Abstract

We show that the far fields generated by a source inside or near a microparticle can be obtained readily by using the reciprocity theorem along with the internal or near fields generated by plane-wave illumination. This method is useful for solving problems for which the scattered fields generated with plane-wave illumination have already been obtained. We illustrate the method for the case of a homogeneous sphere and then apply it to the problem of emission from a dipole inside a sphere that is near a plane interface.

© 1997 Optical Society of America

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  1. R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observations of structure resonances in the fluorescence emission frommicrospheres,” Phys. Rev. Lett. 44, 475–478 (1980).
    [CrossRef]
  2. M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
    [CrossRef] [PubMed]
  3. S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Collection of fluorescence from single molecules inside of droplets:effects of position, orientation and frequency,” Appl. Opt. 35, 6278–6288 (1996).
    [CrossRef] [PubMed]
  4. M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, andS. Arnold, “Molecular fluorescence in a microcavity: solvation dynamicsand single molecule detection,” in Optical Processesin Microcavities, R. K. Chang and A. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 135–165.
  5. R. Thurn and W. Kiefer, “Structural resonances observed in the Raman spectra of optically levitatedliquid droplets,” Appl. Opt. 24, 1515–1519 (1985).
    [CrossRef]
  6. M. F. Buehler, T. M. Allen, and E. J. Davis, “Microparticle Raman spectroscopy of multicomponent aerosols,” J. Colloid Interface Sci. 146, 79–89 (1991).
    [CrossRef]
  7. H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, “Laser emission from individual droplets at wavelengths correspondingto morphology-dependent resonances,” Opt. Lett. 9, 499–501 (1984).
    [CrossRef] [PubMed]
  8. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
    [CrossRef]
  9. H.-B. Lin, J. D. Eversole, and A. J. Campillo, “Spectral properties of lasing microdroplets,” J. Opt. Soc. Am. B 9, 43–50 (1992).
    [CrossRef]
  10. J. L. Cheung, J. M. Hartings, and R. K. Chang, “Nonlinearoptics of microdroplets illuminated by picosecond laser pulses,” in Handbook of Optical Properties, Vol. 2 of Optics of SmallParticles, Interfaces, and Surfaces, R. E. Hummel and P. Wissman, eds. (CRCPress, Boca Raton, Fla, 1997), pp. 233–260.
  11. A. J. Campillo, J. D. Eversole, and H. B. Lin, “CavityQED modified stimulated and spontaneous processes in microdroplets,”in Optical Processes in Microcavities, R. K. Chang andA. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 167–207.
  12. H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded insmall particles,” Phys. Rev. A 13, 396–404 (1976).
    [CrossRef]
  13. Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a sphericalsurface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
    [CrossRef]
  14. W. C. Chew, Waves and Fields in InhomogeneousMedia (Van Nostrand Reinhold, New York, 1995), Chap. 7.
  15. P. W. Barber and S. C. Hill, Light Scatteringby Particles: Computational Methods (World Scientific, Singapore, 1990).
  16. T. E. Ruekgauer, P. Nachman, R. L. Armstrong, and J.-G. Xie, “A nonlinear outcoupling mechanism in a cylindrical dielectric microcavitysupporting stimulated Raman scattering,” Opt. Lett. 20, 2090–2092 (1995).
    [CrossRef] [PubMed]
  17. M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, and S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a hightemperature environment,” in Proceedings of the Conferenceon Laser Applications in Combustion and Combustion Diagnostics, SPIE 1862, 269–286 (1993).
    [CrossRef]
  18. G. Chen, P. Nachman, R. G. Pinnick, S. C. Hill, and R. K. Chang, “Conditional-firing aerosol-fluorescence spectrum analyzer for individualairborne particles with pulsed 266-nm laser excitation,” Opt. Lett. 21, 1307–1309 (1996). Some of the particles studied were composed of several-to-many rod-shapedbacterial cells.
    [CrossRef] [PubMed]
  19. S. C. Hill, R. E. Benner, P. R. Conwell, and C. K. Rushforth, “Structural resonances observed in the fluorescence emission from smallparticles on substrates,” Appl. Opt. 23, 1680–1683 (1984).
    [CrossRef]
  20. S. C. Hill, C. K. Rushforth, R. E. Benner, and P. R. Conwell, “Sizing dielectric spheres and cylinders by aligning structural resonancelocations: algorithm for multiple orders,” Appl. Opt. 24, 2380–2390 (1985).
