Abstract

The polarizability of a dielectrically anisotropic sphere is studied. The anisotropy is general, consisting of a symmetric and an antisymmetric part of the permittivity dyadic. The polarizability is also dyadic, with its components depending on the relations of the permittivity components of the material. In certain special cases the components of the polarizability matrix decouple and become functions only of the corresponding permittivity components, but in general all nine polarizabilities depend on all nine permittivities.

© 1994 Optical Society of America

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References

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  1. C. Kittel, Introduction to Solid-State Physics, 6th ed. (Wiley, New York, 1986), p. 370.
  2. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 151.
  3. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), p. 87.
  4. I. V. Lindell, Methods for Electromagnetic Field Analysis (Clarendon, Oxford, 1992), pp. 100–112.
  5. R. Landauer, AIP Conf. Proc. 40, 2 (1978).
    [CrossRef]
  6. D. Bedeaux, P. Mazur, Physica 67, 23 (1973).
    [CrossRef]
  7. A. Lakhtakia, J. Phys. (Paris) 51, 2235 (1990).(This paper deals with biansotropy, which is more general than anisotropic polarizability but is of course applicable to the present case.)
    [CrossRef]
  8. A. Lakhtakia, V. K. Varadan, V. V. Varadan, Int. J. Infrared Millimeter Waves 12, 1253 (1991)A. H. Sihvola, I. V. Lindell, Int. J. Infrared Millimeter Waves 14, 1547 (1993).
    [CrossRef]
  9. L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, 1982), pp. 31–37.
  10. A. Lakhtakia, Speculations Sci. Technol. 14, 2 (1991).
  11. A. H. Sihvola, I. V. Lindell, Electron. Lett. 26, 118(1990)
    [CrossRef]
  12. A. H. Sihvola, IEEE Trans. Antennas Propag. 40, 188 (1992)
    [CrossRef]

1992 (1)

A. H. Sihvola, IEEE Trans. Antennas Propag. 40, 188 (1992)
[CrossRef]

1991 (2)

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Int. J. Infrared Millimeter Waves 12, 1253 (1991)A. H. Sihvola, I. V. Lindell, Int. J. Infrared Millimeter Waves 14, 1547 (1993).
[CrossRef]

A. Lakhtakia, Speculations Sci. Technol. 14, 2 (1991).

1990 (2)

A. H. Sihvola, I. V. Lindell, Electron. Lett. 26, 118(1990)
[CrossRef]

A. Lakhtakia, J. Phys. (Paris) 51, 2235 (1990).(This paper deals with biansotropy, which is more general than anisotropic polarizability but is of course applicable to the present case.)
[CrossRef]

1978 (1)

R. Landauer, AIP Conf. Proc. 40, 2 (1978).
[CrossRef]

1973 (1)

D. Bedeaux, P. Mazur, Physica 67, 23 (1973).
[CrossRef]

Barron, L. D.

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, 1982), pp. 31–37.

Bedeaux, D.

D. Bedeaux, P. Mazur, Physica 67, 23 (1973).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), p. 87.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 151.

Kittel, C.

C. Kittel, Introduction to Solid-State Physics, 6th ed. (Wiley, New York, 1986), p. 370.

Lakhtakia, A.

A. Lakhtakia, Speculations Sci. Technol. 14, 2 (1991).

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Int. J. Infrared Millimeter Waves 12, 1253 (1991)A. H. Sihvola, I. V. Lindell, Int. J. Infrared Millimeter Waves 14, 1547 (1993).
[CrossRef]

A. Lakhtakia, J. Phys. (Paris) 51, 2235 (1990).(This paper deals with biansotropy, which is more general than anisotropic polarizability but is of course applicable to the present case.)
[CrossRef]

Landauer, R.

R. Landauer, AIP Conf. Proc. 40, 2 (1978).
[CrossRef]

Lindell, I. V.

