Abstract

Equations are developed for Mie scattering by spheres (particles, bubbles, or voids) embedded in an absorbing medium. Computations demonstrate that under certain conditions the extinction-efficiency factor, Qext, can be less than the scattering-efficiency factor, Qs. In fact, Qext, as commonly defined, can be negative. Also, results are shown for the angular scattering distribution by a void, which indicate that the intensity of the backward-scattered light can be greater than the forward-scattered light.

© 1974 Optical Society of America

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Corrections

W. C. Mundy, J. A. Roux, and A. M. Smith, "Errata: Mie scattering by spheres in an absorbing medium," J. Opt. Soc. Am. 65, 974_1-974 (1975)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-65-8-974_1

References

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  1. E. G. Rawson, Appl. Opt. 10, 2778 (1971).
    [Crossref] [PubMed]
  2. A. M. Smith, K. E. Tempelmeyer, P. R. Müller, and B. E. Wood, Am. Inst. Aeronaut. Astronaut. J. 7, 2274 (1969).
    [Crossref]
  3. J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), pp. 563–569.
  4. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–50.
  5. W. D. Ross, Appl. Opt. 11, 1919 (1972).
    [Crossref] [PubMed]

1972 (1)

1971 (1)

1969 (1)

A. M. Smith, K. E. Tempelmeyer, P. R. Müller, and B. E. Wood, Am. Inst. Aeronaut. Astronaut. J. 7, 2274 (1969).
[Crossref]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–50.

Müller, P. R.

A. M. Smith, K. E. Tempelmeyer, P. R. Müller, and B. E. Wood, Am. Inst. Aeronaut. Astronaut. J. 7, 2274 (1969).
[Crossref]

Rawson, E. G.

Ross, W. D.

Smith, A. M.

A. M. Smith, K. E. Tempelmeyer, P. R. Müller, and B. E. Wood, Am. Inst. Aeronaut. Astronaut. J. 7, 2274 (1969).
[Crossref]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), pp. 563–569.

Tempelmeyer, K. E.

A. M. Smith, K. E. Tempelmeyer, P. R. Müller, and B. E. Wood, Am. Inst. Aeronaut. Astronaut. J. 7, 2274 (1969).
[Crossref]

Wood, B. E.

A. M. Smith, K. E. Tempelmeyer, P. R. Müller, and B. E. Wood, Am. Inst. Aeronaut. Astronaut. J. 7, 2274 (1969).
[Crossref]

Am. Inst. Aeronaut. Astronaut. J. (1)

A. M. Smith, K. E. Tempelmeyer, P. R. Müller, and B. E. Wood, Am. Inst. Aeronaut. Astronaut. J. 7, 2274 (1969).
[Crossref]

Appl. Opt. (2)

Other (2)

J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), pp. 563–569.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 39–50.

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Figures (4)

Fig. 1
Fig. 1

Geometry for Mie scattering. Incident light beam is directed parallel to the positive z axis with the electric vector polarized in the direction of the x axis. The scatterer of radius a has its center at the origin. The direction of the scattered light is defined by polar angles θ and ϕ.

Fig. 2
Fig. 2

Unattenuated-scattering and extinction-efficiency factors, Qso and Qexto, plotted as functions of (a) the imaginary part of the index of refraction, K′, of the scatterer for different combinations of the real part of the refractive index, N′, of the scatterer and of the complex refractive index, m, of the medium in which the scatterer is embedded; (b) the imaginary part of the index of refraction, K, of the medium for different combinations of the real part of the refractive index, N, of the medium and of the complex refractive index, m′, of the scatterer. The size parameter, α0, is 5.0 for all plots.

Fig. 3
Fig. 3

Intensity function plotted as a function of angle for a void embedded in a medium that is characterized by a real refractive index of 1.5 and for a range of imaginary refractive indices, K, from 0.0 to 0.2. The size parameter, α0, is 25.0.

Fig. 4
Fig. 4

Intensity function versus angle for a void embedded in a medium characterized by a real refractive index of 2.0 and an imaginary refractive index that ranges from 0.0 to 1.0. The size parameter, α0, is 5.0.

Equations (20)