    [CrossRef] [PubMed]
  21. P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–241 (1986).
    [CrossRef]
  22. B. R. Johnson, “Light-scattering from a spherical particle on a conducting plane: 1.Normal incidence,” J. Opt. Soc. Am. A 9, 1341–1351 (1992); erratum, 10, 766 (1993).
    [CrossRef]
  23. G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991); erratum, 9, 844–845 (1992).
    [CrossRef]
  24. B. R. Johnson, “Morphology-dependent resonances of a dielectric sphere on a conductingplane,” J. Opt. Soc. Am. A 11, 2055–2064 (1994).
    [CrossRef]
  25. B. R. Johnson, “Calculation of light scattering from a spherical particle on a surfaceby the multipole expansion method,” J. Opt. Soc. Am. A 13, 326–337 (1996).
    [CrossRef]
  26. G. Videen, “Light scattering from a particle on or near a perfectly conductingsurface,” Opt. Commun. 115, 1–7 (1995).
    [CrossRef]
  27. T. C. Rao and R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried ina ground plane. I. TM case,” J. Opt. Soc. Am. A 6, 1270–1280 (1989).
    [CrossRef]
  28. T. C. Rao and R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried ina ground plane. II. TE case,” J. Opt. Soc. Am. A 8, 1986–1990 (1991).
    [CrossRef]
  29. J. C. Bertrand and J. W. Young, “Multiple scattering between a cylinder and a plane,” J. Acoust. Soc. Am. 60, 1265–1269 (1975).
    [CrossRef]
  30. P. J. Valle, F. González, and F. Moreno, “Electromagnetic wave scattering from conducting cylindrical structureson flat substrates: study by means of the extinction theorem,” Appl. Opt. 33, 512–523 (1994).
    [CrossRef] [PubMed]
  31. A. Madrazo and M. Nieto-Vesperinas, “Scattering of electromagnetic waves from a cylinder in front of a conductingplane,” J. Opt. Soc. Am. A 12, 1298–1309 (1995).
    [CrossRef]
  32. R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder neara plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A 13, 483–493 (1996).
    [CrossRef]
  33. G. Videen and D. Ngo, “Light scattering from a cylinder near a plane interface: theory andcomparison with experimental data,” J. Opt. Soc. Am. A 14, 70–78 (1997).
    [CrossRef]
  34. S. C. Hill, H. I. Saleheen, and K. A. Fuller, “Volume current method for modeling light scattering by inhomogeneouslyperturbed spheres,” J. Opt. Soc. Am. A 12, 905–915 (1995).
    [CrossRef]
  35. B. V. Bronk, M. J. Smith, and S. Arnold, “Photon-correlation spectroscopy for small spherical inclusions in amicrometer-sized electrodynamically levitated droplet,” Opt. Lett. 18, 93–95 (1993).
    [CrossRef] [PubMed]
  36. D. Ngo and R. G. Pinnick, “Suppression of scattering resonances in inhomogeneous microdroplets,” J. Opt. Soc. Am. A 11, 1352–1359 (1994).
    [CrossRef]
  37. C.-T. Tai, Dyadic Green Functions in ElectromagneticTheory, 2nd ed. (IEEE, Piscataway, N.J., 1994), p. 102.
  38. Another common way to write the Green function relation is E(r)=ω2μVḠ(r, r)⋅P(r)dV, where P(r)=−iωJ(r). The dipole moment p(r) of the source is related to the polarizationper unit volume P(r) by p(r)=VP(r)dv. We use the notation of individual dipoles becausewe have been modeling radiation from individual molecules.
  39. The assumption of a uniform permeability is valid for theproblems we want to model, which are at optical frequencies.
  40. Ref. 14, pp. 410–411. Therelation for regions with varying μ is Ḡ(ra, rb)μ(rb)=ḠT(rb, ra)μ(ra).
  41. R. E. Collin, Field Theory of Guided Waves, 2nd ed. (IEEE, Piscataway, N.J., 1991), p. 102.
  42. Time reversal invariance and spatial reciprocity of acoustic wavesare discussed in M. Fink, “Time reversed acoustics,” Phys. Today 50(3), 34–40 (1997).
    [CrossRef]
  43. J. A. Lock and E. A. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1549 (1991).
    [CrossRef]
  44. D. Q. Chowdhury, P. W. Barber, and S. C. Hill, “Energy density distribution inside large nonabsorbing spheres via Mietheory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
    [CrossRef] [PubMed]
  45. D. S. Benincasa, P. W. Barber, J. Z. Zhang, W.-F. Hsieh, and R. K. Chang, “Spatial distribution of the internal and near-field intensities oflarge cylindrical and spherical scatterers,” Appl. Opt. 26, 1348–1356 (1987).
    [CrossRef] [PubMed]
  46. E. S. C. Ching, P. T. Leung, and K. Young, “OpticalProcesses in Microcavities—The Role of Quasinormal Modes,” in Optical Processes in Microcavities, R. K. Chang and A. J.Campillo, eds. (World Scientific, Singapore, 1996), pp. 18–65.

