Abstract

Mie scattering theory is used to calculate the efficiency factors for absorption by microscopic dielectric spheres. Resonances in the efficiency factors for absorption and resonances in the amplitudes of the electric and magnetic multipoles which occur in an expansion of the fields inside the dielectric sphere are discussed. Several trends in the strengths and width of the various resonances as functions of the absorption coefficient of the sphere, size parameter, multipole order, and multipole resonance number are given. A formal solution for elastic (Mie) and inelastic (Raman) scattering by microscopic particles is derived from the extinction theorem. With this background, some implications of the resonances in the interpretation of absorption, fluorescence, and Raman scattering by microscopic particles are discussed.

© 1978 Optical Society of America

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  1. A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976); H. S. Bennett and R. A. Forman, J. Appl. Phys. 48, 1432 (1977).
  2. "Aerosol Measurements: Proceedings of a Conference," edited by W. A. Cassatt and R. S. Maddock, NBS Special Pub. 412, U.S. Govt. Printing Office (1974); W. A. Bonner, H. R. Hulett, R. G. Sweet, and L. A. Herzenberg, Rev. Sci. Instr. 43, 404 (1972).
  3. R. G. Stafford, R. K. Chang, and P. J. Kindlmann, in "Proc. of the 8th Materials Research Symposium on Methods and Standards for Environmental Measurements," edited by W. H. Kirchhoff, NBS Special Pub. 464, U.S. Govt. Printing Office (1977), p. 659.
  4. H. Rosen and T. Novakov, Nature 266, 708 (1977); R. dos Santos and W. H. Stevenson, Appl. Phys. Lett. 30, 236 (1977).
  5. G. J. Rosasco and E. S. Etz, Ind. Res. Dev. 28, 20 (1977).
  6. H. S. Bennett and G. J. Rosasco, Appl. Opt. 17, 491 (1978).
  7. R. Fuchs and K. L. Kliewer, J. Opt. Soc. Am. 58, 319 (1968).
  8. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  9. M. Kerker, The Scattering of Light (Academic, New York, 1969).
  10. H. C. Van de Hulst, Light Scattering by Small Particles, (Wiley, New York, 1957).
  11. J. V. Dave, "Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere," IBM Report No. 320–3237, May 1968 (unpublished).
  12. H. Oser (private communication).
  13. Professor Milton Kerker, Clarkson College of Technology, has graciously verified our numerical results for x ≤ 10 utilizing his routines, which differ from ours, for Mie scattering calculations (private communication).
  14. H. J. Metz and H. K. Dettmar, Kolloid Z. Z. Polym. 192, 107 (1963).
  15. G. W. Kattawar and G. N. Plass, Appl. Opt. 9, 1549 (1967); G. N. Plass, Appl. Opt. 5, 279 (1966).
  16. P. Chylek, J. Opt. Soc. Am. 66, 285 (1976).
  17. H. M. Nussenzveig, J. Math. Phys. 10, 125 (1969).
  18. H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396 (1976).
  19. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, N.J., 1960), p. 81.
  20. F. W. J. Olver, in Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (U.S. Government Printing Office, Washington, D.C., 1964), p. 364.
  21. A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 38, 351, 1977.
  22. H. S. Bennett and G. J. Rosasco, "Heating microscopic particles with laser beams," J. Appl. Phys. 49, 640 (1978).
  23. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).
  24. A. B. Bhatia and W. J. Noble, Proc. R. Soc. London A220, 356 (1953).
  25. G. J. Rosasco, Thesis, Fordham Univ., 1970 (Univ. Microfilms, Ann Arbor, Michigan) (unpublished).
  26. P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).
  27. R. Ruppin and R. Engleman, Rep. Prog. Phys. 33, 149 (1970).
  28. R. Ruppin, J. Phys. C 8, 1969 (1975).

Ashkin, A.

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 38, 351, 1977.

Barber, P. W.

P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).

Bennett, H. S.

