Abstract

A very efficient method for the calculation of Mie cross sections for absorbing particles is discussed. It is used to calculate an extensive set of curves which illustrate the dependence of the efficiency factors Q for absorption and scattering on the size parameter x and on n1 and n2 (the real and imaginary parts of the index of refraction). The value of Qabs is found to be proportional to n2 over a considerable range of values which are specified. As n2 increases, Qsca first decreases to a minimum value and then passes through a maximum, when x ≫ 1 and for most values of n1. The half-width of the angular intensity function is calculated over a range of values of n1 and n2. This half-width varies as x−1 and x ≥ 10 and is relatively insensitive to the values of n1 and n2.

© 1967 Optical Society of America

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References

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  1. H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).
  2. D. Deirmendjian, R. Clasen, W. Viezee, J. Opt. Soc. Am. 51, 620 (1961).
    [CrossRef]
  3. A. Brockes, Optik 21, 550 (1964).
  4. G. N. Plass, Appl. Opt. 5, 279 (1966).
    [CrossRef] [PubMed]
  5. A. L. Aden, J. Appl. Phys. 22, 601 (1951).
    [CrossRef]
  6. F. T. Corbato, T. L. Uretsky, J. Assoc. Computing Machinery 6, 366 (1959).
    [CrossRef]
  7. R. H. Giese, Z. Astrophys. 51, 119 (1961).
  8. P. J. Wyatt, Phys. Rev. 127, 1837 (1962).
    [CrossRef]
  9. L. Infeld, Quart. J. Appl. Math. 5, 113 (1947).

1966

1964

A. Brockes, Optik 21, 550 (1964).

1962

P. J. Wyatt, Phys. Rev. 127, 1837 (1962).
[CrossRef]

1961

1959

F. T. Corbato, T. L. Uretsky, J. Assoc. Computing Machinery 6, 366 (1959).
[CrossRef]

1951

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

1947

L. Infeld, Quart. J. Appl. Math. 5, 113 (1947).

Aden, A. L.

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

Brockes, A.

A. Brockes, Optik 21, 550 (1964).

Clasen, R.

Corbato, F. T.

F. T. Corbato, T. L. Uretsky, J. Assoc. Computing Machinery 6, 366 (1959).
[CrossRef]

Deirmendjian, D.

Giese, R. H.

R. H. Giese, Z. Astrophys. 51, 119 (1961).

Infeld, L.

L. Infeld, Quart. J. Appl. Math. 5, 113 (1947).

Plass, G. N.

Uretsky, T. L.

F. T. Corbato, T. L. Uretsky, J. Assoc. Computing Machinery 6, 366 (1959).
[CrossRef]

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

Viezee, W.

Wyatt, P. J.

P. J. Wyatt, Phys. Rev. 127, 1837 (1962).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

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

J. Assoc. Computing Machinery

F. T. Corbato, T. L. Uretsky, J. Assoc. Computing Machinery 6, 366 (1959).
[CrossRef]

J. Opt. Soc. Am.

Optik

A. Brockes, Optik 21, 550 (1964).

Phys. Rev.

P. J. Wyatt, Phys. Rev. 127, 1837 (1962).
[CrossRef]

Quart. J. Appl. Math.

L. Infeld, Quart. J. Appl. Math. 5, 113 (1947).

Z. Astrophys.

R. H. Giese, Z. Astrophys. 51, 119 (1961).

Other

H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

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Figures (9)

Fig. 1
Fig. 1

Efficiency factor for absorption as a function of n2 for x = 2πa/λ = 0.1 and various values of n1.

Fig. 2
Fig. 2

Efficiency factor for absorption as a function of n2 for x = 1 and various values of n1.

Fig. 3
Fig. 3

Efficiency factor for absorption as a function of n2 for x = 10 and various values of n1.

Fig. 4
Fig. 4

Efficiency factor for scattering as a function of n2 for x = 0.1 and various values of n1.

Fig. 5
Fig. 5

Efficiency factor for scattering as a function of n2 for x = 1 and various values of n1.

Fig. 6
Fig. 6

Efficiency factor for scattering as a function of n2 for x = 10 and various values of n1.

Fig. 7
Fig. 7

Half-width of angular intensity function in degrees as a function of size parameter x for n2 = 0.

Fig. 8
Fig. 8

Half-width of angular intensity function in degrees as a function of size parameter x for n1 = 1.01.

Fig. 9
Fig. 9

Half-width of angular intensity functions in degrees as a function of size parameter x for n1 = 1.33.

Equations (18)

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a n = ψ n ( y ) ψ n ( x ) - m ψ n ( y ) ψ n ( x ) ψ n ( y ) ζ n ( x ) - m ψ n ( y ) ζ n ( x ) ,
b n = m ψ n ( y ) ψ n ( x ) - ψ n ( y ) ψ n ( x ) m ψ n ( y ) ζ n ( x ) - ψ n ( y ) ζ n ( x ) ,
ψ n ( z ) = z j n ( z ) = ( 1 2 π z ) ½ J n + ½ ( z ) ,
ζ n ( z ) = z h n ( 2 ) ( z ) = ( 1 2 π z ) H n + ½ ( 2 ) ( z ) ,
x = 2 π a / λ ,
y = m x ,
D n ( y ) = [ ln ψ n ( y ) ] ,
G n ( x ) = [ ln ζ n ( x ) ] .
a n = ψ n ( x ) ζ n ( x ) ( D n ( y ) - m D n ( x ) D n ( y ) - m G n ( x ) ) ,
b n = ψ n ( x ) ζ n ( x ) ( m D n ( y ) - D n ( x ) m D n ( y ) - G n ( x ) ) .
D n - 1 ( z ) = n z - [ D n ( z ) + n z - 1 ] - 1 .
f n ( z ) = D n ( z ) + n ( z ) ,
D n - 1 + n - 1 = n z - [ D n ( z ) + n ( z ) + n z - 1 ] - 1 .
n - 1 = n / [ ( D n + n z - 1 ) ( D n + n + n z - 1 ) ] .
D n ( z ) ( n + 1 ) z - 1 .
n - 1 n / ( 2 n + 1 ) z - 1 2
n - 1 n .
Q a b s = ( constant ) n 2 ,

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