1997 (2)

G. Videen and D. Ngo, “Light scattering from a cylinder near a plane interface: theory andcomparison with experimental data,” J. Opt. Soc. Am. A 14, 70–78 (1997).
[CrossRef]

Time reversal invariance and spatial reciprocity of acoustic wavesare discussed in M. Fink, “Time reversed acoustics,” Phys. Today 50(3), 34–40 (1997).
[CrossRef]

1996 (5)

1995 (4)

1994 (3)

1993 (2)

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

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, and S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a hightemperature environment,” in Proceedings of the Conferenceon Laser Applications in Combustion and Combustion Diagnostics, SPIE 1862, 269–286 (1993).
[CrossRef]

1992 (3)

1991 (3)

1989 (1)

1988 (1)

Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a sphericalsurface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
[CrossRef]

1987 (1)

1986 (1)

P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–241 (1986).
[CrossRef]

1985 (2)

1984 (2)

1980 (1)

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observations of structure resonances in the fluorescence emission frommicrospheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

1976 (1)

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

1975 (1)

J. C. Bertrand and J. W. Young, “Multiple scattering between a cylinder and a plane,” J. Acoust. Soc. Am. 60, 1265–1269 (1975).
[CrossRef]

Allen, T. M.

M. F. Buehler, T. M. Allen, and E. J. Davis, “Microparticle Raman spectroscopy of multicomponent aerosols,” J. Colloid Interface Sci. 146, 79–89 (1991).
[CrossRef]

Armstrong, R. L.

Arnold, S.

M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
[CrossRef] [PubMed]

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

Barakat, R.

Barber, P. W.

Barnes, M. D.

Benincasa, D. S.

Benner, R. E.

Bertrand, J. C.

J. C. Bertrand and J. W. Young, “Multiple scattering between a cylinder and a plane,” J. Acoust. Soc. Am. 60, 1265–1269 (1975).
[CrossRef]

Bobbert, P. A.

P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–241 (1986).
[CrossRef]

Borghi, R.

Bronk, B. V.

Buehler, M. F.

M. F. Buehler, T. M. Allen, and E. J. Davis, “Microparticle Raman spectroscopy of multicomponent aerosols,” J. Colloid Interface Sci. 146, 79–89 (1991).
[CrossRef]

Campillo, A. J.

Chang, R. K.

Chen, G.

Chew, H.

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

Chowdhury, D. Q.

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, and S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a hightemperature environment,” in Proceedings of the Conferenceon Laser Applications in Combustion and Combustion Diagnostics, SPIE 1862, 269–286 (1993).
[CrossRef]

D. Q. Chowdhury, P. W. Barber, and S. C. Hill, “Energy density distribution inside large nonabsorbing spheres via Mietheory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
[CrossRef] [PubMed]

Conwell, P. R.

Davis, E. J.