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E s θ = - i E 0 e i ω t e - i ρ ρ cos φ n = 1 2 n + 1 n ( n + 1 ) × [ a n τ n ( cos θ ) + b n π n ( cos θ ) ] , E s φ = i E 0 e i ω t e - i ρ ρ sin φ n = 1 2 n + 1 n ( n + 1 ) × [ a n π n ( cos θ ) + b n τ n ( cos θ ) ] , H s φ = k 2 μ 2 ω E s θ , H s θ = - k 2 μ 2 ω E s φ .
S 1 = n = 1 2 n + 1 n ( n + 1 ) [ a n π n ( cos θ ) + b n τ n ( cos θ ) ] , S 2 = n = 1 2 n + 1 n ( n + 1 ) [ a n τ n ( cos θ ) + b n π n ( cos θ ) ] .
I φ = λ 0 2 4 π 2 r 2 e - 4 π r K / λ 0 ( N 2 + K 2 ) I 0 S 1 2 sin 2 φ I 0 λ 0 2 e - 4 π ( r - a ) K / λ 0 4 π 2 r 2 i 1 sin 2 φ , I θ = λ 0 2 4 π 2 r 2 e - 4 π r K / λ 0 ( N 2 + K 2 ) I 0 S 2 2 cos 2 φ I 0 λ 0 2 e - 4 π ( r - a ) K / λ 0 4 π 2 r 2 i 2 cos 2 φ ,
W s = 1 2 Re 0 2 π [ 0 π ( E s θ H s φ * - E s φ H s θ * ) r 2 sin θ d θ ] d φ = 2 π ( N 2 + K 2 ) I 0 e - 4 π τ K / λ 0 ( 2 π / λ 0 ) 2 n = 1 ( 2 n + 1 ) ( a n 2 + b n 2 ) ,
ξ z = 0 a S ¯ ( z ) 2 π q d q ,
S ¯ ( z ) = N 2 μ 2 E 0 2 e - 4 π z K / λ 0 .
ξ z = 2 π a 2 ( 4 π a K / λ 0 ) 2 I 0 [ 1 + ( 4 π a K / λ 0 - 1 ) e 4 π a K / λ 0 ] .
Q s = W s / ξ z .
Q s = 4 K 2 e - 4 π r K / λ 0 ( N 2 + K 2 ) [ 1 + ( 4 π a K / λ 0 - 1 ) e 4 π a K / λ 0 ] × n = 1 ( 2 n + 1 ) ( a n 2 + b n 2 ) Q s o e - 4 π ( r - a ) K / λ 0 ,
E i θ = E 0 e i ω t 1 ρ cos φ n = 1 ( - i ) n 2 n + 1 n ( n + 1 ) [ cos ( ρ - n + 1 2 π ) × π n ( cos θ ) - i sin ( ρ - n + 1 2 π ) τ n ( cos θ ) ] , = i E 0 e i ω t 2 ρ cos φ n = 1 2 n + 1 n ( n + 1 ) × { ( - 1 ) n + 1 e i ρ [ π n - τ n ] + e - i ρ [ π n + τ n ] } , E i φ = i E 0 e i ω t 2 ρ sin φ n = 1 2 n + 1 n ( n + 1 ) × { ( - 1 ) n + 1 e i ρ [ π n - τ n ] - e - i ρ [ π n + τ n ] } , H i φ = - i k 2 E 0 e i ω t 2 μ 2 ω ρ cos φ n = 1 2 n + 1 n ( n + 1 ) × { ( - 1 ) n + 1 e i ρ [ π n - τ n ] - e - i ρ [ π n + τ n ] } , H i θ = i k 2 E 0 e i ω t 2 μ 2 ω ρ sin φ n = 1 2 n + 1 n ( n + 1 ) × { ( - 1 ) n + 1 e i ρ [ π n - τ n ] + e - i ρ [ π n + τ n ] } .
S = 1 2 ( E θ H φ * - E φ H θ * ) ,
S = 1 2 [ ( E i θ H i φ * - E i φ H i θ * ) + ( E s θ H s φ * - E s φ H s θ * ) + ( E i θ H s φ * + E s θ H i φ * - E i φ H s θ * - E s φ H i θ * ) ] .
- W abs = - W i + W s - W ext ,
- W abs = Re 0 2 π [ 0 π S r 2 sin θ d θ ] d φ , - W i = 1 2 Re 0 2 π [ 0 π ( E i θ H i φ * - E i φ H i θ * ) r 2 sin θ d θ ] d φ , W s = 1 2 Re 0 2 π [ 0 π ( E s θ H s φ * - E s φ H s θ * ) r 2 sin d θ ] d φ , - W ext = 1 2 Re 0 2 π [ 0 π ( E i θ H s φ * + E s θ H i φ * - E i φ H s θ * - E s φ H i θ * ) r 2 sin θ d θ ] d φ .
W abs = W a + ( W i - W m ) ,
W ext = W s + W a - W m .
W ext = 2 π ( N 2 + K 2 ) I 0 e - 4 π τ K / λ 0 ( 2 π / λ 0 ) 2 Re n = 1 ( 2 n + 1 ) ( a n + b n ) .
Q ext = W ext / ξ z = 4 K 2 e - 4 π r K / λ 0 ( N 2 + K 2 ) [ 1 + ( 4 π a K / λ 0 - 1 ) e 4 π a K / λ 0 ] × Re n = 1 ( 2 n + 1 ) ( a n + b n ) Q ext o e - 4 π ( r - a ) K / λ 0 ,
e - 4 π a K / λ 0 = e - 2 K α 0 .
e - 2 K α 0 = e - 10 = 4.54 × 10 - 5 .