A. H. Sihvola, I. V. Lindell, Electron. Lett. 26, 118(1990)
[CrossRef]

I. V. Lindell, Methods for Electromagnetic Field Analysis (Clarendon, Oxford, 1992), pp. 100–112.

Mazur, P.

D. Bedeaux, P. Mazur, Physica 67, 23 (1973).
[CrossRef]

Sihvola, A. H.

A. H. Sihvola, IEEE Trans. Antennas Propag. 40, 188 (1992)
[CrossRef]

A. H. Sihvola, I. V. Lindell, Electron. Lett. 26, 118(1990)
[CrossRef]

Varadan, V. K.

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Int. J. Infrared Millimeter Waves 12, 1253 (1991)A. H. Sihvola, I. V. Lindell, Int. J. Infrared Millimeter Waves 14, 1547 (1993).
[CrossRef]

Varadan, V. V.

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Int. J. Infrared Millimeter Waves 12, 1253 (1991)A. H. Sihvola, I. V. Lindell, Int. J. Infrared Millimeter Waves 14, 1547 (1993).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), p. 87.

AIP Conf. Proc. (1)

R. Landauer, AIP Conf. Proc. 40, 2 (1978).
[CrossRef]

Electron. Lett. (1)

A. H. Sihvola, I. V. Lindell, Electron. Lett. 26, 118(1990)
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. H. Sihvola, IEEE Trans. Antennas Propag. 40, 188 (1992)
[CrossRef]

Int. J. Infrared Millimeter Waves (1)

A. Lakhtakia, V. K. Varadan, V. V. Varadan, Int. J. Infrared Millimeter Waves 12, 1253 (1991)A. H. Sihvola, I. V. Lindell, Int. J. Infrared Millimeter Waves 14, 1547 (1993).
[CrossRef]

J. Phys. (1)

A. Lakhtakia, J. Phys. (Paris) 51, 2235 (1990).(This paper deals with biansotropy, which is more general than anisotropic polarizability but is of course applicable to the present case.)
[CrossRef]

Physica (1)

D. Bedeaux, P. Mazur, Physica 67, 23 (1973).
[CrossRef]

Speculations Sci. Technol. (1)

A. Lakhtakia, Speculations Sci. Technol. 14, 2 (1991).

Other (5)

L. D. Barron, Molecular Light Scattering and Optical Activity (Cambridge U. Press, Cambridge, 1982), pp. 31–37.

C. Kittel, Introduction to Solid-State Physics, 6th ed. (Wiley, New York, 1986), p. 370.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), p. 151.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), p. 87.

I. V. Lindell, Methods for Electromagnetic Field Analysis (Clarendon, Oxford, 1992), pp. 100–112.

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Tables (1)

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Table 1 Gyrotropic and Chiral Parameters of Anisotropic and Chiral Spheres

Equations (18)