M. F. Buehler, T. M. Allen, and E. J. Davis, “Microparticle Raman spectroscopy of multicomponent aerosols,” J. Colloid Interface Sci. 146, 79–89 (1991).
[CrossRef]

Eversole, J. D.

Fink, M.

Time reversal invariance and spatial reciprocity of acoustic wavesare discussed in M. Fink, “Time reversed acoustics,” Phys. Today 50(3), 34–40 (1997).
[CrossRef]

Frezza, F.

Fuller, K. A.

George, T. F.

Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a sphericalsurface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
[CrossRef]

González, F.

Gori, F.

Hill, S. C.

S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Collection of fluorescence from single molecules inside of droplets:effects of position, orientation and frequency,” Appl. Opt. 35, 6278–6288 (1996).
[CrossRef] [PubMed]

G. Chen, P. Nachman, R. G. Pinnick, S. C. Hill, and R. K. Chang, “Conditional-firing aerosol-fluorescence spectrum analyzer for individualairborne particles with pulsed 266-nm laser excitation,” Opt. Lett. 21, 1307–1309 (1996). Some of the particles studied were composed of several-to-many rod-shapedbacterial cells.
[CrossRef] [PubMed]

S. C. Hill, H. I. Saleheen, and K. A. Fuller, “Volume current method for modeling light scattering by inhomogeneouslyperturbed spheres,” J. Opt. Soc. Am. A 12, 905–915 (1995).
[CrossRef]

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, and S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a hightemperature environment,” in Proceedings of the Conferenceon Laser Applications in Combustion and Combustion Diagnostics, SPIE 1862, 269–286 (1993).
[CrossRef]

D. Q. Chowdhury, P. W. Barber, and S. C. Hill, “Energy density distribution inside large nonabsorbing spheres via Mietheory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
[CrossRef] [PubMed]

S. C. Hill, C. K. Rushforth, R. E. Benner, and P. R. Conwell, “Sizing dielectric spheres and cylinders by aligning structural resonancelocations: algorithm for multiple orders,” Appl. Opt. 24, 2380–2390 (1985).
[CrossRef] [PubMed]

S. C. Hill, R. E. Benner, P. R. Conwell, and C. K. Rushforth, “Structural resonances observed in the fluorescence emission from smallparticles on substrates,” Appl. Opt. 23, 1680–1683 (1984).
[CrossRef]

Hirleman, E. D.

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, and S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a hightemperature environment,” in Proceedings of the Conferenceon Laser Applications in Combustion and Combustion Diagnostics, SPIE 1862, 269–286 (1993).
[CrossRef]

Holler, S.

M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
[CrossRef] [PubMed]

Hovenac, E. A.

Hsieh, W.-F.

Johnson, B. R.

Kerker, M.

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

Kiefer, W.

Kim, Y. S.

Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a sphericalsurface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
[CrossRef]

Kung, C.-Y.

M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
[CrossRef] [PubMed]

Leung, P. T.

Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a sphericalsurface: a complete treatment,” Surf. Sci. 195, 1–14 (1988).
[CrossRef]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Lin, H.-B.

Lock, J. A.

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Long, M. B.

Madrazo, A.

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

McNulty, P. J.

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

Moreno, F.

Nachman, P.

Ngo, D.

Nieto-Vesperinas, M.

Owen, J. F.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observations of structure resonances in the fluorescence emission frommicrospheres,” Phys. Rev. Lett. 44, 475–478 (1980).
[CrossRef]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Pinnick, R. G.

Ramsey, J. M.

Rao, T. C.

Ruekgauer, T. E.

Rushforth, C. K.

Saleheen, H. I.

Santarsiero, M.

Schettini, G.

Schneider, M.

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, and S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a hightemperature environment,” in Proceedings of the Conferenceon Laser Applications in Combustion and Combustion Diagnostics, SPIE 1862, 269–286 (1993).
[CrossRef]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Smith, M. J.

Thurn, R.

Tzeng, H.-M.

Valle, P. J.

Videen, G.

Vlieger, J.

P. A. Bobbert and J. Vlieger, “Light scattering by a sphere on a substrate,” Physica A 137, 209–241 (1986).
[CrossRef]

Wall, K. F.

Whitten, W. B.

Xie, J.-G.

Young, J. W.

