Abstract

A volume current method (VCM) for calculating the optical scattering by inhomogeneous spheres is presented. The method is applicable to spheres having small refractive-index perturbations. In this method the internal and scattered fields are approximated with a separation-of-variables solution, in which each mode has its own effective-average refractive index. These fields generate an additional volume polarization current in the regions where the refractive index differs from the average refractive index of the sphere. The fields radiated by these polarization currents are then added to the approximate fields radiated by the unperturbed sphere. When they are tested with off-centered layered spheres, the fields calculated with the VCM compare well with those found with separation of variables so long as the changes in the refractive index are small. When the host sphere is near resonance and the perturbation is in a region where the resonant fields are large, the perturbations must be smaller than when the sphere is off resonance.

© 1995 Optical Society of America

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  1. R. Kneer, M. Schneider, B. Noll, S. Wittig, “Diffusion controlled evaporation of a multicomponent droplet: theoretical studies of the importance of variable liquid properties,” Int. J. Heat Mass Transfer 36, 2403–2415 (1993).
    [Crossref]
  2. H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, P. Chylek, “Internal scattering effects on microdroplet resonant emission structure,” Opt. Lett. 17, 970–972 (1992).
    [Crossref] [PubMed]
  3. B. V. Bronk, M. J. Smith, S. Arnold, “Photon-correlation spectroscopy for small spherical inclusions in a micrometer-sized electrodynamically levitated droplet,” Opt. Lett. 18, 93–95 (1993).
    [Crossref] [PubMed]
  4. D. Ngo, R. G. Pinnick, “Suppression of scattering resonances in inhomogeneous microdroplets,” J. Opt. Soc. Am. A 11, 1352–1359 (1994).
    [Crossref]
  5. Information about the effect of bubble formation on microdroplet cavities may be obtained from A. J. Campillo, U.S. Naval Research Laboratory, Laser Physics Branch, 4555 Overlook Ave., S.W., Washington, D.C. 20375.
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  7. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  8. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  9. D. S. Wang, P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190–1197 (1979).
    [Crossref] [PubMed]
  10. F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327–1335 (1992).
    [Crossref]
  11. K. A. Fuller, “Scattering and absorption by inhomogeneous spheres and sphere aggregates,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1862, 249–257 (1993).
    [Crossref]
  12. F. Borghese, P. Denti, R. Saija, O. I. Sindoni, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt. 33, 484–491 (1994).
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  13. P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962);erratum, Phys. Rev. 134,AB1 (1964).
    [Crossref]
  14. D. Q. Chowdhury, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in radially inhomogeneous spheres,” J. Opt. Soc. Am. A 8, 1702–1705 (1991).
    [Crossref]
  15. M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets evaporating in a high-temperature environment,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1862, 269–286 (1993).
    [Crossref]
  16. M. Kerker, D. D. Cooke, H. Chew, P. J. McNulty, “Light scattering by structured spheres,” J. Opt. Soc. Am. 68, 592–601 (1978).
    [Crossref]
  17. M. Kerker, H. Chew, P. J. McNulty, J. P. Kratohvil, D. D. Cooke, M. Sculley, M.-P. Lee, “Light scattering and fluorescence by small particles having internal structure,” J. Histochem. Cytochem. 27, 250–263 (1979).
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  18. P. Latimer, “Light scattering by a structured particle: the homogeneous sphere with holes,” Appl. Opt. 23, 1844–1847 (1984).
    [Crossref]
  19. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation method for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
    [Crossref] [PubMed]
  20. M. M. Mazumder, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in inhomogeneous spheres: comparison of layered T-matrix and time-independent perturbation method,” J. Opt. Soc. Am. A 9, 1844–1853 (1992).
    [Crossref]
  21. D. Q. Chowdhury, S. C. Hill, M. M. Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption,” IEEE J. Quantum Electron. 29, 2553–2561 (1993).
    [Crossref]
  22. C. Yeh, “Perturbation method in the diffraction of electromagnetic waves by arbitrarily shaped penetrable obstacles,” J. Math. Phys. 6, 2008–2013 (1965).
    [Crossref]
  23. J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation approach to light scattering by non-spherical particles,” in Light Scattering by Irregularly Shaped Particles, D. Schuerman, ed. (Plenum, New York, 1980).
    [Crossref]
  24. H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
    [Crossref]
  25. C. C. Lam, “Wave scattering by slightly deformed spheres,” M.S. thesis (Chinese University of Hong Kong, Hong Kong, 1991).
  26. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [Crossref]
  27. M. Kuznetsov, H. A. Haus, “Radiation loss in dielectric waveguide structures by the volume current method,” IEEE J. Quantum Electron. QE-19, 1505–1514 (1983).
    [Crossref]
  28. A. W. Snyder, “Radiation losses due to variations of radius on dielectric or optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-18, 608–615 (1970).
    [Crossref]
  29. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), Chap. 7.
  30. H. I. Saleheen, “Light scattering by inhomogeneous spheres,” M.S. thesis (New Mexico State University, Las Cruces, N.M., 1993).
  31. K. A. Fuller, “Scattering of light by coated spheres,” Opt. Lett. 18, 257–259 (1993).
    [Crossref] [PubMed]
  32. H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
    [Crossref]
  33. W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990), Chap. 7.
  34. E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
    [Crossref]
  35. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 2, pp. 1874–1875.
  36. H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
    [Crossref] [PubMed]
  37. The dyadic Green’s function is derived in Refs. 32 and 35.We use the mks units of Chew33but use the vector spherical harmonics as defined in J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941) and Ref. 8.In obtaining Eq. (1) from Chew, we have used J = −iωP.
  38. K. A. Fuller, “Resonant scattering by spheres with eccentric inclusions,” Opt. Lett. 19, 1272–1275 (1994).
    [Crossref] [PubMed]
  39. R. L. Armstrong, J.-G. Xie, T. E. Ruekgauer, J. Gu, R. G. Pinnick, “Effects of submicrometer-sized particles on microdroplet lasing,” Opt. Lett. 18, 119–121 (1993).
    [Crossref] [PubMed]
  40. The perturbation method was also tested with the following simple case. The refractive index m1 of the large sphere was set to 1.0, the position of the spherical inclusion was varied, and the calculated scattering intensity patterns were compared with those for a sphere having a size in the Rayleigh range.
  41. K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
    [Crossref] [PubMed]