H. S. Bennett and G. J. Rosasco, "Heating microscopic particles with laser beams," J. Appl. Phys. 49, 640 (1978).

H. S. Bennett and G. J. Rosasco, Appl. Opt. 17, 491 (1978).

Bhatia, A. B.

A. B. Bhatia and W. J. Noble, Proc. R. Soc. London A220, 356 (1953).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

Chang, R. K.

R. G. Stafford, R. K. Chang, and P. J. Kindlmann, in "Proc. of the 8th Materials Research Symposium on Methods and Standards for Environmental Measurements," edited by W. H. Kirchhoff, NBS Special Pub. 464, U.S. Govt. Printing Office (1977), p. 659.

Chew, H.

H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396 (1976).

Chylek, P.

P. Chylek, J. Opt. Soc. Am. 66, 285 (1976).

Dave, J. V.

J. V. Dave, "Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere," IBM Report No. 320–3237, May 1968 (unpublished).

Dettmar, H. K.

H. J. Metz and H. K. Dettmar, Kolloid Z. Z. Polym. 192, 107 (1963).

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 38, 351, 1977.

Edmonds, R.

R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, N.J., 1960), p. 81.

Engleman, R.

R. Ruppin and R. Engleman, Rep. Prog. Phys. 33, 149 (1970).

Etz, E. S.

G. J. Rosasco and E. S. Etz, Ind. Res. Dev. 28, 20 (1977).

Fuchs, R.

R. Fuchs and K. L. Kliewer, J. Opt. Soc. Am. 58, 319 (1968).

Gersho, A.

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976); H. S. Bennett and R. A. Forman, J. Appl. Phys. 48, 1432 (1977).

Kattawar, G. W.

G. W. Kattawar and G. N. Plass, Appl. Opt. 9, 1549 (1967); G. N. Plass, Appl. Opt. 5, 279 (1966).

Kerker, M.

M. Kerker, The Scattering of Light (Academic, New York, 1969).

H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396 (1976).

Kindlmann, P. J.

R. G. Stafford, R. K. Chang, and P. J. Kindlmann, in "Proc. of the 8th Materials Research Symposium on Methods and Standards for Environmental Measurements," edited by W. H. Kirchhoff, NBS Special Pub. 464, U.S. Govt. Printing Office (1977), p. 659.

Kliewer, K. L.

R. Fuchs and K. L. Kliewer, J. Opt. Soc. Am. 58, 319 (1968).

McNulty, P. J.

H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396 (1976).

Metz, H. J.

H. J. Metz and H. K. Dettmar, Kolloid Z. Z. Polym. 192, 107 (1963).

Noble, W. J.

A. B. Bhatia and W. J. Noble, Proc. R. Soc. London A220, 356 (1953).

Novakov, T.

H. Rosen and T. Novakov, Nature 266, 708 (1977); R. dos Santos and W. H. Stevenson, Appl. Phys. Lett. 30, 236 (1977).

Nussenzveig, H. M.

H. M. Nussenzveig, J. Math. Phys. 10, 125 (1969).

Olver, F. W. J.

F. W. J. Olver, in Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (U.S. Government Printing Office, Washington, D.C., 1964), p. 364.

Oser, H.

H. Oser (private communication).

Plass, G. N.

G. W. Kattawar and G. N. Plass, Appl. Opt. 9, 1549 (1967); G. N. Plass, Appl. Opt. 5, 279 (1966).

Rosasco, G. J.

H. S. Bennett and G. J. Rosasco, "Heating microscopic particles with laser beams," J. Appl. Phys. 49, 640 (1978).

G. J. Rosasco and E. S. Etz, Ind. Res. Dev. 28, 20 (1977).

H. S. Bennett and G. J. Rosasco, Appl. Opt. 17, 491 (1978).

G. J. Rosasco, Thesis, Fordham Univ., 1970 (Univ. Microfilms, Ann Arbor, Michigan) (unpublished).

Rosen, H.

