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  1. This limit, called the extinction paradox, is clearly explained in H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).In our discussion of Mie theory and phase angles, we use the same notation as van de Hulst.
  2. A previous proof has recently been invalidated.See C. Acquista, A. Cohen, J. A. Cooney, J. Wimp, J. Opt. Soc. Am. 70, August0000 (1980).
  3. If the scatterers are nonspherical, approximations must be made to Mie theory.See A. C. Holland, G. Gagne, Appl. Opt. 9, 1113 (1970).
    [CrossRef] [PubMed]
  4. C. Acquista, Appl. Opt. 17, 3851 (1978).
    [CrossRef] [PubMed]
  5. G. Kattawar, M. Eisner, Appl. Opt. 9, 2685 (1970).
    [CrossRef] [PubMed]
  6. H. S. Bennett, G. J. Rosasco, Appl. Opt. 17, 491 (1978).
    [CrossRef] [PubMed]
  7. G. Mie, Ann. Phys. (Leipzig) 25, 377 (1908).
  8. M. Abramowitz, I. A. Segun, Eds., Handbook of Mathematical Functions (Dover, New York, 1965), Sec. 9.3.

1980

A previous proof has recently been invalidated.See C. Acquista, A. Cohen, J. A. Cooney, J. Wimp, J. Opt. Soc. Am. 70, August0000 (1980).

1978

1970

1908

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

Acquista, C.

A previous proof has recently been invalidated.See C. Acquista, A. Cohen, J. A. Cooney, J. Wimp, J. Opt. Soc. Am. 70, August0000 (1980).

C. Acquista, Appl. Opt. 17, 3851 (1978).
[CrossRef] [PubMed]

Bennett, H. S.

Cohen, A.

A previous proof has recently been invalidated.See C. Acquista, A. Cohen, J. A. Cooney, J. Wimp, J. Opt. Soc. Am. 70, August0000 (1980).

Cooney, J. A.

A previous proof has recently been invalidated.See C. Acquista, A. Cohen, J. A. Cooney, J. Wimp, J. Opt. Soc. Am. 70, August0000 (1980).

Eisner, M.

Gagne, G.

Holland, A. C.

Kattawar, G.

Mie, G.

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

Rosasco, G. J.

van de Hulst, H. C.

This limit, called the extinction paradox, is clearly explained in H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).In our discussion of Mie theory and phase angles, we use the same notation as van de Hulst.

Wimp, J.

A previous proof has recently been invalidated.See C. Acquista, A. Cohen, J. A. Cooney, J. Wimp, J. Opt. Soc. Am. 70, August0000 (1980).

Ann. Phys. (Leipzig)

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

Appl. Opt.

J. Opt. Soc. Am.

A previous proof has recently been invalidated.See C. Acquista, A. Cohen, J. A. Cooney, J. Wimp, J. Opt. Soc. Am. 70, August0000 (1980).

Other

This limit, called the extinction paradox, is clearly explained in H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).In our discussion of Mie theory and phase angles, we use the same notation as van de Hulst.

M. Abramowitz, I. A. Segun, Eds., Handbook of Mathematical Functions (Dover, New York, 1965), Sec. 9.3.

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Equations (25)

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Q ext = 2 x 2 n = 1 ( 2 n + 1 ) Re ( a n + b n ) .
a n = ψ n ( x ) ψ n ( mx ) m ψ n ( mx ) ψ n ( x ) ζ n ( x ) ψ n ( mx ) m ψ n ( mx ) ζ n ( x ) ,
b n = m ψ n ( x ) ψ n ( mx ) ψ n ( mx ) ψ n ( x ) m ζ n ( x ) ψ n ( mx ) ψ n ( mx ) ζ n ( x ) .
a n = ψ n ( x ) / ζ n ( x ) ,
b n = ψ n ( x ) / ζ n ( x ) .
tan δ n = ψ n ( x ) / χ n ( x ) ; δ n = 0 at x = 0 ,
tan n = ψ n ( x ) / χ n ( x ) ; n = 0 at x = 0 .
Re ( a n ) = sin 2 n ,
Re ( b n ) = sin 2 δ n ,
Q ext = 2 x 2 n = 1 ( 2 n + 1 ) ( sin 2 n + sin 2 δ n ) .
Q ext 2 x 2 n = 1 x ( 2 n + 1 ) ( sin 2 n + cos 2 n ) 2 , Q.E.D .
ψ n ( x ) ( sin γ n ) 1 / 2 cos [ ν ( tan γ n γ n ) π / 4 ] ,
χ n ( x ) ( sin γ n ) 1 / 2 sin [ ν ( tan γ n γ n ) π / 4 ] .
( i ) γ n γ n 1 , ( ii ) E n E n 1 γ n 1 , ( iii ) E n n .
x = ( n ½ ) cos γ n 1 = ( n + ½ ) cos γ n .
E n E n 1 = ( n + ½ ) [ sin ( γ n γ n 1 ) cos γ n cos γ n 1 ( γ n γ n 1 ) ] + tan γ n 1 γ n 1 .
γ n γ n 1 1 / ( x sin γ n 1 ) .
E n E n 1 1 sin γ n 1 ( x 2 n 2 nx ) + tan γ n 1 γ n 1 .
ψ n ( x ) = ψ n 1 ( x ) n x ψ n ( x ) .
ψ n ( x ) / χ n ( x ) tan E n .
ψ n ( x ) / ζ n ( x ) cot E n = tan ( E n + π / 2 ) .
n = tan γ n γ n π / 4 ,
δ n = tan γ n γ n + π / 4 .
ψ n ( x ) ½ ( sinh α n ) 1 / 2 exp [ ν ( α n tanh α n ) ] ,
χ n ( x ) ( sinh α n ) 1 / 2 exp [ ν ( α n tanh α n ) ] ,

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