1994 (3)

1993 (6)

R. L. Armstrong, J.-G. Xie, T. E. Ruekgauer, J. Gu, R. G. Pinnick, “Effects of submicrometer-sized particles on microdroplet lasing,” Opt. Lett. 18, 119–121 (1993).
[Crossref] [PubMed]

K. A. Fuller, “Scattering of light by coated spheres,” Opt. Lett. 18, 257–259 (1993).
[Crossref] [PubMed]

E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
[Crossref]

B. V. Bronk, M. J. Smith, S. Arnold, “Photon-correlation spectroscopy for small spherical inclusions in a micrometer-sized electrodynamically levitated droplet,” Opt. Lett. 18, 93–95 (1993).
[Crossref] [PubMed]

R. Kneer, M. Schneider, B. Noll, S. Wittig, “Diffusion controlled evaporation of a multicomponent droplet: theoretical studies of the importance of variable liquid properties,” Int. J. Heat Mass Transfer 36, 2403–2415 (1993).
[Crossref]

D. Q. Chowdhury, S. C. Hill, M. M. Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption,” IEEE J. Quantum Electron. 29, 2553–2561 (1993).
[Crossref]

1992 (3)

1991 (3)

1990 (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation method for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

1988 (2)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[Crossref] [PubMed]

1984 (1)

1983 (1)

M. Kuznetsov, H. A. Haus, “Radiation loss in dielectric waveguide structures by the volume current method,” IEEE J. Quantum Electron. QE-19, 1505–1514 (1983).
[Crossref]

1979 (2)

M. Kerker, H. Chew, P. J. McNulty, J. P. Kratohvil, D. D. Cooke, M. Sculley, M.-P. Lee, “Light scattering and fluorescence by small particles having internal structure,” J. Histochem. Cytochem. 27, 250–263 (1979).
[Crossref] [PubMed]

D. S. Wang, P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190–1197 (1979).
[Crossref] [PubMed]

1978 (1)

1976 (1)

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[Crossref]

1970 (1)

A. W. Snyder, “Radiation losses due to variations of radius on dielectric or optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-18, 608–615 (1970).
[Crossref]

1965 (1)

C. Yeh, “Perturbation method in the diffraction of electromagnetic waves by arbitrarily shaped penetrable obstacles,” J. Math. Phys. 6, 2008–2013 (1965).
[Crossref]

1962 (1)

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962);erratum, Phys. Rev. 134,AB1 (1964).
[Crossref]

Armstrong, R. L.

