Abstract

We examine the scattering properties of particles contained in absorbing media. Rather than consider energy fluxes through arbitrary integrating spheres, we examine the extinction from its fundamental definition: the energy removed from the plane wave, or incident beam. The resulting energy received by a detector contains two terms: one the result of the incident beam traversing through the medium that would have occurred if the particle were not present, and a correction term due to the presence of the particle. Both terms have the same dependence on the pathlength that the beam travels between two arbitrarily located parallel planes and are independent of where the particle is located within the medium. The result is that the definition of the extinction cross section is not dependent on a reference plane or the particle location within the medium.

© 2003 Optical Society of America

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References

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  1. W. C. Mundy, J. A. Roux, A. M. Smith, “Mie scattering by spheres in an absorbing medium,” J. Opt. Soc. Am. 64, 1593–1597 (1974).
    [CrossRef]
  2. P. Chýlek, “Light scattering by small particles in an absorbing medium,” J. Opt. Soc. Am. 67, 561–563 (1977).
    [CrossRef]
  3. C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
    [CrossRef]
  4. A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).
  5. I. W. Sudiarta, P. Chýlek, “Mie scattering by a spherical particle in an absorbing medium,” Appl. Opt. 41, 3545–3546 (2002).
    [CrossRef] [PubMed]
  6. I. W. Sudiarta, P. Chýlek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18, 1275–1278 (2001).
    [CrossRef]
  7. I. W. Sudiarta, P. Chýlek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
    [CrossRef]
  8. Q. Fu, W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40, 1354–1361 (2001).
    [CrossRef]
  9. P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
    [CrossRef] [PubMed]
  10. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

2002 (2)

2001 (3)

1999 (1)

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).

1979 (1)

C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[CrossRef]

1977 (1)

1974 (1)

Baum, B. A.

Bohren, C. F.

C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[CrossRef]

Chýlek, P.

Fu, Q.

Gao, B.-C.

Gartz, M.

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).

Gilra, D. P.

C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[CrossRef]

Hu, Y. X.

Huang, H.-L.

Kreibig, U.

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).

Lebedev, A. N.

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).

Mishchenko, M. I.

Mundy, W. C.

Park, S. K.

Platnick, S. E.

Roux, J. A.

Smith, A. M.

Stenzel, O.

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).

Sudiarta, I. W.

Sun, W.

Tsay, S.-C.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Winker, D. M.

Wiscombe, W. J.

Yang, P.

Appl. Opt. (3)

Eur. Phys. J. D (1)

A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).

J. Colloid Interface Sci. (1)

C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Radiat. Transfer (1)

I. W. Sudiarta, P. Chýlek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[CrossRef]

Other (1)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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Figures (1)

Fig. 1
Fig. 1

System under consideration. Surface P encompasses the particle in Region III and is surrounded by the absorbing medium of Region II. Surface S is the surface over which the integrals are calculated. It is sometimes spherical and other times is identical to Surface P. The mediums of Regions II and III are identical, homogeneous and absorbing. The wave travels a long but finite distance from what we call the source at the bottom (z = z o ) to the detector located at z = z 1 at the top. The coordinate system is centered on the particle, located at z = 0, so z o is negative.

Equations (10)

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-WabsS=12ReSE×H*·nˆdS,
WscaS=12ReSEsca×Hsca*·nˆdS,
WextS=WscaS+WabsS=-12ReSEinc×Hinc*+Einc×Hsca*+Esca×Hinc*·nˆdS,
Wi=12ReSEinc×Hinc*·nˆdS.
I=uo expikz1-zo+uo expikz1-zoS0ikz1exp-ikx2+y2/2z12=uo*uo exp-2kiz21+2 ReS0ikz1exp-ikx2+y2/2z1,
Wextobj=obj 2uo*uo exp-2kiz2ReS0ikz1exp-ikx2+y2/2z1dA.
Wextobj=4πuo*uo exp-2kiz2ReS0k2.
Cext=Wextobj/Iincobj,
Iincobj=uo*uo exp-2kiz2.
Cext=4π ReS0k2.

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