H. Rosen and T. Novakov, Nature 266, 708 (1977); R. dos Santos and W. H. Stevenson, Appl. Phys. Lett. 30, 236 (1977).

Rosencwaig, A.

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976); H. S. Bennett and R. A. Forman, J. Appl. Phys. 48, 1432 (1977).

Ruppin, R.

R. Ruppin, J. Phys. C 8, 1969 (1975).

R. Ruppin and R. Engleman, Rep. Prog. Phys. 33, 149 (1970).

Stafford, R. G.

R. G. Stafford, R. K. Chang, and P. J. Kindlmann, in "Proc. of the 8th Materials Research Symposium on Methods and Standards for Environmental Measurements," edited by W. H. Kirchhoff, NBS Special Pub. 464, U.S. Govt. Printing Office (1977), p. 659.

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).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

Other

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976); H. S. Bennett and R. A. Forman, J. Appl. Phys. 48, 1432 (1977).

"Aerosol Measurements: Proceedings of a Conference," edited by W. A. Cassatt and R. S. Maddock, NBS Special Pub. 412, U.S. Govt. Printing Office (1974); W. A. Bonner, H. R. Hulett, R. G. Sweet, and L. A. Herzenberg, Rev. Sci. Instr. 43, 404 (1972).

R. G. Stafford, R. K. Chang, and P. J. Kindlmann, in "Proc. of the 8th Materials Research Symposium on Methods and Standards for Environmental Measurements," edited by W. H. Kirchhoff, NBS Special Pub. 464, U.S. Govt. Printing Office (1977), p. 659.

H. Rosen and T. Novakov, Nature 266, 708 (1977); R. dos Santos and W. H. Stevenson, Appl. Phys. Lett. 30, 236 (1977).

G. J. Rosasco and E. S. Etz, Ind. Res. Dev. 28, 20 (1977).

H. S. Bennett and G. J. Rosasco, Appl. Opt. 17, 491 (1978).

R. Fuchs and K. L. Kliewer, J. Opt. Soc. Am. 58, 319 (1968).

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

M. Kerker, The Scattering of Light (Academic, New York, 1969).

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

J. V. Dave, "Subroutines for Computing the Parameters of the Electromagnetic Radiation Scattered by a Sphere," IBM Report No. 320–3237, May 1968 (unpublished).

H. Oser (private communication).

Professor Milton Kerker, Clarkson College of Technology, has graciously verified our numerical results for x ≤ 10 utilizing his routines, which differ from ours, for Mie scattering calculations (private communication).

H. J. Metz and H. K. Dettmar, Kolloid Z. Z. Polym. 192, 107 (1963).

G. W. Kattawar and G. N. Plass, Appl. Opt. 9, 1549 (1967); G. N. Plass, Appl. Opt. 5, 279 (1966).

P. Chylek, J. Opt. Soc. Am. 66, 285 (1976).

H. M. Nussenzveig, J. Math. Phys. 10, 125 (1969).

H. Chew, P. J. McNulty, and M. Kerker, Phys. Rev. A 13, 396 (1976).

R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, N.J., 1960), p. 81.

F. W. J. Olver, in Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (U.S. Government Printing Office, Washington, D.C., 1964), p. 364.

A. Ashkin and J. M. Dziedzic, Phys. Rev. Lett. 38, 351, 1977.

H. S. Bennett and G. J. Rosasco, "Heating microscopic particles with laser beams," J. Appl. Phys. 49, 640 (1978).

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1965).

A. B. Bhatia and W. J. Noble, Proc. R. Soc. London A220, 356 (1953).

G. J. Rosasco, Thesis, Fordham Univ., 1970 (Univ. Microfilms, Ann Arbor, Michigan) (unpublished).

P. W. Barber, IEEE Trans. Microwave Theory Tech. MTT-25, 373 (1977).

R. Ruppin and R. Engleman, Rep. Prog. Phys. 33, 149 (1970).

R. Ruppin, J. Phys. C 8, 1969 (1975).

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