Abstract

The electrodichroic ratio qr0 for suspensions of absorbing spheroids has been calculated using dipolar light scattering theory. This theory predicts, in accordance with experimental observations on Varad suspensions, that the transmission will usually be higher when the particles are aligned nose-on in the incident beam than in the random state. The effect of complex refractive index and of the axial ratio of the spheroids upon qr0 is discussed in some detail. It appears that metals having the refractive properties of aluminum offer the best possibility for preparing optical windows from these suspensions.

© 1971 Optical Society of America

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References

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  1. A. M. Marks, Appl. Opt. 8, 1397 (1969).
    [CrossRef] [PubMed]
  2. Rayleigh, Philos. Mag. 44, 28 (1897).
  3. R. Gans, Ann. Phys. 37, 881 (1912).
    [CrossRef]
  4. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), Chap. 10.
  5. E. W. Washburn, Ed., International Critical Tables (McGrawHill, New York, 1929), Vol. 5, p. 249.

1969 (1)

1912 (1)

R. Gans, Ann. Phys. 37, 881 (1912).
[CrossRef]

1897 (1)

Rayleigh, Philos. Mag. 44, 28 (1897).

Gans, R.

R. Gans, Ann. Phys. 37, 881 (1912).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), Chap. 10.

Marks, A. M.

Rayleigh,

Rayleigh, Philos. Mag. 44, 28 (1897).

Ann. Phys. (1)

R. Gans, Ann. Phys. 37, 881 (1912).
[CrossRef]

Appl. Opt. (1)

Philos. Mag. (1)

Rayleigh, Philos. Mag. 44, 28 (1897).

Other (2)

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), Chap. 10.

E. W. Washburn, Ed., International Critical Tables (McGrawHill, New York, 1929), Vol. 5, p. 249.

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Figures (9)

Fig. 1
Fig. 1

Contour plot in the complex refractive index domain for axial ratio B/A = 0.70. The contours delineate constant values of the electrodichroic ratio qr0 as indicated. The points locate positions of metals as follows: ○ aluminum; □ silver; △ gold or copper; ao-10-12-2670-i001 chromium.

Fig. 2
Fig. 2

Contour plot in the complex refractive index domain for axial ratio B/A = 0.50. The contours delineate constant values of the electrodichroic ratio qr0 as indicated. The points locate positions of metals as follows: ○ aluminum; □ silver; △ gold or copper; ao-10-12-2670-i001 chromium.

Fig. 3
Fig. 3

Contour plot in the complex refractive index domain for axial ratio B/A = 0.30. The contours delineate constant values of the electrodichroic ratio qr0 as indicated. The points locate positions of metals as follows: ○ aluminum; □ silver; △ gold or copper; ao-10-12-2670-i001 chromium.

Fig. 4
Fig. 4

Contour plot in the complex refractive index domain for axial ratio B/A = 0.10. The contours delineate constant values of the electrodichroic ratio qr0 as indicated. The points locate positions of metals as follows: ○ aluminum; □ silver; △ gold or copper; ao-10-12-2670-i001 chromium.

Fig. 5
Fig. 5

Contour plot in the complex refractive index domain for axial ratio B/A = 0.05. The contours delineate constant values of the electrodichroic ratio qr0 as indicated. The points locate positions of metals as follows: ○ aluminum; □ silver; △ gold or copper; ao-10-12-2670-i001 chromium.

Fig. 6
Fig. 6

Contour plot in the complex refractive index domain for axial ratio B/A = 0.01. The contours delineate constant values of the electrodichroic ratio qr0 as indicated. The points locate positions of metals as follows: ○ aluminum; □ silver; △ gold or copper; ao-10-12-2670-i001 chromium.

Fig. 7
Fig. 7

Contour plot in the complex refractive index domain for axial ratio B/A = 0.005. The contours delineate constant values of the electrodichroic ratio qr0 as indicated. The points locate positions of metals as follows: ○ aluminum; □ silver; △ gold or copper; ao-10-12-2670-i001 chromium.

Fig. 8
Fig. 8

Electrodichroic ratio qr0 vs purely real refractive index for axial ratios B/A = 0.70, 0.50, 0.30, 0.10, 0.05, 0.01, and 0.005.

