Abstract

The internal and external field solutions for a composite particle are used to show the importance of the few angstroms closest to the surface in determining the radiative properties of micron-sized particulates. The physical mechanism responsible for the enhanced emissivity and the connection with surface waves are presented.

© 1981 Optical Society of America

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References

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  1. D. W. Schuerman, Ed., Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1980).
    [CrossRef]
  2. A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
    [CrossRef]
  3. V. A. Güttler, Ann. Phy., 6, 65 (1952).
    [CrossRef]
  4. P. W. Dusel, M. Kerker, D. D. Cooke, J. Opt. Soc. Am. 69, 55 (1979).
    [CrossRef]
  5. R. G. Newton, Scattering Theory of Waves and Particles (McGraw–Hill, New York, 1966).
  6. G. J. Rosasco, H. S. Bennett, J. Opt. Soc. Am. 68, 1242 (1978).
    [CrossRef]
  7. R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
    [CrossRef]
  8. P. Chỳlek, J. Opt. Soc. Am. 66, 285 (1976).
    [CrossRef]
  9. P. Chỳlek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A: 18, 2229 (1978).
    [CrossRef]
  10. P. Chỳlek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1980).
  11. R. Ruppin, R. Englman, Rep. Prog. Phys. 33, 149 (1970).
    [CrossRef]
  12. R. Ruppin, Surf. Sci. 34, 20 (1973).
    [CrossRef]
  13. R. Fuchs, K. L. Kliewer, J. Opt. Soc. Am. 58, 319 (1968).
    [CrossRef]
  14. H. M. Nussenzveig, J. Math. Phys. 10, 82 (1969).
    [CrossRef]
  15. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  16. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  17. A. B. Pluchino, Appl. Opt. 20, 531 (1981).
    [CrossRef] [PubMed]
  18. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964).
  19. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  20. R. F. Wallis, Prog. Surf. Sci. 4 (1973).
    [CrossRef]

1981 (1)

1980 (1)

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

1979 (1)

1978 (2)

G. J. Rosasco, H. S. Bennett, J. Opt. Soc. Am. 68, 1242 (1978).
[CrossRef]

P. Chỳlek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A: 18, 2229 (1978).
[CrossRef]

1976 (1)

1973 (2)

R. F. Wallis, Prog. Surf. Sci. 4 (1973).
[CrossRef]

R. Ruppin, Surf. Sci. 34, 20 (1973).
[CrossRef]

1970 (1)

R. Ruppin, R. Englman, Rep. Prog. Phys. 33, 149 (1970).
[CrossRef]

1969 (1)

H. M. Nussenzveig, J. Math. Phys. 10, 82 (1969).
[CrossRef]

1968 (1)

1952 (1)

V. A. Güttler, Ann. Phy., 6, 65 (1952).
[CrossRef]

1951 (1)

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Aden, A. L.

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Ashkin, A.

P. Chỳlek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1980).

Barber, P. W.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Bennett, H. S.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964).

Ch?lek, P.

P. Chỳlek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A: 18, 2229 (1978).
[CrossRef]

P. Chỳlek, J. Opt. Soc. Am. 66, 285 (1976).
[CrossRef]

P. Chỳlek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1980).

Chang, R. K.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Cooke, D. D.

Dusel, P. W.

Englman, R.

R. Ruppin, R. Englman, Rep. Prog. Phys. 33, 149 (1970).
[CrossRef]

Fuchs, R.

Güttler, V. A.

V. A. Güttler, Ann. Phy., 6, 65 (1952).
[CrossRef]

Kerker, M.

P. W. Dusel, M. Kerker, D. D. Cooke, J. Opt. Soc. Am. 69, 55 (1979).
[CrossRef]

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

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

Kiehl, J. T.

P. Chỳlek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A: 18, 2229 (1978).
[CrossRef]

P. Chỳlek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1980).

Kliewer, K. L.

Ko, M. K. W.

P. Chỳlek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A: 18, 2229 (1978).
[CrossRef]

P. Chỳlek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1980).

Newton, R. G.

