Abstract

Most of the Mie-scattering calculations have been done for a particle embedded in a nonabsorbing host medium. Generalization to an absorbing host medium can be achieved (a) by modifying the calculation of the spherical Bessel functions to account for a complex argument and (b) by accounting properly for the net rate of incident, scattered, and absorbed energy. We present an extended formalism of Mie scattering for the case of an absorbing host medium. Numerical calculations show that for a large spherical particle embedded in an absorbing host medium the extinction efficiency approaches 1 compared with 2 for a nonabsorbing host medium. We conjecture that this difference is due to the suppression of diffraction when the radius of the sphere is large.

© 2001 Optical Society of America

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References

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  1. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  4. P. Chylek, “Light scattering by small particles in an absorbing medium,” J. Opt. Soc. Am. 67, 561–563 (1977).
    [CrossRef]
  5. 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]
  6. M. Quinten, J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
    [CrossRef]
  7. 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).
  8. D. J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, Englewood Cliffs, N. J., 1981).
  9. P. Chylek, J. Zhan, “Interference structure of the Mie extinction cross section,” J. Opt. Soc. Am. A 6, 1846–1851 (1989).
    [CrossRef]
  10. P. Chylek, J. Zhan, “Absorption and scattering of light by small particles: the interference structure,” Appl. Opt. 29, 3984– (1990).
    [CrossRef] [PubMed]
  11. P. Chylek, “Partial-wave resonances and the ripple structure in the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1976).
    [CrossRef]
  12. P. Chylek, “Resonance structure of Mie scattering: distance between resonances,” J. Opt. Soc. Am. A 7, 1609–1613 (1990).
    [CrossRef]

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).

1996 (1)

M. Quinten, J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

1990 (2)

1989 (1)

1977 (1)

1976 (1)

1974 (1)

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Chylek, P.

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).

Griffiths, D. J.

D. J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, Englewood Cliffs, N. J., 1981).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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).

Mundy, W. C.

Quinten, M.

M. Quinten, J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

Rostalski, J.

M. Quinten, J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

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).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Zhan, J.

Appl. Opt. (1)

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. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

Part. Part. Syst. Charact. (1)

M. Quinten, J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[CrossRef]

Other (4)

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

D. J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, Englewood Cliffs, N. J., 1981).

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Figures (4)

Fig. 1
Fig. 1

Extinction efficiency (Qext) of a nonabsorbing sphere, with a refractive index msphere=1.33, placed in a medium of a given refractive index (1; 1+0.01i; 1+0.001i) as a function of the real part of the size parameter x. The size parameter x=2πammed/λ, where a is the radius of the sphere and λ is the wavelength of the considered radiation in vacuum.

Fig. 2
Fig. 2

Distribution of |E|2 in an equatorial plane of a spherical particle with the real part of the size parameter Re(x)=10 (x=2πammed/λ, a is the radius of sphere, and λ is the wavelength in vacuum) embedded in a nonabsorbing medium (msphere=1.33 and mmed=1.0). The spherical particle is illuminated by x-polarized electromagnetic plane waves propagating in the positive z direction.

Fig. 3
Fig. 3

Same as Fig. 2 except that the refractive index of the medium is mmed=1.0+0.5i.

Fig. 4
Fig. 4

Absorption efficiency (Qabs) of a spherical particle with a given refractive index (msphere=1.33; 1.33+0.01i; 1.33+0.001i) embedded in an absorbing medium (mmed=1+0.001i) as a function of the real part of the size parameter x. A spherical particle with a real refractive index does not absorb any electromagnetic radiation even when its relative refractive index (with respect to the absorbing medium) is complex.

Equations (12)

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E=Ei+Esca,
H=Hi+Hsca.
an=mrψn(mr x)ψn(x)-ψn(x)ψn(mr x)mrψn(mr x)ξn(x)-ξn(x)ψn(mr x),
bn=ψn(mr x)ψn(x)-mrψn(x)ψn(mr x)ψn(mr x)ξn(x)-mrξn(x)ψn(mr x),
Wsca=12Re sphere(Esca×Hsca*)·rˆdA,
Wsca=π|E0|2μω|k|2Rek*n=1(2n+1)[-i|an|2ξn(x)ξn*(x)+i|bn|2ξn(x)ξn*(x)],
Wabs=12Re sphere(E×H*)·rˆdA,
Wabs=π|E0|2μω|k|2Rek*n=1(2n+1)[iψn*(x)ψn(x)-iψn(x)ψn*(x)+ibnψn*(x)ξn(x)+ibn*ψn(x)ξn*(x)+i|an|2ξn(x)ξn*(x)-i|bn|2ξn(x)ξn*(x)-ianψn*(x)ξn(x)-ian*ψn(x)ξn*(x)].
Wext=π|E0|2μω|k|2Rek*n=1(2n+1)[iψn*(x)ψn(x)-iψn(x)ψn*(x)+ibnψn*(x)ξn(x)+ibn*ψn(x)ξn*(x)-ianψn*(x)ξn(x)-ian*ψn(x)ξn*(x)].
I=12πa2Re halfsphere(Ei×Hi*)·rˆdA.
I=|E0|2μωRe{k}exp(2akI)2akI+1-exp(2akI)(2akI)2,
I=12c|E0|2.

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