Abstract

The natural resonant frequencies and poles associated with the electromagnetic modes of a dielectric sphere with a relative index of refraction of 1.4 have been calculated for size parameters ranging from 1 to 50. Determining pole locations in the complex plane entailed the computation of spherical Bessel functions for large complex arguments. The symbolic programming language reduce was used to provide independent verifications of the convergence and accuracy of the numerical Bessel function routines required in these computations. To determine pole locations, we used a standard zero-finding routine to find the zeros of the scattering coefficient denominators. In addition, we used a separate zero-counting routine in conjunction with the search routine to ensure that all poles within a given region of the complex plane were found. The real parts of the calculated poles agree with the location of peaks in the resonance spectrum (calculated for real frequency excitation), whereas the imaginary parts are related to the widths of these peaks. The intensity inside the sphere, averaged over all spherical angles, was computed as a function of radius. When the particle is excited at resonance, the internal intensity exhibits a sharp peak near, but not on, the surface. The intensity was found to be the strongest when the particle is driven at resonant frequencies whose poles have small imaginary components in the complex plane.

© 1984 Optical Society of America

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References

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  1. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), p. 50.
  2. M. Kerker, “Lorenz–Mie Scattering by spheres: some newly recognized phenomena,” Aerosol Sci. Tech. 1, 275–291 (1982).
    [Crossref]
  3. J. V. Dave, “Subroutines for computing the parameters of the electromagnetic radiation scattered by a sphere,” Report 320-3237, IBM Scientific Center, Palo Alto, California, 1968.
  4. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
    [Crossref] [PubMed]
  5. P. Chylek, “Partial-wave resonances and the ripple structure in the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1976).
    [Crossref]
  6. P. Chylek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
    [Crossref] [PubMed]
  7. P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
    [Crossref]
  8. G. J. Rosasco, H. S. Bennett, “Internal field resonance structure: implications for optical absorption and scattering by microscopic particles,” J Opt. Soc. Am. 68, 1242–1250 (1978).
    [Crossref]
  9. A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
    [Crossref]
  10. R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
    [Crossref]
  11. J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-dependent resonances in Raman scattering, fluroescence emission, and elastic scattering from microparticles,” Areosol Sci. Tech. 1, 293–302 (1982).
    [Crossref]
  12. J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, “Determination of optical fiber diameter from resonances in the elastic scattering spectrum,” Opt. Lett. 6, 272–274 (1981).
    [Crossref] [PubMed]
  13. P. W. Barber, J. F. Owen, R. K. Chang, “Resonance scattering for characterization of axisymmetric dielectric objects,” IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
    [Crossref]
  14. M. Gastine, L. Courtois, J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
    [Crossref]
  15. P. Affolter, B. Eliasson, “Electromagnetic resonances and Q-factors of lossy dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-21, 573–578 (1973).
    [Crossref]
  16. F. M. Tesche, “On the analysis of scattering and antenna problems using the singularity expansion technique,” IEEE Trans. Antennas Propag. AP-21, 53–62 (1973).
    [Crossref]
  17. C. F. Gerald, Applied Numerical Analysis, 2nd ed. (Addison-Wesley, Reading, Mass., 1978), pp. 495–503.
  18. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematic Functions (U.S. Government Printing Office, Washington, D.C., 1970), p. 435.
  19. F. J. Corbato, J. L. Uretsky, “Generation of spherical Bessel functions in digital computers,” J. Assoc. Comput. Mach. 6, 366–375 (1959).
    [Crossref]
  20. W. Gautschi, “Computational aspects of three-term recurrence relations,” SIAM Rev. 9, 24–82 (1967).
    [Crossref]
  21. A. C. Hearn, Reduce 2 User’s Manual, 2nd ed. (Department of Computer Science, University of Utah, Salt Lake City, Utah, 1974, unpublished).
  22. R. W. Hamming, Numerical Methods for Scientists and Engineers (McGraw-Hill, New York, 1973), pp. 78–97.
  23. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 565.
  24. J. D. Murphy, P. J. Moser, A. Nagl, H. Uberall, “A surface wave interpretation for the resonances of a dielectric sphere,” IEEE Trans. Antennas Propag. AP-28, 924–927 (1980).
    [Crossref]
  25. P. J. Moser, J. D. Murphy, A. Nagl, H. Uberall, “Creeping-wave excitation of the eigenvibrations of dielectric resonators,” J. Wave Motion 3, 283–295 (1981).
    [Crossref]
  26. H. Inada, M. A. Plonus, “The diffracted field contribution to the scattering from a large dense dielectric sphere,” IEEE Trans. Antennas Propag. AP-18, 649–660 (1970).
    [Crossref]
  27. J. F. Owen, R. K. Chang, P. W. Barber, “Internal electric field distributions of a dielectric cylinder at resonance wavelengths,” Opt. Lett. 6, 540–542 (1981).
    [Crossref] [PubMed]

