Abstract

The Mie scattering and absorption cross sections for spherical particles are calculated as a function of the complex index of refraction, n = n1in2. Curves of the efficiency factors for absorption, scattering, and extinction are given for n1 = 1.01, 1.33, 1.5, and 2 and for n2 = 10−4, 10−2, 10−1, 1, and 10. The influence of the absorption on the efficiency factors is discussed. The results are compared with previously proposed simplified expressions for these factors. The variation of the scattered intensity with angle as n2 is varied is illustrated in some typical cases. Finally the influence of n2 on the narrow resonances which occur for large values of n1 is discussed.

© 1966 Optical Society of America

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References

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  1. R. C. Van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 50, 121 (1960).
    [CrossRef]
  3. G. N. Plass, Appl. Opt. 3, 867 (1964).
    [CrossRef]
  4. G. N. Plass, Appl. Opt. 5, 149 (1966).
    [CrossRef] [PubMed]
  5. D. Deirmendjian, R. Clasen, W. Viezee, J. Opt. Soc. Am. 51, 620 (1961).
    [CrossRef]
  6. D. Deirmendjian, Appl. Opt. 3, 187 (1964).
    [CrossRef]
  7. G. Mie, Ann. Physik 25, 377 (1908).
    [CrossRef]
  8. D. Deirmendjian, Quart. J. Roy. Meteorol. Soc. 86, 371 (1960).
    [CrossRef]

1966

1964

1961

1960

V. R. Stull, G. N. Plass, J. Opt. Soc. Am. 50, 121 (1960).
[CrossRef]

D. Deirmendjian, Quart. J. Roy. Meteorol. Soc. 86, 371 (1960).
[CrossRef]

1908

G. Mie, Ann. Physik 25, 377 (1908).
[CrossRef]

Ann. Physik

G. Mie, Ann. Physik 25, 377 (1908).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

Quart. J. Roy. Meteorol. Soc.

D. Deirmendjian, Quart. J. Roy. Meteorol. Soc. 86, 371 (1960).
[CrossRef]

Other

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

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Figures (18)

Fig. 1
Fig. 1

Efficiency factor for absorption as a function of x = 2πa/λ, where a is the particle radius and λ is the wavelength for n1 = 1.01. Curves are shown for n2 = 10−4, 10−2, 10−1, 1, and 10. The solid curves are the exact results and the dashed curves are the approximate Eq. (1). These curves coincide on this scale for n2 = 10−1 and 10−2.

Fig. 2
Fig. 2

Efficiency factor for absorption as a function of x = 2πa/λ for n1 = 1.33. The solid curves are the exact results and the dashed curves are the approximate Eq. (1).

Fig. 3
Fig. 3

Efficiency factor for absorption as a function of x = 2πa/λ for n1 = 1.5. The solid curves are the exact results and the dashed curves are the approximate Eq. (1).

Fig. 4
Fig. 4

Efficiency factor for absorption as a function of x = 2πa/λ for n1 = 2.

Fig. 5
Fig. 5

Efficiency factor for scattering as a function of x = 2πa/λ for n1 = 1.01.

Fig. 6
Fig. 6

Efficiency factor for scattering as a function of x = 2πa/λ for n1 = 1.33.

Fig. 7
Fig. 7

Efficiency factor for scattering as a function of x = 2πa/λ for n1 = 1.5.

Fig. 8
Fig. 8

Efficiency factor for scattering as a function of x = 2πa/λ for n1 = 2.

Fig. 9
Fig. 9

Efficiency factor for extinction as a function of x = 2πa/λ for n1 = 1.01. The solid curves are the exact results and the dashed curves are the approximate Eq. (3). These curves coincide on this scale for n2 = 10−4 and 10−2.

Fig. 10
Fig. 10

Efficiency factor for extinction as a function of x = 2πa/λ for n1 = 1.33. The solid curves (use left-hand scale) are the exact results and the dashed curves (use right-hand scale) are the approximate Eq. (3).

Fig. 11
Fig. 11

Efficiency factor for extinction as a function of x = 2πa/λ for n1 = 1.5. The solid curves (use left-hand scale) are the exact results and the dashed curves (use right-hand scale) are the approximate Eq. (3).

Fig. 12
Fig. 12

Efficiency factor for extinction as a function of x = 2πa/λ for n1 = 2.

Fig. 13
Fig. 13

Scattered intensity as a function of scattering angle for n1 = 1.33 and x = 2πa/λ = 5. The solid curve is the intensity i1 (as defined by Van de Hulst1) and the dashed curve is the intensity i2. The logarithm of the intensity (1 division = a factor 10) is plotted against the scattering angle. The values of the intensity at 0° and 180° are indicated above the curves near the margin.

Fig. 14
Fig. 14

Scattered intensity as a function of scattering angle for n1 = 1.5 and x = 2πa/λ = 5. See caption for Fig. 13.

Fig. 15
Fig. 15

Scattered intensity as a function of scattering angle for n1 = 2 and x = 2πa/λ = 5. See caption for Fig. 13.

Fig. 16
Fig. 16

Scattered intensity as a function of scattering angle for n1 = 1.33 and x = 2πa/λ = 1. See caption for Fig. 13.

Fig. 17
Fig. 17

Scattered intensity as a function of scattering angle for n1 = 1.33 and x = 2πa/λ = 8. See caption for Fig. 13.

Fig. 18
Fig. 18

Efficiency factors for both absorption and scattering as a function of x = 2πa/λ for n1 = 50 and various values of n2. The curves for scattering coincide on this scale for n2 ≤ 10−2.

Equations (7)

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Q abs = 2 K ( 4 x n 2 ) ,
K ( w ) = ( 1 / 2 ) + w - 1 e - w + w - 2 ( e - w - 1 ) .
Q ext = 2 - 4 exp ( - ρ tan β ) ( ρ - 1 cos β ) sin ( ρ - β ) - 4 exp ( - ρ tan β ) ( ρ - 1 cos β ) 2 cos ( ρ - 2 β ) + 4 ( ρ - 1 cos β ) 2 cos 2 β ,
ρ = 2 x ( n 1 - 1 ) ,
tan β = n 2 ( n 1 - 1 ) - 1 .
n 1 2 = 1 2 μ [ ( 1 + 4 σ 2 - 2 ν - 2 ) ½ + 1 ] ,
n 2 2 = 1 2 μ [ ( 1 + 4 σ 2 - 2 ν - 2 ) ½ - 1 ] ,

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