R. G. Newton, Scattering Theory of Waves and Particles (McGraw–Hill, New York, 1966).

Nussenzveig, H. M.

H. M. Nussenzveig, J. Math. Phys. 10, 82 (1969).
[CrossRef]

Owen, J. F.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Pluchino, A. B.

Rosasco, G. J.

Ruppin, R.

R. Ruppin, Surf. Sci. 34, 20 (1973).
[CrossRef]

R. Ruppin, R. Englman, Rep. Prog. Phys. 33, 149 (1970).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

van de Hulst, H. C.

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

Wallis, R. F.

R. F. Wallis, Prog. Surf. Sci. 4 (1973).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964).

Ann. Phy. (1)

V. A. Güttler, Ann. Phy., 6, 65 (1952).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

J. Math. Phys. (1)

H. M. Nussenzveig, J. Math. Phys. 10, 82 (1969).
[CrossRef]

J. Opt. Soc. Am. (4)

Phys. Rev. A (1)

P. Chỳlek, J. T. Kiehl, M. K. W. Ko, Phys. Rev. A: 18, 2229 (1978).
[CrossRef]

Phys. Rev. Lett. (1)

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Prog. Surf. Sci. (1)

R. F. Wallis, Prog. Surf. Sci. 4 (1973).
[CrossRef]

Rep. Prog. Phys. (1)

R. Ruppin, R. Englman, Rep. Prog. Phys. 33, 149 (1970).
[CrossRef]

Surf. Sci. (1)

R. Ruppin, Surf. Sci. 34, 20 (1973).
[CrossRef]

Other (7)

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

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

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1964).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

P. Chỳlek, J. T. Kiehl, M. K. W. Ko, A. Ashkin, Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1980).

R. G. Newton, Scattering Theory of Waves and Particles (McGraw–Hill, New York, 1966).

D. W. Schuerman, Ed., Light Scattering by Irregularly Shaped Particles (Plenum, New York, 1980).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Geometry and parameters used in the calculations for a sphere coated with a spherical shell.

Fig. 2
Fig. 2

Comparison of the emissivity spectrum of an alumina sphere (top) to r2 = 3.0 μm, and a composite alumina-carbon particle (bottom) to r2 = 3.0 and carbon layer thickness τ = 10 Å. Bottom spectrum also shows contributions from the electric and magnetic multipoles.

Fig. 3
Fig. 3

Composite alumina-carbon particle (top) emissivity spectrum with ninth partial wave removed. Real and imaginary parts of b9 shown below.

Fig. 4
Fig. 4

Composite alumina-carbon particle (top) emissivity spectrum with tenth partial wave removed. Real and imaginary parts of b10 shown below.

Fig. 5
Fig. 5

Energy density for an equatorial slice through a 3.0-μm alumina particle calculated for ν = 4480 cm−1. Plot is for a 4.0-μm radius, i.e., a 1.0-μm thick layer external to the particle is included.

Fig. 6
Fig. 6

Energy density for an equatorial slice through a 3.0-μm radius alumina particle calculated for ν = 4420 cm−1.

Fig. 7
Fig. 7

Energy density for an equatorial slice through a 3.0-μm radius alumina particle calculated for ν = 2780 cm−1.

Fig. 8
Fig. 8

Energy density for a equatorial slice through a 3.0-μm radius alumina particle calculated for ν = 2600 cm−1.

Fig. 9
Fig. 9

Coordinate system used in the calculation of the energy density, properly oriented to show equatorial slice plotted in previous four figures.

Fig. 10
Fig. 10

Emissivity spectra of alumina-carbon particles with r2 = 3.0 μm and carbon thickness τ = 30, 50, and 100 Å.

Fig. 11
Fig. 11

Emissivity spectrum of a carbon particle with r = 3.0 μm.

Fig. 12
Fig. 12

Emissivity spectrum of a composite carbon-alumina particle with r2 = 3.0 μm and alumina layer thickness τ = 2.4 μm.