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α = 3 0 V - 0 + 2 0 ,
D ¯ = ¯ ¯ · E ¯ .
¯ ¯ = ¯ ¯ S + ¯ ¯ A = x u ¯ x u ¯ x + y u ¯ y u ¯ y + z u ¯ z u ¯ z + g u ¯ g × I ¯ ¯ ,
α ¯ ¯ = 3 0 V ( ¯ ¯ - 0 I ¯ ¯ ) · ( ¯ ¯ + 2 0 I ¯ ¯ ) - 1 ,
B ¯ ¯ - 1 = 3 ( B ¯ ¯ × × B ¯ ¯ ) T B ¯ ¯ × × B ¯ ¯ : B ¯ ¯ ,
α ¯ ¯ = 3 0 V A ¯ ¯ + I ¯ ¯ g 2 ( c + 2 0 ) - u ¯ g u ¯ g 3 0 g 2 + 3 0 g [ ( ¯ ¯ S + 2 0 I ¯ ¯ ) · u ¯ g ] × I ¯ ¯ ( x + 2 0 ) ( y + 2 0 ) ( z + 2 0 ) + g 2 ( c + 2 0 ) ,
c = ¯ ¯ S : u ¯ g u ¯ g = x c s 2 + y c y 2 + z c z 2 ,
A ¯ ¯ = 1 2 ( ¯ ¯ S - 0 I ¯ ¯ ) · ( ¯ ¯ S + 2 0 I ¯ ¯ ) × ( ¯ ¯ S + 2 0 I ¯ ¯ ) = u ¯ x u ¯ x ( x - 0 ) ( y + 2 0 ) ( z + 2 0 ) + u ¯ y u ¯ y ( y - 0 ) ( z + 2 0 ) ( x + 2 0 ) + u ¯ z u ¯ z ( z - 0 ) ( x + 2 0 ) ( y + 2 0 ) .
α ¯ ¯ = 3 0 V ( x + 2 0 ) ( y + 2 0 ) ( z + 2 0 ) + g 2 ( c + 2 0 ) × [ A x x - 3 0 g 2 c x 2 + g 2 ( c + 2 0 ) - 3 0 g 2 c x c y - 3 0 g c z ( z + 2 0 ) - 3 0 g 2 c x c z + 3 0 g c y ( y + 2 0 ) - 3 0 g 2 c x c y + 3 0 g c z ( z + 2 0 ) A y y - 3 0 g 2 c y 2 + g 2 ( c + 2 0 ) - 3 0 g 2 c y c z - 3 0 g c x ( x + 2 0 ) - 3 0 g 2 c x c z - 3 0 g c y ( y + 2 0 ) - 3 0 g 2 c y c z + 3 0 g c x ( x + 2 0 ) A z z - 3 0 g 2 c z 2 + g 2 ( c + 2 0 ) ] ,
A x x = u ¯ x u ¯ x : A ¯ ¯ = ( x - 0 ) ( y + 2 0 ) ( z + 2 0 ) ,
A y y = u ¯ y u ¯ y : A ¯ ¯ = ( y - 0 ) ( z + 2 0 ) ( x + 2 0 ) ,
A z z = u ¯ z u ¯ z : A ¯ ¯ = ( z - 0 ) ( x + 2 0 ) ( y + 2 0 ) .
α ¯ ¯ = 3 0 V i = x , y , z u ¯ i u ¯ i i - 0 i + 2 0 ,
α ¯ ¯ = 3 0 V [ I ¯ ¯ ( + 2 0 ) ( - 0 ) + g 2 ( + 2 0 ) 2 + g 2 - u ¯ g u ¯ g 3 0 + 2 0 g 2 ( + 2 0 ) 2 + g 2 + u ¯ g × I ¯ ¯ 3 0 g ( + 2 0 ) 2 + g 2 ] ,
α x x = 3 0 V ( x - 0 ) ( y + 2 0 ) + g 2 ( x + 2 0 ) ( y + 2 0 ) + g 2 , α y y = 3 0 V ( y - 0 ) ( x + 2 0 ) + g 2 ( x + 2 0 ) ( y + 2 0 ) + g 2 , α z z = 3 0 V z - 0 z + 2 0 , a x y = - α y x = 3 0 V - 3 0 g ( x + 2 0 ) ( x + 2 0 ) + g 2 , a x z = α z x = α y z = α z y = 0.
α e e = 3 0 V ( - 0 ) ( μ + 2 μ 0 ) - κ 2 μ 0 0 ( μ + 2 μ 0 ) ( + 2 0 ) - κ 2 μ 0 0 ,
α e m = - α m e = 3 μ 0 0 V - j k μ 0 0 ( μ + 2 μ 0 ) ( + 2 0 ) - κ 2 μ 0 0 ,
α m m = 3 μ 0 V ( μ - μ 0 ) ( + 2 0 ) - κ 2 μ 0 0 ( μ + 2 μ 0 ) ( + 2 0 ) - κ 2 μ 0 0 ,

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