Abstract

For <i>x</i> / <i>n</i> ≫ 1, the following relations between the Mie-scattering functions <i>a<sub>n</sub></i> (<i>x</i>,<i>m</i>) and <i>b<sub>n</sub></i> (<i>x</i>,<i>m</i>) are satisfied: <i>a</i><sub>1</sub> (<i>x</i>,<i>m</i>)= <i>b</i><sub>2</sub> (<i>x</i>,<i>m</i>)= <i>a</i><sub>3</sub> (<i>x</i>,<i>m</i>) = … = <i>a</i><sub><i>n</i>-1</sub> (<i>x</i>,<i>m</i>) = <i>b<sub>n</sub></i> (<i>x</i>,<i>m</i>) and <i>b</i><sub>1</sub> (<i>x</i>,<i>m</i>) = <i>a</i><sub>2</sub> (<i>x</i>,<i>m</i>)= <i>b</i><sub>3</sub> (<i>x</i>,<i>m</i>) = … = <i>b</i><sub><i>n</i>-1</sub> (<i>x</i>,<i>m</i>) = <i>a<sub>n</sub></i>(<i>x</i>,<i>m</i>) for arbitrary refractive index <i>m</i>. By use of these relations, the Van de Hulst and Deirmendjian conjectures about the <i>x</i> → ∞ behavior of the scattering functions or their linear and bilinear combinations, as well as several new relations, are rigorously proved.

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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).

Aden, A. L.

A. L. Aden, J. Appl. Phys. 22, 601 (1951).

Battan, L. J.

B. M. Herman and L. J. Battan, Q. J. R. Meteorol. Soc. 87, 223 (1961).

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969), p. 41.

Herman, B. M.

B. M. Herman, Q. J. R. Meteorol. Soc. 88, 143 (1962).

B. M. Herman and L. J. Battan, Q. J. R. Meteorol. Soc. 87, 223 (1961).

Irvine, W. M.

W. M. Irvine, J. Opt. Soc. Am. 55, 16 (1965).

Mie, G.

G. Mie, Ann. Phys. (Leipz.) 25, 377 (1908).

van de Hulst, H. C.

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

Other (10)

G. Mie, Ann. Phys. (Leipz.) 25, 377 (1908).

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

Reference 2, p. 107.

W. M. Irvine, J. Opt. Soc. Am. 55, 16 (1965).

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969), p. 41.

B. M. Herman, Q. J. R. Meteorol. Soc. 88, 143 (1962).

A. L. Aden, J. Appl. Phys. 22, 601 (1951).

Reference 2, p. 276.

Reference 5, p. 27.

B. M. Herman and L. J. Battan, Q. J. R. Meteorol. Soc. 87, 223 (1961).

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