Fig. 13
Fig. 13

Energy density for an equatorial slice through a 3.0-μm composite carbon-alumina particle with alumina thickness layer τ = 2.4 μm calculated for ν = 4480 cm−1.

Fig. 14
Fig. 14

Scattergram for an alumina particle 3.0 μm in radius.

Fig. 15
Fig. 15

Scattergram for a composite alumina-carbon particle with r2 = 3.0 μm and carbon layer thickness τ = 100 Å.

Tables (1)

Tables Icon

Table I Resonance Data for Al2O3 Particle

Equations (35)

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r π 1 i = 1 k 3 2 n = 1 i n - 1 2 n + 1 n ( n + 1 ) ψ n ( k 3 r ) P n ( 1 ) ( cos θ ) cos ϕ ,
r π 2 i = 1 k 3 k 0 n = 1 i n - 1 2 n + 1 n ( n + 1 ) ψ n ( k 3 r ) P n ( 1 ) ( cos θ ) sin ϕ ;
r π 1 v = 1 k 1 2 n = 1 i n - 1 2 n + 1 n ( n + 1 ) g n ψ n ( k 1 r ) P n ( 1 ) ( cos θ ) cos ϕ ,
r π 2 v = 1 k 1 k 0 n = 1 i n - 1 2 n + 1 n ( n + 1 ) h n ψ n ( k 1 r ) P n ( 1 ) ( cos θ ) sin ϕ ,
r π 1 u = 1 k 2 2 n = 1 i n - 1 2 n + 1 n ( n + 1 ) [ c n ψ n ( k 2 r ) + d n χ n ( k 2 r ) ] P n ( 1 ) ( cos θ ) cos ϕ ,
r π 2 u = 1 k 2 k 0 n = 1 i n - 1 2 n + 1 n ( n + 1 ) [ e n ψ n ( k 2 r ) + f n χ n ( k 2 r ) ] P n ( 1 ) ( cos θ ) sin ϕ ,
r π 1 s = - 1 k 3 2 n = 1 i n - 1 2 n + 1 n ( n + 1 ) a n ζ n ( k 3 r ) P n ( 1 ) ( cos θ ) cos ϕ ,
r π 2 s = - 1 k 3 k 0 n = 1 i n - 1 2 n + 1 n ( n + 1 ) b n ζ n ( k 3 r ) P n ( 1 ) ( cos θ ) sin ϕ ,
n ^ 1 c n ψ n ( n ^ 2 α ) + n ^ 1 d n χ n ( n ^ 2 α ) - n ^ 2 g n ψ n ( n ^ 1 α ) = 0 ,
c n ψ n ( n ^ 2 α ) + d n χ n ( n ^ 2 α ) - g n ψ n ( n 1 α ) = 0 ,
c n ψ n ( n ^ 2 ν ) + d n χ n ( n ^ 2 ν ) + n ^ 2 a n ζ n ( ν ) = n ^ 2 ψ n ( ν ) ,
c n ψ n ( n ^ 2 ν ) + d n χ n ( n ^ 2 ν ) + a n ζ n ( ν ) = ψ n ( ν ) ,
e n ψ n ( n ^ 2 α ) + f n χ n ( n ^ 2 α ) - h n ψ n ( n ^ 1 α ) = 0 ,
n ^ 1 e n ψ n ( n ^ 2 α ) + n ^ 1 f n χ n ( n ^ 2 α ) - n ^ 2 h n ψ n ( n ^ 1 α ) = 0 ,
e n ψ n ( n ^ 2 ν ) + f n χ n ( n ^ 2 ν ) + b n ζ n ( ν ) = ψ n ( ν ) ,
e n ψ n ( n ^ 2 ν ) + f n χ n ( n ^ 2 ν ) + n ^ 2 b n ζ n ( ν ) = n ^ 2 ψ n ( ν ) .