Arnold, S.

Barber, P. W.

E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
[Crossref]

M. M. Mazumder, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in inhomogeneous spheres: comparison of layered T-matrix and time-independent perturbation method,” J. Opt. Soc. Am. A 9, 1844–1853 (1992).
[Crossref]

D. Q. Chowdhury, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in radially inhomogeneous spheres,” J. Opt. Soc. Am. A 8, 1702–1705 (1991).
[Crossref]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation method for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

D. S. Wang, P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190–1197 (1979).
[Crossref] [PubMed]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Borghese, F.

Bronk, B. V.

Campillo, A. J.

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, P. Chylek, “Internal scattering effects on microdroplet resonant emission structure,” Opt. Lett. 17, 970–972 (1992).
[Crossref] [PubMed]

Information about the effect of bubble formation on microdroplet cavities may be obtained from A. J. Campillo, U.S. Naval Research Laboratory, Laser Physics Branch, 4555 Overlook Ave., S.W., Washington, D.C. 20375.

Chew, H.

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
[Crossref] [PubMed]

M. Kerker, H. Chew, P. J. McNulty, J. P. Kratohvil, D. D. Cooke, M. Sculley, M.-P. Lee, “Light scattering and fluorescence by small particles having internal structure,” J. Histochem. Cytochem. 27, 250–263 (1979).
[Crossref] [PubMed]

M. Kerker, D. D. Cooke, H. Chew, P. J. McNulty, “Light scattering by structured spheres,” J. Opt. Soc. Am. 68, 592–601 (1978).
[Crossref]

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[Crossref]

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990), Chap. 7.

Chowdhury, D. Q.

D. Q. Chowdhury, S. C. Hill, M. M. Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption,” IEEE J. Quantum Electron. 29, 2553–2561 (1993).
[Crossref]

D. Q. Chowdhury, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in radially inhomogeneous spheres,” J. Opt. Soc. Am. A 8, 1702–1705 (1991).
[Crossref]

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets evaporating in a high-temperature environment,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1862, 269–286 (1993).
[Crossref]

Chylek, P.

H.-B. Lin, A. L. Huston, J. D. Eversole, A. J. Campillo, P. Chylek, “Internal scattering effects on microdroplet resonant emission structure,” Opt. Lett. 17, 970–972 (1992).
[Crossref] [PubMed]

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation approach to light scattering by non-spherical particles,” in Light Scattering by Irregularly Shaped Particles, D. Schuerman, ed. (Plenum, New York, 1980).
[Crossref]

Cooke, D. D.

M. Kerker, H. Chew, P. J. McNulty, J. P. Kratohvil, D. D. Cooke, M. Sculley, M.-P. Lee, “Light scattering and fluorescence by small particles having internal structure,” J. Histochem. Cytochem. 27, 250–263 (1979).
[Crossref] [PubMed]

M. Kerker, D. D. Cooke, H. Chew, P. J. McNulty, “Light scattering by structured spheres,” J. Opt. Soc. Am. 68, 592–601 (1978).
[Crossref]

Denti, P.

Draine, B. T.

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

Eversole, J. D.

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 2, pp. 1874–1875.

Fuller, K. A.

Gu, J.

Haus, H. A.

M. Kuznetsov, H. A. Haus, “Radiation loss in dielectric waveguide structures by the volume current method,” IEEE J. Quantum Electron. QE-19, 1505–1514 (1983).
[Crossref]

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), Chap. 7.

Hill, S. C.

