Abstract

Internal and scattered time-dependent intensities are calculated for a dielectric sphere illuminated with a pulsed Gaussian beam. The center frequency of the pulse spectrum is chosen to be on, near, or far from a morphology-dependent resonance of the sphere. The center of the beam is positioned inside, on the edge, or outside the sphere. The transfer function at a point, i.e., the electric field at each frequency of the pulse spectrum, is calculated with the plane-wave spectrum technique and the T-matrix method. The frequency spectrum of the field at a point is calculated by means of the incident field spectrum and the transfer function at that point. The time dependence of the electric field at a point inside or outside the sphere is obtained by inverse Fourier transforming the frequency spectrum. Two different decay rates in the internal and the scattered time-dependent intensity are observed: a decay rate that depends on the incident pulse spectrum and a rate that depends on the line shape of the resonant mode of the sphere.

© 1994 Optical Society of America

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References

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  1. D. Q. Chowdhury, S. C. Hill, P. W. Barber, “Time dependence of internal intensity of a dielectric sphere on and near resonance,” J. Opt. Soc. Am. A 9, 1364–1373 (1992).
    [CrossRef]
  2. K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulsed-wave radiation in spherical models of dispersive biological substances,” Bioelectromagnetics 12, 319–333 (1991).
    [CrossRef] [PubMed]
  3. J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
    [CrossRef]
  4. E. E. M. Khaled, S. C. Hill, P. W. Barber, D. Q. Chowdhury, “Near-resonance excitation of dielectric spheres with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
    [CrossRef] [PubMed]
  5. J. R. Snow, S.-X. Qian, R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985).
    [CrossRef] [PubMed]
  6. A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,’”Phys. Rev. A 40, 7413–7416 (1989).
    [CrossRef] [PubMed]
  7. S.-X. Qian, J. B. Snow, R. K. Chang, “Coherent Raman mixing and coherent anti-Stokes Raman scattering from micrometer-size droplets,” Opt. Lett. 10, 499–501 (1985).
    [CrossRef] [PubMed]
  8. W. P. Acker, D. H. Leach, R. K. Chang, “Third-order optical sum-frequency generation in micrometer-sized liquid droplets,” Opt. Lett. 14, 402–404 (1989).
    [CrossRef] [PubMed]
  9. S. C. Hill, D. H. Leach, R. K. Chang, “Third-order sum-frequency generation in droplets: model with numerical results for third-harmonic generation,” J. Opt. Soc. Am. B 10, 16–33 (1993).
    [CrossRef]
  10. H. M. Tzeng, K. F. Wall, M. B. Long, R. K. Chang, “Laser emission from individual droplets at wavelengths corresponding to morphology-dependent resonances,” Opt. Lett. 9, 499–501 (1984).
    [CrossRef] [PubMed]
  11. A. J. Campillo, J. D. Eversole, H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
    [CrossRef] [PubMed]
  12. J. D. Eversole, H.-B. Lin, A. J. Campillo, “Cavity-mode identification of fluorescence and lasing in dye-doped micro-droplets,” Appl. Opt. 31, 1982–1991 (1992).
    [CrossRef] [PubMed]
  13. S. C. Hill, R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.
  14. S. C. Ching, H. M. Lai, K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am. B 4, 1995–2003 (1987).
    [CrossRef]
  15. S. C. Ching, H. M. Lai, K. Young, “Dielectric microspheres as optical cavities: Einstein Aand Bcoefficients and level shifts,” J. Opt. Soc. Am. B 4, 2004–2009 (1987).
    [CrossRef]
  16. H. Chew, “Radiation lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
    [CrossRef] [PubMed]
  17. P. Chylek, J. D. Pendleton, R. G. Pinnick, “Internal and near-surface scattered field of a spherical particle at resonant conditions,” Appl. Opt. 24, 3940–3942 (1985).
    [CrossRef] [PubMed]
  18. D. S. Benincasa, P. W. Barber, J-Z. Zhang, W-F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 26, 1348–1356 (1987).
    [CrossRef] [PubMed]
  19. T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. (Japan) Part 1 71, 74–86 (1988).
    [CrossRef]
  20. W. E. Howell, H. Überall, “Selective observation of resonances via their ringing in transient radar scattering, as illustrated for conducting and coated spheres,” IEEE Trans. Antennas Propag. 38, 293–298 (1990).
    [CrossRef]
  21. J. Rheinstein, “Backscatter from spheres: a short pulse view,” IEEE Trans. Antennas Propag. AP-16, 89–97 (1968).
    [CrossRef]
  22. R. Mittra, “Integral equation methods for transient scattering,” in Transient Electromagnetic Fields, L. B. Felson, ed. (Springer-Verlag, New York, 1976).
    [CrossRef]
  23. H. Shirai, “Time transient analysis of wave scattering by simple shapes,” presented at the Analytic and Numerical Methods in Wave Theory Seminar, Adana, Turkey, 1991;H. Shirai, A. Hamakoshi, “Transient response by a dielectric cylinder due to a line source at the center,” Trans. Inst. Electron. Inf. Commun. Eng. (Japan) E 74, 157–166 (1991).
  24. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  25. 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]
  26. E. E. M. Khaled, “Theoretical investigation of scattering by homogeneous or coated dielectric spheres illuminated with a steady state or pulsed laser beam” (Clarkson University, Potsdam, N.Y., 1993).
  27. P. W. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [CrossRef] [PubMed]
  28. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  29. D. Q. Chowdhury, S. C. Hill, M. M. Mazumder, “Quality factors and effective-average modal gain or loss in inho-mogeneous spherical resonators: application to two-photon absorption,” IEEE J. Quantum Electron. 29, 2553–2561 (1993).
    [CrossRef]