1982 (3)

M. Kerker, “Lorenz–Mie Scattering by spheres: some newly recognized phenomena,” Aerosol Sci. Tech. 1, 275–291 (1982).
[Crossref]

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-dependent resonances in Raman scattering, fluroescence emission, and elastic scattering from microparticles,” Areosol Sci. Tech. 1, 293–302 (1982).
[Crossref]

P. W. Barber, J. F. Owen, R. K. Chang, “Resonance scattering for characterization of axisymmetric dielectric objects,” IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[Crossref]

1981 (3)

1980 (3)

J. D. Murphy, P. J. Moser, A. Nagl, H. Uberall, “A surface wave interpretation for the resonances of a dielectric sphere,” IEEE Trans. Antennas Propag. AP-28, 924–927 (1980).
[Crossref]

W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[Crossref] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[Crossref]

1978 (3)

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
[Crossref] [PubMed]

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

G. J. Rosasco, H. S. Bennett, “Internal field resonance structure: implications for optical absorption and scattering by microscopic particles,” J Opt. Soc. Am. 68, 1242–1250 (1978).
[Crossref]

1977 (1)

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

1976 (1)

1973 (2)

P. Affolter, B. Eliasson, “Electromagnetic resonances and Q-factors of lossy dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-21, 573–578 (1973).
[Crossref]

F. M. Tesche, “On the analysis of scattering and antenna problems using the singularity expansion technique,” IEEE Trans. Antennas Propag. AP-21, 53–62 (1973).
[Crossref]

1970 (1)

H. Inada, M. A. Plonus, “The diffracted field contribution to the scattering from a large dense dielectric sphere,” IEEE Trans. Antennas Propag. AP-18, 649–660 (1970).
[Crossref]

1967 (2)

W. Gautschi, “Computational aspects of three-term recurrence relations,” SIAM Rev. 9, 24–82 (1967).
[Crossref]

M. Gastine, L. Courtois, J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
[Crossref]

1959 (1)

F. J. Corbato, J. L. Uretsky, “Generation of spherical Bessel functions in digital computers,” J. Assoc. Comput. Mach. 6, 366–375 (1959).
[Crossref]

Affolter, P.

P. Affolter, B. Eliasson, “Electromagnetic resonances and Q-factors of lossy dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-21, 573–578 (1973).
[Crossref]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

Barber, P. W.

P. W. Barber, J. F. Owen, R. K. Chang, “Resonance scattering for characterization of axisymmetric dielectric objects,” IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[Crossref]

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-dependent resonances in Raman scattering, fluroescence emission, and elastic scattering from microparticles,” Areosol Sci. Tech. 1, 293–302 (1982).
[Crossref]

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, “Determination of optical fiber diameter from resonances in the elastic scattering spectrum,” Opt. Lett. 6, 272–274 (1981).
[Crossref] [PubMed]

J. F. Owen, R. K. Chang, P. W. Barber, “Internal electric field distributions of a dielectric cylinder at resonance wavelengths,” Opt. Lett. 6, 540–542 (1981).
[Crossref] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[Crossref]

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[Crossref]

Bennett, H. S.

G. J. Rosasco, H. S. Bennett, “Internal field resonance structure: implications for optical absorption and scattering by microscopic particles,” J Opt. Soc. Am. 68, 1242–1250 (1978).
[Crossref]

Chang, R. K.