J. C. Bertrand and J. W. Young, “Multiple scattering between a cylinder and a plane,” J. Acoust. Soc. Am. 60, 1265–1269 (1975).
[CrossRef]

Zhang, J. Z.

Appl. Opt. (7)

S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Collection of fluorescence from single molecules inside of droplets:effects of position, orientation and frequency,” Appl. Opt. 35, 6278–6288 (1996).
[CrossRef] [PubMed]

R. Thurn and W. Kiefer, “Structural resonances observed in the Raman spectra of optically levitatedliquid droplets,” Appl. Opt. 24, 1515–1519 (1985).
[CrossRef]

S. C. Hill, R. E. Benner, P. R. Conwell, and C. K. Rushforth, “Structural resonances observed in the fluorescence emission from smallparticles on substrates,” Appl. Opt. 23, 1680–1683 (1984).
[CrossRef]

S. C. Hill, C. K. Rushforth, R. E. Benner, and P. R. Conwell, “Sizing dielectric spheres and cylinders by aligning structural resonancelocations: algorithm for multiple orders,” Appl. Opt. 24, 2380–2390 (1985).
[CrossRef] [PubMed]

P. J. Valle, F. González, and F. Moreno, “Electromagnetic wave scattering from conducting cylindrical structureson flat substrates: study by means of the extinction theorem,” Appl. Opt. 33, 512–523 (1994).
[CrossRef] [PubMed]

D. Q. Chowdhury, P. W. Barber, and S. C. Hill, “Energy density distribution inside large nonabsorbing spheres via Mietheory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
[CrossRef] [PubMed]

D. S. Benincasa, P. W. Barber, J. Z. Zhang, W.-F. Hsieh, and R. K. Chang, “Spatial distribution of the internal and near-field intensities oflarge cylindrical and spherical scatterers,” Appl. Opt. 26, 1348–1356 (1987).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

J. Acoust. Soc. Am. (1)

J. C. Bertrand and J. W. Young, “Multiple scattering between a cylinder and a plane,” J. Acoust. Soc. Am. 60, 1265–1269 (1975).
[CrossRef]

J. Colloid Interface Sci. (1)

M. F. Buehler, T. M. Allen, and E. J. Davis, “Microparticle Raman spectroscopy of multicomponent aerosols,” J. Colloid Interface Sci. 146, 79–89 (1991).
[CrossRef]

J. Opt. Soc. Am. A (10)

A. Madrazo and M. Nieto-Vesperinas, “Scattering of electromagnetic waves from a cylinder in front of a conductingplane,” J. Opt. Soc. Am. A 12, 1298–1309 (1995).
[CrossRef]

R. Borghi, F. Gori, M. Santarsiero, F. Frezza, and G. Schettini, “Plane-wave scattering by a perfectly conducting circular cylinder neara plane surface: cylindrical-wave approach,” J. Opt. Soc. Am. A 13, 483–493 (1996).
[CrossRef]

G. Videen and D. Ngo, “Light scattering from a cylinder near a plane interface: theory andcomparison with experimental data,” J. Opt. Soc. Am. A 14, 70–78 (1997).
[CrossRef]

S. C. Hill, H. I. Saleheen, and K. A. Fuller, “Volume current method for modeling light scattering by inhomogeneouslyperturbed spheres,” J. Opt. Soc. Am. A 12, 905–915 (1995).
[CrossRef]

D. Ngo and R. G. Pinnick, “Suppression of scattering resonances in inhomogeneous microdroplets,” J. Opt. Soc. Am. A 11, 1352–1359 (1994).
[CrossRef]

B. R. Johnson, “Morphology-dependent resonances of a dielectric sphere on a conductingplane,” J. Opt. Soc. Am. A 11, 2055–2064 (1994).
[CrossRef]

B. R. Johnson, “Calculation of light scattering from a spherical particle on a surfaceby the multipole expansion method,” J. Opt. Soc. Am. A 13, 326–337 (1996).
[CrossRef]

T. C. Rao and R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried ina ground plane. I. TM case,” J. Opt. Soc. Am. A 6, 1270–1280 (1989).
[CrossRef]

