Abstract

A group-theory expansion of scalar spherical harmonics is used to obtain an expansion of vector spherical harmonics. This expansion is applied to the multipole-expansion treatment of Mie theory, and explicit expressions suitable for computation of the coefficients of the expansion are obtained. The result is a Mie-theory solution given in the variables and basis vectors of the spherical-coordinate system associated with a Cartesian system that is rotated with respect to the conventionally chosen coordinate system. This result is then used to obtain an analyticalseries solution for the power scattered into a conical solid angle centered on any chosen direction from the scattering sphere.

© 1982 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 9.
  2. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Chap. 13.
  3. P. Chylek, "Mie scattering into the backward hemisphere," J. Opt. Soc. Am. 63, 1467–1471 (1973).
  4. W. P. Chu and D. M. Robinson, "Scattering from a moving spherical particle by two crossed coherent plane waves," Appl. Opt. 16, 619–626 (1977).
  5. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Chaps. 3, 16.
  6. J. D. Pendleton, "Mie scattering theory for particle sizing interferometry with the dual beam laser velocimeter" (U.S. Department of Energy, Washington, D.C., 1982). Also published as "A generalized Mie theory solution and its application to particle sizing interferometry," Ph.D. Thesis (University of Tennessee, Knoxville, Tennessee, 1982).
  7. M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957), Chap. 4.
  8. G. Goertzel, "Angular correction of gamma-rays," Phys. Rev. 70, 897–909 (1946).
  9. D. M. Brink and G. R. Satchler, Angular Momentum (Oxford U. Press, 1968), p. 147.
  10. I. S. Gradsteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 1005.

1977 (1)

1973 (1)

1946 (1)

G. Goertzel, "Angular correction of gamma-rays," Phys. Rev. 70, 897–909 (1946).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Chap. 13.

Brink, D. M.

D. M. Brink and G. R. Satchler, Angular Momentum (Oxford U. Press, 1968), p. 147.

Chu, W. P.

Chylek, P.

Goertzel, G.

G. Goertzel, "Angular correction of gamma-rays," Phys. Rev. 70, 897–909 (1946).

Gradsteyn, I. S.

I. S. Gradsteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 1005.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Chaps. 3, 16.

Pendleton, J. D.

J. D. Pendleton, "Mie scattering theory for particle sizing interferometry with the dual beam laser velocimeter" (U.S. Department of Energy, Washington, D.C., 1982). Also published as "A generalized Mie theory solution and its application to particle sizing interferometry," Ph.D. Thesis (University of Tennessee, Knoxville, Tennessee, 1982).

Robinson, D. M.

Rose, M. E.

M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957), Chap. 4.

Ryzhik, I. M.

I. S. Gradsteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 1005.

Satchler, G. R.

D. M. Brink and G. R. Satchler, Angular Momentum (Oxford U. Press, 1968), p. 147.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 9.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Chap. 13.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Phys. Rev. (1)

G. Goertzel, "Angular correction of gamma-rays," Phys. Rev. 70, 897–909 (1946).

Other (7)

D. M. Brink and G. R. Satchler, Angular Momentum (Oxford U. Press, 1968), p. 147.

I. S. Gradsteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 1005.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 9.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1975), Chap. 13.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Chaps. 3, 16.

J. D. Pendleton, "Mie scattering theory for particle sizing interferometry with the dual beam laser velocimeter" (U.S. Department of Energy, Washington, D.C., 1982). Also published as "A generalized Mie theory solution and its application to particle sizing interferometry," Ph.D. Thesis (University of Tennessee, Knoxville, Tennessee, 1982).

M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957), Chap. 4.

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