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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 4, Iss. 3 — Mar. 1, 1987
  • pp: 612–613

Recurrence relations for the Mie scattering coefficients

Craig F. Bohren  »View Author Affiliations


JOSA A, Vol. 4, Issue 3, pp. 612-613 (1987)
http://dx.doi.org/10.1364/JOSAA.4.000612


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Abstract

The Mie scattering coefficients satisfy recurrence relations:an−1, bn−1, an, and bn determine an+1, and bn+1. It is therefore possible, in principle, to generate the entire set from the first four, which has a simple interpretation. Each term in a multipole expansion of an electrostatic field can be obtained by differentiating the preceding term. The Mie coefficients are terms in a multipole expansion of a particular electromagnetic field, namely, that scattered by an arbitrary sphere. By analogy, it is not surprising that all these coefficients can be generated from the electric and magnetic dipole and quadrupole terms. Moreover, the recurrence relations for the Mie coefficients contain finite differences, in analogy with the infinitesimal differences (derivatives) in the multipole expansion of an electrostatic field.

© 1987 Optical Society of America

History
Original Manuscript: April 18, 1986
Manuscript Accepted: June 9, 1986
Published: March 1, 1987

Citation
Craig F. Bohren, "Recurrence relations for the Mie scattering coefficients," J. Opt. Soc. Am. A 4, 612-613 (1987)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-4-3-612


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References

  1. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), Sec. 9.25.
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 9.
  3. M. Born, E. Wolf, Principles of Optics, 3rd ed. (Pergamon, Oxford, 1965), Sec. 13.5.
  4. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), Chaps. 3 and 4.
  5. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small ParticlesWiley-Interscience, New York, 1983), Chap. 4.
  6. J. V. Dave, Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere, IBM Order No. 360D-17.4.002 (IBM Scientific Center, Palo Alto, Calif., 1968).
  7. W. J. Lentz, “Generating Bessel functions in Mie scattering calculations using continued fractions,” Appl. Opt. 15, 668–671 (1976). [CrossRef] [PubMed]
  8. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980). [CrossRef] [PubMed]
  9. B. Verner, “Note on the recurrence between Mie’s coefficients,”J. Opt. Soc. Am. 66, 1424–1425 (1976). [CrossRef]
  10. J. C. Maxwell, A Treatise on Electricity and Magnetism (Dover, New York, 1954) Vol. 1, p. 196.
  11. E. W. Hobson, The Theory of Spherical and Ellipsoidal Harmonics (Cambridge U. Press, Cambridge, 1931), pp. 129–132.
  12. W. K. H. Panofsky, M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, Mass., 1962), p. 15.

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