E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
[Crossref]

D. Q. Chowdhury, S. C. Hill, M. M. Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption,” IEEE J. Quantum Electron. 29, 2553–2561 (1993).
[Crossref]

M. M. Mazumder, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in inhomogeneous spheres: comparison of layered T-matrix and time-independent perturbation method,” J. Opt. Soc. Am. A 9, 1844–1853 (1992).
[Crossref]

D. Q. Chowdhury, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in radially inhomogeneous spheres,” J. Opt. Soc. Am. A 8, 1702–1705 (1991).
[Crossref]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation method for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets evaporating in a high-temperature environment,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1862, 269–286 (1993).
[Crossref]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

Hirleman, E. D.

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets evaporating in a high-temperature environment,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1862, 269–286 (1993).
[Crossref]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Huston, A. L.

Kerker, M.

M. Kerker, H. Chew, P. J. McNulty, J. P. Kratohvil, D. D. Cooke, M. Sculley, M.-P. Lee, “Light scattering and fluorescence by small particles having internal structure,” J. Histochem. Cytochem. 27, 250–263 (1979).
[Crossref] [PubMed]

M. Kerker, D. D. Cooke, H. Chew, P. J. McNulty, “Light scattering by structured spheres,” J. Opt. Soc. Am. 68, 592–601 (1978).
[Crossref]

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[Crossref]

Khaled, E. E. M.

E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
[Crossref]

Kiehl, J. T.

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation approach to light scattering by non-spherical particles,” in Light Scattering by Irregularly Shaped Particles, D. Schuerman, ed. (Plenum, New York, 1980).
[Crossref]

Kneer, R.

R. Kneer, M. Schneider, B. Noll, S. Wittig, “Diffusion controlled evaporation of a multicomponent droplet: theoretical studies of the importance of variable liquid properties,” Int. J. Heat Mass Transfer 36, 2403–2415 (1993).
[Crossref]

Ko, M. W.

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation approach to light scattering by non-spherical particles,” in Light Scattering by Irregularly Shaped Particles, D. Schuerman, ed. (Plenum, New York, 1980).
[Crossref]

Kratohvil, J. P.

M. Kerker, H. Chew, P. J. McNulty, J. P. Kratohvil, D. D. Cooke, M. Sculley, M.-P. Lee, “Light scattering and fluorescence by small particles having internal structure,” J. Histochem. Cytochem. 27, 250–263 (1979).
[Crossref] [PubMed]

Kuznetsov, M.

M. Kuznetsov, H. A. Haus, “Radiation loss in dielectric waveguide structures by the volume current method,” IEEE J. Quantum Electron. QE-19, 1505–1514 (1983).
[Crossref]

Lai, H. M.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[Crossref]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation method for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Lam, C. C.

Latimer, P.

Lee, M.-P.

M. Kerker, H. Chew, P. J. McNulty, J. P. Kratohvil, D. D. Cooke, M. Sculley, M.-P. Lee, “Light scattering and fluorescence by small particles having internal structure,” J. Histochem. Cytochem. 27, 250–263 (1979).
[Crossref] [PubMed]

Leung, P. T.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[Crossref]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation method for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Lin, H.-B.

Mazumder, M. M.

D. Q. Chowdhury, S. C. Hill, M. M. Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption,” IEEE J. Quantum Electron. 29, 2553–2561 (1993).
[Crossref]

M. M. Mazumder, S. C. Hill, P. W. Barber, “Morphology-dependent resonances in inhomogeneous spheres: comparison of layered T-matrix and time-independent perturbation method,” J. Opt. Soc. Am. A 9, 1844–1853 (1992).
[Crossref]

McNulty, P. J.

M. Kerker, H. Chew, P. J. McNulty, J. P. Kratohvil, D. D. Cooke, M. Sculley, M.-P. Lee, “Light scattering and fluorescence by small particles having internal structure,” J. Histochem. Cytochem. 27, 250–263 (1979).
[Crossref] [PubMed]

M. Kerker, D. D. Cooke, H. Chew, P. J. McNulty, “Light scattering by structured spheres,” J. Opt. Soc. Am. 68, 592–601 (1978).
[Crossref]

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[Crossref]

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 2, pp. 1874–1875.

Mugnai, A.