Fig. 9
Fig. 9

Electrodichroic ratio qr0 vs purely imaginary refractive index for axial ratios B/A = 0.70, 0.50, 0.30, 0.10, 0.05, 0.01, and 0.005.

Equations (31)

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e = [ ( A 2 - B 2 ) / A 2 ] 1 2 ,
P = ( 4 π / e 2 ) { 1 - [ ( 1 - e 2 ) / e 2 ] 1 2 sin - 1 c } .
P = 4 π ( 1 - e 2 / e 2 ) [ ( 1 / 2 e ) ln [ ( 1 + e ) / ( 1 - e ) - 1 ] .
P = ( 4 π - P ) / 2.
α = ( 3 V / 4 π ) L exp ( - i ψ ) = [ V ( m 2 - 1 ) ] / [ 4 π + ( m 2 - 1 ) P ] ,
α = ( 3 V / 4 π ) L exp ( - i ψ ) = [ V ( m 2 - 1 ) ] / [ 4 π + ( m 2 - 1 ) P ] ,
T = ( I / I 0 ) = exp ( - N C ext l ) ,
D = log 10 ( I 0 / I ) = 0.43 N C ext l ,
C ext = C sca + C abs .
( C sca ) r = ( 2 π / λ ) 4 ( 8 π / 9 ) ( α 2 + 2 α 2 ) ,
( C sca ) r = ( 8 π 3 / λ 4 ) V 2 [ ( L ) 2 + 2 ( L ) 2 ] ,
( C abs ) r = ( 8 π 2 / 3 λ ) Im ( - α - 2 α ) ,
( C abs ) r = ( 2 π V / λ ) ( L sin ψ + 2 L sin ψ ) ,
( C sca ) 0 = ( 2 π / λ ) 4 ( 8 π / 3 ) ( α 2 ) ,
( C abs ) 0 = ( 8 π 2 / λ ) Im ( - α ) .
( C sca ) s = ( 2 π / λ ) 4 ( 4 π / 3 ) ( α 2 + α 2 ) ,
( C abs ) s = ( 4 π 2 / λ ) Im ( - α - α ) .
q r 0 = D r / D 0 = ( C ext ) r / ( C ext ) 0 .
( B / A ) = 1.0 , 0.7 , 0.5 , 0.3 , 0.1 , 0.05 , 0.04 , 0.03 , 0.02 , 0.01 , 0.005 ,
Re ( m ) = 0 , 0.05 , 0.10 , 0.30 , 0.60 , 0.80 , 0.90 , 0.95 , 0.98 , 1.02 , 1.05 , 1.10 , 1.20 , 1.30 , 1.50 , 2.00 , 3.00 , 5.00 , 7.00 , 9.00.
I m ( - m ) = 0 , 0.05 , 0.10 , 0.30 , 0.60 , 0.90 , 1.20 , 1.30 , 1.38 , 1.40 , 1.42 , 1.44 , 1.50 , 1.60 , 1.80 , 2.00 , 3.00 , 4.00 , 6.00 , 9.00.
B / A = 0.70 , 0.50 , 0.30 , 0.10 , 0.05 , 0.01 and 0.005 ,
q r 0 = ( C ext ) r / ( C ext ) 0 = ( C abs ) r / ( C abs ) 0 = ( C sca ) r / ( C sca ) 0 .
α / V = ( k + P + l i ) - 1 ,
α / V = [ k - ( P / 2 ) + 2 π + l i ] - 1 ,
k = Re [ 4 π / ( m 2 - 1 ) ] ,
l = Im [ 4 π / ( m 2 - 1 ) ] .
α 2 α 2 = Im ( α ) Im ( α ) = [ k - ( P / 2 ) + 2 π ] 2 + l 2 ( k + P ) 2 + l 2 .
( C sca ) r ( C sca ) 0 = α 2 + 2 α 2 3 α 2 = 1 3 ( a 2 a 2 + 2 ) ,
( C abs ) r ( C abs ) 0 = Im ( - α - 2 α ) 3 Im ( - α ) = 1 3 ( Im ( α ) Im ( a ) + 2 ) .
α = α = ( 3 V / 4 π ) [ ( m 2 - 1 ) / ( m 2 + 2 ) ] .

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