1993

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 inho-mogeneous spherical resonators: application to two-photon absorption,” IEEE J. Quantum Electron. 29, 2553–2561 (1993).
[CrossRef]

S. C. Hill, D. H. Leach, R. K. Chang, “Third-order sum-frequency generation in droplets: model with numerical results for third-harmonic generation,” J. Opt. Soc. Am. B 10, 16–33 (1993).
[CrossRef]

1992

1991

K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulsed-wave radiation in spherical models of dispersive biological substances,” Bioelectromagnetics 12, 319–333 (1991).
[CrossRef] [PubMed]

A. J. Campillo, J. D. Eversole, H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

1990

W. E. Howell, H. Überall, “Selective observation of resonances via their ringing in transient radar scattering, as illustrated for conducting and coated spheres,” IEEE Trans. Antennas Propag. 38, 293–298 (1990).
[CrossRef]

1989

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,’”Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

W. P. Acker, D. H. Leach, R. K. Chang, “Third-order optical sum-frequency generation in micrometer-sized liquid droplets,” Opt. Lett. 14, 402–404 (1989).
[CrossRef] [PubMed]

1988

T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. (Japan) Part 1 71, 74–86 (1988).
[CrossRef]

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

1987

1985

1984

1975

1968

J. Rheinstein, “Backscatter from spheres: a short pulse view,” IEEE Trans. Antennas Propag. AP-16, 89–97 (1968).
[CrossRef]

Acker, W. P.

Alexander, D. R.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Armstrong, R. L.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,’”Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Barber, P. W.

Barton, J. P.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Benincasa, D. S.

Benner, R. E.

S. C. Hill, R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.

Biswas, A.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,’”Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Campillo, A. J.

J. D. Eversole, H.-B. Lin, A. J. Campillo, “Cavity-mode identification of fluorescence and lasing in dye-doped micro-droplets,” Appl. Opt. 31, 1982–1991 (1992).
[CrossRef] [PubMed]

A. J. Campillo, J. D. Eversole, H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Chang, R. K.

Chew, H.

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

Ching, S. C.

Chowdhury, D. Q.

Chylek, P.

Durney, C. H.

K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulsed-wave radiation in spherical models of dispersive biological substances,” Bioelectromagnetics 12, 319–333 (1991).
[CrossRef] [PubMed]

Eversole, J. D.

J. D. Eversole, H.-B. Lin, A. J. Campillo, “Cavity-mode identification of fluorescence and lasing in dye-doped micro-droplets,” Appl. Opt. 31, 1982–1991 (1992).
[CrossRef] [PubMed]

A. J. Campillo, J. D. Eversole, H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hill, S. C.

S. C. Hill, D. H. Leach, R. K. Chang, “Third-order sum-frequency generation in droplets: model with numerical results for third-harmonic generation,” J. Opt. Soc. Am. B 10, 16–33 (1993).
[CrossRef]

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

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]

E. E. M. Khaled, S. C. Hill, P. W. Barber, D. Q. Chowdhury, “Near-resonance excitation of dielectric spheres with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
[CrossRef] [PubMed]

D. Q. Chowdhury, S. C. Hill, P. W. Barber, “Time dependence of internal intensity of a dielectric sphere on and near resonance,” J. Opt. Soc. Am. A 9, 1364–1373 (1992).
[CrossRef]

S. C. Hill, R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.

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

Hosono, T.

T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. (Japan) Part 1 71, 74–86 (1988).
[CrossRef]

Howell, W. E.

W. E. Howell, H. Überall, “Selective observation of resonances via their ringing in transient radar scattering, as illustrated for conducting and coated spheres,” IEEE Trans. Antennas Propag. 38, 293–298 (1990).
[CrossRef]

Hsieh, W-F.

Ikeda, K.

T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. (Japan) Part 1 71, 74–86 (1988).
[CrossRef]

Itoh, A.

T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. (Japan) Part 1 71, 74–86 (1988).
[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]

E. E. M. Khaled, S. C. Hill, P. W. Barber, D. Q. Chowdhury, “Near-resonance excitation of dielectric spheres with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
[CrossRef] [PubMed]

E. E. M. Khaled, “Theoretical investigation of scattering by homogeneous or coated dielectric spheres illuminated with a steady state or pulsed laser beam” (Clarkson University, Potsdam, N.Y., 1993).