k 1 = n ^ 1 2 π λ             k 2 = n ^ 2 2 π λ             α = 2 π r 1 λ             ν = 2 π r 2 λ ,
a n = | n ^ 1 ψ n ( n ^ 2 α ) n ^ 1 χ n ( n ^ 2 α ) - n ^ 2 ψ n ( n ^ 1 α ) 0 ψ n ( n ^ 2 α ) χ n ( n ^ 2 α ) - ψ n ( n ^ 1 α ) 0 ψ n ( n ^ 2 ν ) χ n ( n ^ 2 ν ) 0 n ^ 2 ψ n ( ν ) ψ n ( n ^ 2 ν ) χ n ( n ^ 2 ν ) 0 ψ n ( ν ) | | n ^ 1 ψ n ( n ^ 2 α ) n ^ 1 χ n ( n ^ 2 α ) - n ^ 2 ψ n ( n ^ 1 α ) 0 ψ n ( n ^ 2 α ) χ n ( n ^ 2 α ) - ψ n ( n ^ 1 α ) 0 ψ n ( n ^ 2 ν ) χ n ( n ^ 2 ν ) 0 n ^ 2 ζ n ( ν ) ψ n ( n ^ 2 ν ) χ n ( n ^ 2 ν ) 0 ζ n ( ν ) | .
σ ext = λ 2 2 π n = 1 ( 2 n + 1 ) [ Re ( a n + b n ) ] ,
σ sca = λ 2 2 π n = 1 ( 2 n + 1 ) ( a n 2 + b n 2 ) ,
σ abs = σ ext - σ sca .
ɛ = σ abs / π r 2 2 ,
E r = cos ϕ k 1 2 r 2 n = 1 i n - 1 ( 2 n + 1 ) g n ψ n ( k 1 r ) π n ( cos θ ) sin θ ,
E θ = - cos ϕ k 1 r n = 1 i n = 1 ( 2 n + 1 ) n ( n + 1 ) [ - g n ψ n ( k 1 r ) τ n ( cos θ ) - i h n ψ n ( k 1 r ) π n ( cos θ ) ] ,
E ϕ = - sin ϕ k 1 r n = 1 i n - 1 ( 2 n + 1 ) n ( n + 1 ) [ g n ψ n ( k 1 r ) π n ( cos θ ) + i h n ψ n ( k 1 r ) τ n ( cos θ ) ] .
E r = cos ϕ k 2 2 r 2 n = 1 i n - 1 ( 2 n + 1 ) [ c n ψ n ( k 2 r ) + d n χ n ( k 2 r ) ] π n ( cos θ ) sin θ ,
E θ = - cos ϕ k 2 r n = 1 i n - 1 ( 2 n + 1 ) n ( n + 1 ) { [ - c n ψ n ( k 2 r ) - d n χ n ( k 2 r ) ] τ n ( cos θ ) - [ e n ψ n ( k 2 r ) + f n χ n ( k 2 r ) ] π n ( cos θ ) } ,
E ϕ = - sin ϕ k 2 r n = 1 i n - 1 ( 2 n + 1 ) n ( n + 1 ) { [ c n ψ n ( k 2 r ) + d n χ n ( k 2 r ) ] π n ( cos θ ) + [ e n ψ n ( k 2 r ) + f n χ n ( k 2 r ) ] τ n ( cos θ ) } ,
E r = - cos ϕ k 3 2 r 2 n = 1 i n - 1 ( 2 n + 1 ) a n ζ n ( k 3 r ) π n ( cos θ ) sin θ ,
E θ = cos ϕ k 3 r n = 1 i n - 1 ( 2 n + 1 ) n ( n + 1 ) [ - a n ζ n ( k 3 r ) τ n ( cos θ ) - i b n ζ n ( k 3 r ) τ n ( cos θ ) ] ,
E ϕ = sin ϕ k 3 r n = 1 i n - 1 ( 2 n + 1 ) n ( n + 1 ) [ a n ζ ( k 3 r ) n 1 π n ( cos θ ) + b n ζ n ( k 3 r ) τ n ( cos θ ) ] ,
S * = ½ E × H * ,
Re · S * = - ½ σ E · E * ,
S = ½ σ E · E * ,
σ = - Re ( n ^ ) Im ( n ^ ) c λ ,

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