T. C. Rao and R. Barakat, “Plane-wave scattering by a conducting cylinder partially buried ina ground plane. II. TE case,” J. Opt. Soc. Am. A 8, 1986–1990 (1991).
[CrossRef]

J. A. Lock and E. A. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1549 (1991).
[CrossRef]

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

Opt. Commun. (1)

G. Videen, “Light scattering from a particle on or near a perfectly conductingsurface,” Opt. Commun. 115, 1–7 (1995).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (1)

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

Phys. Rev. Lett. (2)

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J. L. Cheung, J. M. Hartings, and R. K. Chang, “Nonlinearoptics of microdroplets illuminated by picosecond laser pulses,” in Handbook of Optical Properties, Vol. 2 of Optics of SmallParticles, Interfaces, and Surfaces, R. E. Hummel and P. Wissman, eds. (CRCPress, Boca Raton, Fla, 1997), pp. 233–260.

A. J. Campillo, J. D. Eversole, and H. B. Lin, “CavityQED modified stimulated and spontaneous processes in microdroplets,”in Optical Processes in Microcavities, R. K. Chang andA. J. Campillo, eds. (World Scientific, Singapore, 1996), pp. 167–207.

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C.-T. Tai, Dyadic Green Functions in ElectromagneticTheory, 2nd ed. (IEEE, Piscataway, N.J., 1994), p. 102.

Another common way to write the Green function relation is E(r)=ω2μVḠ(r, r)⋅P(r)dV, where P(r)=−iωJ(r). The dipole moment p(r) of the source is related to the polarizationper unit volume P(r) by p(r)=VP(r)dv. We use the notation of individual dipoles becausewe have been modeling radiation from individual molecules.

The assumption of a uniform permeability is valid for theproblems we want to model, which are at optical frequencies.

Ref. 14, pp. 410–411. Therelation for regions with varying μ is Ḡ(ra, rb)μ(rb)=ḠT(rb, ra)μ(ra).

R. E. Collin, Field Theory of Guided Waves, 2nd ed. (IEEE, Piscataway, N.J., 1991), p. 102.

E. S. C. Ching, P. T. Leung, and K. Young, “OpticalProcesses in Microcavities—The Role of Quasinormal Modes,” in Optical Processes in Microcavities, R. K. Chang and A. J.Campillo, eds. (World Scientific, Singapore, 1996), pp. 18–65.

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Equations (57)

