Total intensity for different volume densities: A = 4.775% (τ = 63.3), B = 2.39% (τ = 31.6), C = 1.19% (τ = 15.8), D = 0.597% (τ = 7.9), E = 0.298% (τ = 3.95), F = 0.149% (τ = 1.98).

Fig. 10
Fig. 10

Copolarized and cross-polarized intensities at 178° and 180°. Solid lines are for the copolarized intensity and dashed lines are for the cross-polarized intensity.

Equations (2)

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data = ( nor .  exp data at 178 ° ) ( factor ) ( nor .  SOMS at 178 ° ) .
data = ( exp .  data ) ( factor ) ( exp .  data at 178 ° ) × ( nor .  SOMS at 178 ° 1 ) .

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