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation approach to light scattering by non-spherical particles,” in Light Scattering by Irregularly Shaped Particles, D. Schuerman, ed. (Plenum, New York, 1980).
[Crossref]

Ngo, D.

Noll, B.

R. Kneer, M. Schneider, B. Noll, S. Wittig, “Diffusion controlled evaporation of a multicomponent droplet: theoretical studies of the importance of variable liquid properties,” Int. J. Heat Mass Transfer 36, 2403–2415 (1993).
[Crossref]

Pinnick, R. G.

Ruekgauer, T. E.

Saija, R.

Saleheen, H. I.

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets evaporating in a high-temperature environment,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1862, 269–286 (1993).
[Crossref]

H. I. Saleheen, “Light scattering by inhomogeneous spheres,” M.S. thesis (New Mexico State University, Las Cruces, N.M., 1993).

Schneider, M.

R. Kneer, M. Schneider, B. Noll, S. Wittig, “Diffusion controlled evaporation of a multicomponent droplet: theoretical studies of the importance of variable liquid properties,” Int. J. Heat Mass Transfer 36, 2403–2415 (1993).
[Crossref]

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets evaporating in a high-temperature environment,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1862, 269–286 (1993).
[Crossref]

Sculley, M.

M. Kerker, H. Chew, P. J. McNulty, J. P. Kratohvil, D. D. Cooke, M. Sculley, M.-P. Lee, “Light scattering and fluorescence by small particles having internal structure,” J. Histochem. Cytochem. 27, 250–263 (1979).
[Crossref] [PubMed]

Sindoni, O. I.

Smith, M. J.

Snyder, A. W.

A. W. Snyder, “Radiation losses due to variations of radius on dielectric or optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-18, 608–615 (1970).
[Crossref]

Stratton, J. A.

The dyadic Green’s function is derived in Refs. 32 and 35.We use the mks units of Chew33but use the vector spherical harmonics as defined in J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941) and Ref. 8.In obtaining Eq. (1) from Chew, we have used J = −iωP.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Wang, D. S.

Wittig, S.

R. Kneer, M. Schneider, B. Noll, S. Wittig, “Diffusion controlled evaporation of a multicomponent droplet: theoretical studies of the importance of variable liquid properties,” Int. J. Heat Mass Transfer 36, 2403–2415 (1993).
[Crossref]

Wyatt, P. J.

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962);erratum, Phys. Rev. 134,AB1 (1964).
[Crossref]

Xie, J.-G.

Yeh, C.

C. Yeh, “Perturbation method in the diffraction of electromagnetic waves by arbitrarily shaped penetrable obstacles,” J. Math. Phys. 6, 2008–2013 (1965).
[Crossref]

Young, K.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “Effect of perturbations on the widths of narrow morphology dependent resonances in Mie scattering,” J. Opt. Soc. Am. B 8, 1962–1973 (1991).
[Crossref]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation method for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

Appl. Opt. (4)

Astrophys. J. (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[Crossref]

IEEE J. Quantum Electron. (2)

M. Kuznetsov, H. A. Haus, “Radiation loss in dielectric waveguide structures by the volume current method,” IEEE J. Quantum Electron. QE-19, 1505–1514 (1983).
[Crossref]

D. Q. Chowdhury, S. C. Hill, M. M. Mazumder, “Quality factors and effective-average modal gain or loss in inhomogeneous spherical resonators: application to two-photon absorption,” IEEE J. Quantum Electron. 29, 2553–2561 (1993).
[Crossref]

IEEE Trans. Antennas Propag. (1)

E. E. M. Khaled, S. C. Hill, P. W. Barber, “Scattered and internal intensity of a sphere illuminated with a Gaussian beam,” IEEE Trans. Antennas Propag. 41, 295–303 (1993).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

A. W. Snyder, “Radiation losses due to variations of radius on dielectric or optical fibers,” IEEE Trans. Microwave Theory Tech. MTT-18, 608–615 (1970).
[Crossref]

Int. J. Heat Mass Transfer (1)

R. Kneer, M. Schneider, B. Noll, S. Wittig, “Diffusion controlled evaporation of a multicomponent droplet: theoretical studies of the importance of variable liquid properties,” Int. J. Heat Mass Transfer 36, 2403–2415 (1993).
[Crossref]