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E1(ra)E2(ra)E3(ra)=ω2μG11(ra, rb)G12(ra, rb)G13(ra, rb)G21(ra, rb)G22(ra, rb)G23(ra, rb)G31(ra, rb)G32(ra, rb)G33(ra, rb)×p1(rb)p2(rb)p3(rb),
G¯(ra, rb)=G¯T(rb, ra),
E1(rb)E2(rb)E3(rb)=F11(rb, ra)F12(rb, ra)F13(rb, ra)F21(rb, ra)F22(rb, ra)F23(rb, ra)F31(rb, ra)F32(rb, ra)F33(rb, ra)×Eoeo·i1(ra)Eoeo·i2(ra)Eoeo·i3(ra),
Einc(r)=Eoeo exp(ik·r),
E(r)=ω2μ4πexp[ik·(r-ra)]|r-ra|p(ra)eo.
Eo=ω2μ exp(-ik·ra)4πrap(ra),
E1(rb)E2(rb)E3(rb)=ω2μG11(rb, ra)G12(rb, ra)G13(rb, ra)G21(rb, ra)G22(rb, ra)G23(rb, ra)G31(rb, ra)G32(rb, ra)G33(rb, ra)×p1(ra)p2(ra)p3(ra),
Gij(rb, ra)=exp(-ik·ra)4πraFij(rb, ra).
E1(ra)E2(ra)E3(ra)=ω2μG11(rb, ra)G21(rb, ra)G31(rb, ra)G12(rb, ra)G22(rb, ra)G32(rb, ra)G13(rb, ra)G23(rb, ra)G33(rb, ra)×p1(rb)p2(rb)p3(rb).
Er(rb)Eθ(rb)Eϕ(rb)=U11F(rb, ra)F12(rb, ra)F13(rb, ra)U21F(rb, ra)F22(rb, ra)F23(rb, ra)U31F(rb, ra)F32(rb, ra)F33(rb, ra)×0Eoeo·iθEoeo·iϕ,
Er(ra)Eθ(ra)Eϕ(ra)=ω2μU11G(rb, ra)U21G(rb, ra)U31G(rb, ra)G12(rb, ra)G22(rb, ra)G32(rb, ra)G13(rb, ra)G23(rb, ra)G33(rb, ra)×pr(rb)pθ(rb)pϕ(rb),
Er(rb)Eθ(rb)Eϕ(rb)=U11F(rb, ra)F12(rb, ra)0U21F(rb, ra)F22(rb, ra)0U31F(rb, ra)0F33(rb, ra)×0Eoeo·iθ(ra)Eoeo·iϕ(ra).
Er(ra)Eθ(ra)Eϕ(ra)=ω2μU11G(rb, ra)U21G(rb, ra)U31G(rb, ra)G12(rb, ra)G22(rb, ra)000G33(rb, ra)×pr(rb)pθ(rb)pϕ(rb).
Eϕ(ra)=ω2μG33(rb, ra)pϕ=ω2μpϕ exp(ikra)4πraF33(rb, ra),
Eϕ(ra)=ω2μpϕ exp(ikra)4πran-jn(mkrb)×ddθbPn1(cos θb)ce1n+1mkrb×ddrb[rbjn(mkrb)] Pn1(cos θb)sin θbdo1n,
ce1n=-in2n+1n(n+1)×ixjn(mx)[xhn(1)(x)]-[mxjn(mx)]xhn(1)(x),
do1n=-in+1 2n+1n(n+1)×mim2xjn(mx)[xhn(1)(x)]-[mxjn(mx)]xhn(1)(x),
Eϕ(ra)
=exp(ikra)kran ω2μkpϕ4π(2n+1)n(n+1)×in+1jn(mkrb) ddθbPn1(cos θb)xjn(mx)[xhn(1)(x)]-[mxjn(mx)]xhn(1)(x)+inkrbddrb[rbjn(mkrb)]Pn1(cosθb)sinθbm2xjn(mx)[xhn(1)(x)]-[mxjn(mx)]xhn(1)(x).
fvG=-ω2μpϕkπx×iϕ·Mv1(mkrb)jn(mx)[xhn(1)(x)]-[mxjn(mx)]hn(1)(x),
gvG=-ω2μpϕkπx×miϕ·Nv1(mkrb)m2jn(mx)[xhn(1)(x)]-[mxjn(mx)]hn(1)(x),
femnG=ω2μkpϕπx×jn(mkrb) ddθbPnm(cos θb)jn(mx)[xhn(1)(x)]-[mxjn(mx)]hn(1)(x),
gomnG=-ω2μpϕπxrb×ddrb[rjn(mkrb)] Pnm(cos θb)sin θbm2jn(mx)[xhn(1)(x)]-[mxjn(mx)]hn(1)(x).
Pn1(cos θa)sin θaθa=π=(-1)n+1 n(n+1)2,
ddθaPn1(cos θa)θa=π=(-1)n n(n+1)2,
hn(1)(kr)=i-(n+1)krexp(ikr),
Me1n(kr)|θ=π=in+1 n(n+1)2exp(ikr)kriϕ,