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-dependent resonances in Raman scattering, fluroescence emission, and elastic scattering from microparticles,” Areosol Sci. Tech. 1, 293–302 (1982).
[Crossref]

P. W. Barber, J. F. Owen, R. K. Chang, “Resonance scattering for characterization of axisymmetric dielectric objects,” IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[Crossref]

J. F. Owen, R. K. Chang, P. W. Barber, “Internal electric field distributions of a dielectric cylinder at resonance wavelengths,” Opt. Lett. 6, 540–542 (1981).
[Crossref] [PubMed]

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, “Determination of optical fiber diameter from resonances in the elastic scattering spectrum,” Opt. Lett. 6, 272–274 (1981).
[Crossref] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[Crossref]

Chylek, P.

Corbato, F. J.

F. J. Corbato, J. L. Uretsky, “Generation of spherical Bessel functions in digital computers,” J. Assoc. Comput. Mach. 6, 366–375 (1959).
[Crossref]

Courtois, L.

M. Gastine, L. Courtois, J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
[Crossref]

Dave, J. V.

J. V. Dave, “Subroutines for computing the parameters of the electromagnetic radiation scattered by a sphere,” Report 320-3237, IBM Scientific Center, Palo Alto, California, 1968.

Dormann, J. L.

M. Gastine, L. Courtois, J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
[Crossref]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

Eliasson, B.

P. Affolter, B. Eliasson, “Electromagnetic resonances and Q-factors of lossy dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-21, 573–578 (1973).
[Crossref]

Gastine, M.

M. Gastine, L. Courtois, J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
[Crossref]

Gautschi, W.

W. Gautschi, “Computational aspects of three-term recurrence relations,” SIAM Rev. 9, 24–82 (1967).
[Crossref]

Gerald, C. F.

C. F. Gerald, Applied Numerical Analysis, 2nd ed. (Addison-Wesley, Reading, Mass., 1978), pp. 495–503.

Hamming, R. W.

R. W. Hamming, Numerical Methods for Scientists and Engineers (McGraw-Hill, New York, 1973), pp. 78–97.

Hearn, A. C.

A. C. Hearn, Reduce 2 User’s Manual, 2nd ed. (Department of Computer Science, University of Utah, Salt Lake City, Utah, 1974, unpublished).

Inada, H.

H. Inada, M. A. Plonus, “The diffracted field contribution to the scattering from a large dense dielectric sphere,” IEEE Trans. Antennas Propag. AP-18, 649–660 (1970).
[Crossref]

Kerker, M.

M. Kerker, “Lorenz–Mie Scattering by spheres: some newly recognized phenomena,” Aerosol Sci. Tech. 1, 275–291 (1982).
[Crossref]

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), p. 50.

Kiehl, J. T.

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
[Crossref] [PubMed]

Ko, M. K. W.

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
[Crossref] [PubMed]

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

Messinger, B. J.

Moser, P. J.

P. J. Moser, J. D. Murphy, A. Nagl, H. Uberall, “Creeping-wave excitation of the eigenvibrations of dielectric resonators,” J. Wave Motion 3, 283–295 (1981).
[Crossref]

J. D. Murphy, P. J. Moser, A. Nagl, H. Uberall, “A surface wave interpretation for the resonances of a dielectric sphere,” IEEE Trans. Antennas Propag. AP-28, 924–927 (1980).
[Crossref]

Murphy, J. D.

P. J. Moser, J. D. Murphy, A. Nagl, H. Uberall, “Creeping-wave excitation of the eigenvibrations of dielectric resonators,” J. Wave Motion 3, 283–295 (1981).
[Crossref]

J. D. Murphy, P. J. Moser, A. Nagl, H. Uberall, “A surface wave interpretation for the resonances of a dielectric sphere,” IEEE Trans. Antennas Propag. AP-28, 924–927 (1980).
[Crossref]

Nagl, A.

P. J. Moser, J. D. Murphy, A. Nagl, H. Uberall, “Creeping-wave excitation of the eigenvibrations of dielectric resonators,” J. Wave Motion 3, 283–295 (1981).
[Crossref]

J. D. Murphy, P. J. Moser, A. Nagl, H. Uberall, “A surface wave interpretation for the resonances of a dielectric sphere,” IEEE Trans. Antennas Propag. AP-28, 924–927 (1980).
[Crossref]

Owen, J. F.