J. Histochem. Cytochem. (1)

M. Kerker, H. Chew, P. J. McNulty, J. P. Kratohvil, D. D. Cooke, M. Sculley, M.-P. Lee, “Light scattering and fluorescence by small particles having internal structure,” J. Histochem. Cytochem. 27, 250–263 (1979).
[Crossref] [PubMed]

J. Math. Phys. (1)

C. Yeh, “Perturbation method in the diffraction of electromagnetic waves by arbitrarily shaped penetrable obstacles,” J. Math. Phys. 6, 2008–2013 (1965).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (1)

Opt. Lett. (5)

Phys. Rev. (1)

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962);erratum, Phys. Rev. 134,AB1 (1964).
[Crossref]

Phys. Rev. A (3)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation method for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref]

Other (14)

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, New York, 1990), Chap. 7.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 2, pp. 1874–1875.

The dyadic Green’s function is derived in Refs. 32 and 35.We use the mks units of Chew33but use the vector spherical harmonics as defined in J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941) and Ref. 8.In obtaining Eq. (1) from Chew, we have used J = −iωP.

The perturbation method was also tested with the following simple case. The refractive index m1 of the large sphere was set to 1.0, the position of the spherical inclusion was varied, and the calculated scattering intensity patterns were compared with those for a sphere having a size in the Rayleigh range.

C. C. Lam, “Wave scattering by slightly deformed spheres,” M.S. thesis (Chinese University of Hong Kong, Hong Kong, 1991).

J. T. Kiehl, M. W. Ko, A. Mugnai, P. Chylek, “Perturbation approach to light scattering by non-spherical particles,” in Light Scattering by Irregularly Shaped Particles, D. Schuerman, ed. (Plenum, New York, 1980).
[Crossref]

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), Chap. 7.

H. I. Saleheen, “Light scattering by inhomogeneous spheres,” M.S. thesis (New Mexico State University, Las Cruces, N.M., 1993).

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets evaporating in a high-temperature environment,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1862, 269–286 (1993).
[Crossref]

K. A. Fuller, “Scattering and absorption by inhomogeneous spheres and sphere aggregates,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1862, 249–257 (1993).
[Crossref]

Information about the effect of bubble formation on microdroplet cavities may be obtained from A. J. Campillo, U.S. Naval Research Laboratory, Laser Physics Branch, 4555 Overlook Ave., S.W., Washington, D.C. 20375.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).

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Figures (14)

Fig. 1
Fig. 1

Scattering of an incident electric field Es by a perturbed sphere. The perturbation need not consist of homogeneous layered regions, and the perturbed sphere need not be axisymmetric.

Fig. 2
Fig. 2

Geometry for scattering by a sphere that contains an arbitrarily positioned sphere. The angle α is the zenith angle to the center of the inclusion.

Fig. 3
Fig. 3

Scattering intensity at 90° as a function of the angle of the inclusion, α. The refractive indices of the host sphere and the inclusion are m1 = 1.34 and m2r = 1.36, respectively. The diameter of the host sphere is 2a1 = 0.3275 μm. The inclusion is centered at a radial position ri/a1 = 0.7 and has a diameter 2a2 = 0.08188 μm.

Fig. 4
Fig. 4

Scattering intensity at 90° as a function of the angle of the inclusion, α. The refractive indices of the host sphere and the inclusion are m1 = 1.34 and m2r = 1.36, respectively. The diameter of the host sphere is 2a1 = 0.3275 μm. The inclusion is centered at a radial position ri/a1 = 0.6 and has a diameter 2a2 = 0.131 μm.

Fig. 5
Fig. 5

Scattering intensity as a function of the scattering angle for different angles of the inclusion, a = 0°, 90°, and 180°. Intensities computed with the VCM are shown as solid curves. The refractive indices of the host sphere and the inclusion are m1 = 1.34 and m2r = 1.5, respectively. The diameter of the host sphere is 2a1 = 0.4913 μm. The inclusion is centered at a radial position ri/a1 = 0.6667 and has a diameter 2a2 = 0.1637 μm.

