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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 63, Iss. 6 — Jun. 1, 1973
  • pp: 699–706

Large-sphere limits of the Mie-scattering functions

Petr Chýlek  »View Author Affiliations

JOSA, Vol. 63, Issue 6, pp. 699-706 (1973)

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For x / n ≫ 1, the following relations between the Mie-scattering functions an (x,m) and bn (x,m) are satisfied: a1 (x,m)= b2 (x,m)= a3 (x,m) = … = an-1 (x,m) = bn (x,m) and b1 (x,m) = a2 (x,m)= b3 (x,m) = … = bn-1 (x,m) = an(x,m) for arbitrary refractive index m. By use of these relations, the Van de Hulst and Deirmendjian conjectures about the x → ∞ behavior of the scattering functions or their linear and bilinear combinations, as well as several new relations, are rigorously proved.

Petr Chýlek, "Large-sphere limits of the Mie-scattering functions," J. Opt. Soc. Am. 63, 699-706 (1973)

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  1. G. Mie, Ann. Phys. (Leipz.) 25, 377 (1908).
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  3. Reference 2, p. 107.
  4. W. M. Irvine, J. Opt. Soc. Am. 55, 16 (1965).
  5. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969), p. 41.
  6. B. M. Herman, Q. J. R. Meteorol. Soc. 88, 143 (1962).
  7. A. L. Aden, J. Appl. Phys. 22, 601 (1951).
  8. Reference 2, p. 276.
  9. Reference 5, p. 27.
  10. B. M. Herman and L. J. Battan, Q. J. R. Meteorol. Soc. 87, 223 (1961).

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