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-dependent resonances in Raman scattering, fluroescence emission, and elastic scattering from microparticles,” Areosol Sci. Tech. 1, 293–302 (1982).
[Crossref]

P. W. Barber, J. F. Owen, R. K. Chang, “Resonance scattering for characterization of axisymmetric dielectric objects,” IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[Crossref]

J. F. Owen, P. W. Barber, B. J. Messinger, R. K. Chang, “Determination of optical fiber diameter from resonances in the elastic scattering spectrum,” Opt. Lett. 6, 272–274 (1981).
[Crossref] [PubMed]

J. F. Owen, R. K. Chang, P. W. Barber, “Internal electric field distributions of a dielectric cylinder at resonance wavelengths,” Opt. Lett. 6, 540–542 (1981).
[Crossref] [PubMed]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[Crossref]

Plonus, M. A.

H. Inada, M. A. Plonus, “The diffracted field contribution to the scattering from a large dense dielectric sphere,” IEEE Trans. Antennas Propag. AP-18, 649–660 (1970).
[Crossref]

Rosasco, G. J.

G. J. Rosasco, H. S. Bennett, “Internal field resonance structure: implications for optical absorption and scattering by microscopic particles,” J Opt. Soc. Am. 68, 1242–1250 (1978).
[Crossref]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 565.

Tesche, F. M.

F. M. Tesche, “On the analysis of scattering and antenna problems using the singularity expansion technique,” IEEE Trans. Antennas Propag. AP-21, 53–62 (1973).
[Crossref]

Uberall, H.

P. J. Moser, J. D. Murphy, A. Nagl, H. Uberall, “Creeping-wave excitation of the eigenvibrations of dielectric resonators,” J. Wave Motion 3, 283–295 (1981).
[Crossref]

J. D. Murphy, P. J. Moser, A. Nagl, H. Uberall, “A surface wave interpretation for the resonances of a dielectric sphere,” IEEE Trans. Antennas Propag. AP-28, 924–927 (1980).
[Crossref]

Uretsky, J. L.

F. J. Corbato, J. L. Uretsky, “Generation of spherical Bessel functions in digital computers,” J. Assoc. Comput. Mach. 6, 366–375 (1959).
[Crossref]

Wiscombe, W. J.

Aerosol Sci. Tech. (1)

M. Kerker, “Lorenz–Mie Scattering by spheres: some newly recognized phenomena,” Aerosol Sci. Tech. 1, 275–291 (1982).
[Crossref]

Appl. Opt. (2)

Areosol Sci. Tech. (1)

J. F. Owen, R. K. Chang, P. W. Barber, “Morphology-dependent resonances in Raman scattering, fluroescence emission, and elastic scattering from microparticles,” Areosol Sci. Tech. 1, 293–302 (1982).
[Crossref]

IEEE Trans. Antennas Propag. (4)

P. W. Barber, J. F. Owen, R. K. Chang, “Resonance scattering for characterization of axisymmetric dielectric objects,” IEEE Trans. Antennas Propag. AP-30, 168–172 (1982).
[Crossref]

F. M. Tesche, “On the analysis of scattering and antenna problems using the singularity expansion technique,” IEEE Trans. Antennas Propag. AP-21, 53–62 (1973).
[Crossref]

J. D. Murphy, P. J. Moser, A. Nagl, H. Uberall, “A surface wave interpretation for the resonances of a dielectric sphere,” IEEE Trans. Antennas Propag. AP-28, 924–927 (1980).
[Crossref]

H. Inada, M. A. Plonus, “The diffracted field contribution to the scattering from a large dense dielectric sphere,” IEEE Trans. Antennas Propag. AP-18, 649–660 (1970).
[Crossref]

IEEE Trans. Microwave Theory Tech. (2)

M. Gastine, L. Courtois, J. L. Dormann, “Electromagnetic resonances of free dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-15, 694–700 (1967).
[Crossref]

P. Affolter, B. Eliasson, “Electromagnetic resonances and Q-factors of lossy dielectric spheres,” IEEE Trans. Microwave Theory Tech. MTT-21, 573–578 (1973).
[Crossref]

J Opt. Soc. Am. (1)

G. J. Rosasco, H. S. Bennett, “Internal field resonance structure: implications for optical absorption and scattering by microscopic particles,” J Opt. Soc. Am. 68, 1242–1250 (1978).
[Crossref]

J. Assoc. Comput. Mach. (1)

F. J. Corbato, J. L. Uretsky, “Generation of spherical Bessel functions in digital computers,” J. Assoc. Comput. Mach. 6, 366–375 (1959).
[Crossref]