Fig. 6
Fig. 6

Scattering intensity at 90° as a function of the angle of the inclusion, α. The refractive indices of the host sphere and the inclusion are m1 = 1.4746 and m2r = 1.592, respectively. The diameter of the host sphere is 2a1 = 6.36434 μm. The inclusion is centered at a radial position ri/a1 = 0.835. The diameter of the inclusion is 2a2 = 0.064 μm. The size parameter of the host sphere is 38.86135, which is off resonance.

Fig. 7
Fig. 7

Scattering intensity at 90° as a function of the angle of the inclusion, α. The refractive indices of the host sphere and the included sphere are m1 = 1.4746 and m2r = 1.592, respectively. The diameter of the host sphere is 2a1 = 6.36434 μm. The inclusion is centered at a radial position ri/a1 = 0.835. The diameter of the inclusion is 2a2 = 0.14 μm. The size parameter of the host sphere is 38.86135, which is off resonance.

Fig. 8
Fig. 8

Scattering intensity at 90° as a function of the angle of the inclusion, α, with different numbers of points used in integration in the VCM. The refractive indices of the host sphere and the inclusion are m1 = 1.4746 and m2r = 1.592, respectively. The diameters of the host and the inclusion are 2a1 = 6.36434 μm and 2a2 = 0.12 μm respectively. The inclusion is centered at a radial position ri/a1 = 0.835.

Fig. 9
Fig. 9

Internal intensity and scattered intensity at 90° plotted as a function of position through the center of the sphere. The refractive indices of the host sphere and the inclusion are m1 = 1.4746 and m2r = 1.592, respectively. The diameters of the host and the inclusion are 2a1 = 6.36434 μm and 2a2 = 0.14 μm, respectively. The inclusion is centered at a radial position ri/a1 = 0.835.

Fig. 10
Fig. 10

Scattering intensity at 90° as a function of the angle of the inclusion, α, calculated with the approximate method, the approximate method using the Rayleigh approximation for the fields inside the inclusion, and the SV method. The refractive indices of the host sphere and the inclusion are m1 = 1.4746 and m2r = 2.5, respectively. The diameters of the host and the inclusion are 2a1 = 6.36434 μm and 2a2 = 0.064 μm, respectively. The inclusion is centered at a radial position ri/a1 = 0.835.

Fig. 11
Fig. 11

Scattered intensity at 90° as a function of the angle of the inclusion, α, when the included sphere has an imaginary component of refractive index. The refractive indices of the host sphere and the inclusion are m1 = 1.4746 and m2r = 1.592 + i0.01, respectively. The diameters of the host and the inclusion are 2a1 = 6.36434 μm and 2a2 = 0.08 μm, respectively. The inclusion is centered at a radial position ri/a1 = 0.75.

Fig. 12
Fig. 12

Scattered intensity at 90° as a function of the size parameter of the host. The inclusion is at α = 0° and is centered at ri/a = 0.835. The refractive indices of the host sphere and the inclusion are m1 = 1.4746 and m2r = 1.592, respectively. The diameter of the inclusion is 2a2 = 0.064 μm.

Fig. 13
Fig. 13

Scattered intensity at 90° as a function of the angle of inclusion, α, when the host is on or near resonance. The inclusion is centered at ri/a1 = 0.80. The refractive indices of the host sphere and the inclusion are m1 = 1.4746 and m2r = 1.5, respectively. The diameters of the host and the inclusion are 2a1 = 6.37635 μm. and 2a2 = 0.06 μm, respectively.

Fig. 14
Fig. 14

Scattered intensities as a function of scattering angle θ. The host contains 400 randomly positioned spherical inclusions. Results for two orientations of the inclusions are shown, as is the result for the homogeneous sphere. The refractive indices of the host sphere and the inclusions are m1 = 1.4746 and m2 = 1.592, respectively. The diameters of the host and the inclusions are 2a1 = 4.0 μm and 2a2 = 0.14 μm, respectively.