No1n(kr)|θ=π=-in n(n+1)2exp(ikr)kriϕ.
Eϕs=exp(ikra)kran n(n+1)2D1n[i(n+1)fe1n+ingo1n],
Eϕs=exp(ikra)kran ω2μkpϕ4π(2n+1)n(n+1)×i(n+1)jn(mkrb) ddθbPn1(cos θb)xjn(mx)[xhn(1)(x)]-[mxjn(mx)]xhn(1)(x)+inkrbddrb[rbjn(mkrb)] Pn1(cos θb)sin θbm2xjn(mx)[xhn(1)(x)]-[mxjn(mx)]xhn(1)(x).
M˜nm(ρ)=θˆ imsin θzn(ρ)(kr)P˜nm(cos θ)exp(imφ)-φˆzn(ρ)(kr) ddθP˜nm(cos θ)exp(imφ),
N˜nm(ρ)=rˆ 1krzn(ρ)(kr)n(n+1)P˜nm(cos θ)exp(imφ)+θˆ 1krddr[rzn(ρ)(kr)] ddθP˜nm(cos θ)×exp(imφ)+φˆ 1krddr[rzn(ρ)(kr)] ×imsin θP˜nm(cos θ)exp(imφ).
E1int(mkr)=n,menm(1)M˜nm(1)(mkr)+enm(2)N˜nm(1)(mkr),
enm(1)jn(mkr)=anm(1)jn(ka)+bnm(1)hn(ka)+cnm(1)jn(ka),
menm(2)jn(mkr)=anm(2)jn(ka)+bnm(2)hn(ka)+cnm(2)jn(ka).
F12(rb, ra)=n,menm(2)TM 1mkrbzn(1)(mkrb)n(n+1)×P˜nm(cos θb)exp(imφb),
F13(rb, ra)=n,menm(2)TE 1mkrbzn(1)(mkrb)n(n+1)×P˜nm(cos θb)exp(imφb),
F22(rb, ra)=n,menm(1)TM imsin θbzn(1)(mkrb)×P˜nm(cos θb)exp(imφb)+enm(2)TM 1mkrbddrb[rbzn(1)(mkrb)]×ddθbP˜nm(cos θb)exp(imφb),
F23(rb, ra)=n,menm(1)TE imsin θbzn(1)(mkrb)×P˜nm(cos θb)exp(imφb)+enm(2)TE 1mkrbddrb[rbzn(1)(mkrb)]×ddθbP˜nm(cos θb)exp(imφb),
F32(rb, ra)=n,m-enm(1)TMzn(1)(mkrb)×ddθbP˜nm(cos θb)exp(imφb)+enm(2)TM 1mkrbddrb[rbzn(1)(mkrb)]×imsin θbP˜nm(cos θb)exp(imφb),
F33(rb, ra)=n,m-enm(1)TEzn(1)(mkrb)×ddθbP˜nm(cos θb)exp(imφb)+enm(2)TE 1mkrbddrb[rbzn(1)(mkrb)]×imsin θbP˜nm(cos θb)exp(imφb),
F12=n,mn(n+1) jn(mkrb)mkrb×cos mϕb Pnm(cos θb)sin θbsin θbdemn,
F22=n,mjn(mkrb)cos mϕb mPnm(cos θb)sin θbcomn+1mkrbddrb[rbjn(mkrb)]cos mϕ×ddθPnm(cos θb)demn,
F32=n,m-jn(mkrb)sin mϕb ddθPnm(cos θb)comn-1mkrbddrb[rbjn(mkrb)]sin mϕb×mPnm(cos θb)sin θbdemn,
F13=n,mn(n+1) jn(mkrb)mkrb×sin mϕb Pnm(cos θb)sin θbsin θbdomn,
F23=n,m-jn(mkrb)sin mϕb mPnm(cos θb)sin θbcemn+1mkrbddrb[rbjn(mkrb)]sin mϕb×ddθPnm(cos θb)domn,
F33=n,m-jn(mkrb)cos mϕb ddθPnm(cos θb)cemn+1mkrbddrb[rbjn(mkrb)]cos mϕb×mPnm(cos θb)sin θbdomn.
ET(mkr)=EH(mkr)+EiG(mkr).
EH(mkr)=ν=1Dν[cνHMν3(mkr)+dνHNν3(mkr)].
Dmn=m(2n+1)(n-m)!4n(n+1)(n+m)!,
cνH=iω2μ kmπp(rb)·Mν1(mkrb),
dνH=iω2μ kmπp(rb)·Nν1(mkrb),
EsG(kr)=ν=1Dν[fνGMν3(kr)+gνGNν3(kr)],
fνG=cνHimxjn(mx)[xhn(1)(x)]-m[mxjn(mx)]xhn(1)(x),
gνG=dνH im2xjn(mx)[xhn(1)(x)]-[mxjn(mx)]xhn(1)(x),
E(r)=ω2μVG¯(r, r)·P(r)dV,
p(r)=VP(r)dv.

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