J. Opt. Soc. Am. (1)

J. Wave Motion (1)

P. J. Moser, J. D. Murphy, A. Nagl, H. Uberall, “Creeping-wave excitation of the eigenvibrations of dielectric resonators,” J. Wave Motion 3, 283–295 (1981).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref]

Phys. Rev. Lett. (2)

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[Crossref]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[Crossref]

SIAM Rev. (1)

W. Gautschi, “Computational aspects of three-term recurrence relations,” SIAM Rev. 9, 24–82 (1967).
[Crossref]

Other (7)

A. C. Hearn, Reduce 2 User’s Manual, 2nd ed. (Department of Computer Science, University of Utah, Salt Lake City, Utah, 1974, unpublished).

R. W. Hamming, Numerical Methods for Scientists and Engineers (McGraw-Hill, New York, 1973), pp. 78–97.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 565.

J. V. Dave, “Subroutines for computing the parameters of the electromagnetic radiation scattered by a sphere,” Report 320-3237, IBM Scientific Center, Palo Alto, California, 1968.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), p. 50.

C. F. Gerald, Applied Numerical Analysis, 2nd ed. (Addison-Wesley, Reading, Mass., 1978), pp. 495–503.

M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematic Functions (U.S. Government Printing Office, Washington, D.C., 1970), p. 435.

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Figures (6)

Fig. 1
Fig. 1

Scattering efficiency versus size parameter for a dielectric sphere.

Fig. 2
Fig. 2

An expanded view of Fig. 1 over a narrow size-parameter range. The n, l subscripts indicate the mode and the order of each resonance, respectively.

Fig. 3
Fig. 3

Pole distribution for the an coefficients of a perfectly conducting sphere, n = 1–10.

Fig. 4
Fig. 4

(a) Pole distribution for the an coefficients of a dielectric sphere with m = 1.4; n = 10 (●), 20 (+), 30 (*), and 40(○). (b) Corresponding bn coefficients.

Fig. 5
Fig. 5

Poles over the size parameter range of Fig. 2.

Fig. 6
Fig. 6

Internal intensity Ē · Ē* at size parameters corresponding to the four high Q poles of Fig. 5.

Tables (1)

Tables Icon

Table 1 Spherical Bessel Functions of the First Kind for Selected Complex Arguments

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

Q s = 2 x 2 n = 1 ( 2 n + 1 ) ( a n 2 + b n 2 ) ,
a n = j n ( x ) [ m x j n ( m x ) ] - m 2 j n ( m x ) [ x j n ( x ) ] h n ( 2 ) ( x ) [ m x j n ( m x ) ] - m 2 j n ( m x ) [ x h n ( 2 ) ( x ) ]
b n = j n ( x ) [ m x j n ( m x ) ] - j n ( m x ) [ x j n ( x ) ] h n ( 2 ) ( x ) [ m x j n ( m x ) ] - j n ( m x ) [ x h n ( 2 ) ( x ) ] ,
i = 1 ( x - x i ) j = 1 ( x - x j ) .
[ i = 1 x - x i j = 1 x - x j ] exp { i [ i θ i - j θ j ] } .
j n - 1 ( z ) = ( 2 n + 1 ) z j n ( z ) - j n + 1 ( z ) .
< z 2 ( ν - N + 1 ) [ ( N + 2 ) ! ( N - 2 ) ! ( ν + 3 ) ! ( ν - 1 ) ! ] .
j n ( z ) y n - 1 ( z ) - j n - 1 ( z ) y n ( z ) = 1 z 2 ,
0 ( 2 n + 1 ) j n 2 ( z ) = 1.
E 0 2 2 × n = 1 ( 2 n + 1 ) { j n 2 ( m 2 π r / λ ) d n 2 + 1 2 n + 1 [ ( n + 1 ) j n - 1 2 ( m 2 π r / λ ) + n j n + 1 2 ( m 2 π r / λ ) ] c n 2 } .
c n = ( m i x ) h n ( 2 ) ( x ) [ m x j n ( m x ) ] - m 2 j n ( m x ) [ x h n ( 2 ) ( x ) ]
d n = ( i x ) h n ( 2 ) ( x ) [ m x j n ( m x ) ] - j n ( m x ) [ x h n ( 2 ) ( x ) ] ,

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