Tables (1)

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Table 1 Parameters Used in the Figures

Equations (30)

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J ( r ) = i ω P ( r ) = i ω 0 [ m 2 ( r ) m avg 2 ] E int ( r ) ,
E ( k r ) = ω 2 μ G ( r , r ) · P ( r ) d υ ,
G ( r , r ) = i m k π n = 1 m = 0 n D m , n σ = e , o [ M ν 3 ( m k r ) M ν 1 ( m k r ) + N ν 3 ( m k r ) N ν 1 ( m k r ) ] ,
D m n = m ( 2 n + 1 ) ( n m ) ! 4 n ( n + 1 ) ( n + m ) ! ,
E H ( m k r ) = ν = 1 D ν [ c ν H ( r < r ) M ν 3 ( m k r ) + d ν H ( r < r ) N ν 3 ( m k r ) + c ν H ( r > r ) M ν 1 ( m k r ) + d ν H ( r > r ) N ν 1 ( m k r ) ] ,
c ν H ( r < r ) = ( i k m / π ) ω 2 μ V P ( r ) · M ν 1 ( m k r ) d υ ,
d ν H ( r < r ) = ( i k m / π ) ω 2 μ V P ( r ) · N ν 1 ( m k r ) d υ ,
E i G ( m k r ) = E 0 ν = 1 [ c ν i G M ν 1 ( m k r ) + d ν i G N ν 1 ( m k r ) ] ,
E T ( m k r ) = E H ( m k r ) + E i G ( m k r ) ,
E s G ( k r ) = E 0 ν = 1 D ν [ f ν G M ν 3 ( k r ) + g ν G N ν 3 ( k r ) ] ,
c ν i G = c ν H D ν h n ( 1 ) ( m x ) [ x h n ( 1 ) ( x ) ] [ m x h n ( 1 ) ( m x ) ] h n ( 1 ) ( x ) j n ( m x ) [ x h n ( 1 ) ( x ) ] [ m x j n ( m x ) ] h n ( 1 ) ( x ) ,
d ν i G = d ν H D ν m 2 h n ( 1 ) ( m x ) [ x h n ( 1 ) ( x ) ] [ m x h n ( 1 ) ( m x ) ] h n ( 1 ) ( x ) m 2 j n ( m x ) [ x h n ( 1 ) ( x ) ] [ m x j n ( m x ) ] h n ( 1 ) ( x ) ,
f ν G = c ν H i / m x j n ( m x ) [ x h n ( 1 ) ( x ) ] [ m x j n ( m x ) ] h n ( 1 ) ( x ) ,
g ν G = d ν H i / x m 2 j n ( m x ) [ x h n ( 1 ) ( x ) ] [ m x j n ( m x ) ] h n ( 1 ) ( x ) ,
m ν = V s ½ m ( r ) r ( r ) | E ν int ( r ) | 2 d υ V s ½ r ( r ) | E ν int ( r ) | 2 d υ ,
c ν H = ( i k 3 m π ) V [ m 2 ( r ) m avg 2 ] E int ( r ) · M ν 1 ( m k r ) d υ ,
d ν H = ( i k 3 m π ) V [ m 2 ( r ) m avg 2 ] E int ( r ) · N ν 1 ( m k r ) d υ ,
f ν = f ν host + f ν G ,
g ν = g ν host + g ν G ,
1 x 2 ν = 1 D ν ( | f ν | 2 + | g ν | 2 ) .
| f ν | 2 = | f ν host | 2 + | f ν G | 2 + 2 Re [ f ν host ( f ν G ) * ] .
I ( z ) = I 0 exp ( b ext z ) ,
b ext = N η ext π a 2 2 ,
I ( z ) = I 0 exp [ ( 4 π m 1 i / λ ) z ] .
m 1 i = N η ext λ a 2 2 / 4 .
N ν = V s ½ N ( r ) r ( r ) | E ν ( r ) | 2 d υ V s ½ r ( r ) | E ν ( r ) | 2 d υ .
N ( r ) = 1 ( 4 π / 3 ) a 2 3 .
N ν = 1 ( 4 π / 3 ) a 2 3 i V i | E ν ( r ) | 2 d υ V s | E ν ( r ) | 2 d υ .
E incl ( r ) E ( r ) 3 m rel 2 + 2 .
P ( r ) 0 ( m 2 2 m avg 2 ) 3 m rel 2 + 2 E ( r ) .

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