Lai, H. M.

Latifi, H.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,’”Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

Leach, D. H.

Lin, H.-B.

J. D. Eversole, H.-B. Lin, A. J. Campillo, “Cavity-mode identification of fluorescence and lasing in dye-doped micro-droplets,” Appl. Opt. 31, 1982–1991 (1992).
[CrossRef] [PubMed]

A. J. Campillo, J. D. Eversole, H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Long, M. B.

Mazumder, M. M.

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

Mittra, R.

R. Mittra, “Integral equation methods for transient scattering,” in Transient Electromagnetic Fields, L. B. Felson, ed. (Springer-Verlag, New York, 1976).
[CrossRef]

Moten, K.

K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulsed-wave radiation in spherical models of dispersive biological substances,” Bioelectromagnetics 12, 319–333 (1991).
[CrossRef] [PubMed]

Pendleton, J. D.

Pinnick, R. G.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,’”Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

P. Chylek, J. D. Pendleton, R. G. Pinnick, “Internal and near-surface scattered field of a spherical particle at resonant conditions,” Appl. Opt. 24, 3940–3942 (1985).
[CrossRef] [PubMed]

Qian, S.-X.

Rheinstein, J.

J. Rheinstein, “Backscatter from spheres: a short pulse view,” IEEE Trans. Antennas Propag. AP-16, 89–97 (1968).
[CrossRef]

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Shirai, H.

H. Shirai, “Time transient analysis of wave scattering by simple shapes,” presented at the Analytic and Numerical Methods in Wave Theory Seminar, Adana, Turkey, 1991;H. Shirai, A. Hamakoshi, “Transient response by a dielectric cylinder due to a line source at the center,” Trans. Inst. Electron. Inf. Commun. Eng. (Japan) E 74, 157–166 (1991).

Snow, J. B.

Snow, J. R.

Stockham, T. G.

K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulsed-wave radiation in spherical models of dispersive biological substances,” Bioelectromagnetics 12, 319–333 (1991).
[CrossRef] [PubMed]

Tzeng, H. M.

Überall, H.

W. E. Howell, H. Überall, “Selective observation of resonances via their ringing in transient radar scattering, as illustrated for conducting and coated spheres,” IEEE Trans. Antennas Propag. 38, 293–298 (1990).
[CrossRef]

Wall, K. F.

Yeh, C.

Young, K.

Zhang, J-Z.

Appl. Opt.

Bioelectromagnetics

K. Moten, C. H. Durney, T. G. Stockham, “Electromagnetic pulsed-wave radiation in spherical models of dispersive biological substances,” Bioelectromagnetics 12, 319–333 (1991).
[CrossRef] [PubMed]

Electron. Commun. (Japan)

T. Hosono, K. Ikeda, A. Itoh, “Analysis of transient response of electromagnetic waves scattered by a perfectly conducting sphere. The case of back- and forward-scattering,” Electron. Commun. (Japan) Part 1 71, 74–86 (1988).
[CrossRef]

IEEE J. Quantum Electron.

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

IEEE Trans. Antennas Propag.

W. E. Howell, H. Überall, “Selective observation of resonances via their ringing in transient radar scattering, as illustrated for conducting and coated spheres,” IEEE Trans. Antennas Propag. 38, 293–298 (1990).
[CrossRef]

J. Rheinstein, “Backscatter from spheres: a short pulse view,” IEEE Trans. Antennas Propag. AP-16, 89–97 (1968).
[CrossRef]

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]

J. Appl. Phys.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,’”Phys. Rev. A 40, 7413–7416 (1989).
[CrossRef] [PubMed]

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

Phys. Rev. Lett.

A. J. Campillo, J. D. Eversole, H.-B. Lin, “Cavity quantum electrodynamic enhancement of stimulated emission in microdroplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Other

S. C. Hill, R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.

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

E. E. M. Khaled, “Theoretical investigation of scattering by homogeneous or coated dielectric spheres illuminated with a steady state or pulsed laser beam” (Clarkson University, Potsdam, N.Y., 1993).

R. Mittra, “Integral equation methods for transient scattering,” in Transient Electromagnetic Fields, L. B. Felson, ed. (Springer-Verlag, New York, 1976).
[CrossRef]

H. Shirai, “Time transient analysis of wave scattering by simple shapes,” presented at the Analytic and Numerical Methods in Wave Theory Seminar, Adana, Turkey, 1991;H. Shirai, A. Hamakoshi, “Transient response by a dielectric cylinder due to a line source at the center,” Trans. Inst. Electron. Inf. Commun. Eng. (Japan) E 74, 157–166 (1991).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (9)

Fig. 1
Fig. 1

Spherical particle of radius a centered at the origin of a right-handed Cartesian coordinate system (x, y, z) along with a spherical coordinate system (r,θ, ϕ). The incident pulse is a Gaussian function in time propagating in the z direction. The pulsed Gaussian beam has a spot size of ω0 = 1.0 μm, and the focal point is arbitrarily located at (x0,y0,z0).

Fig. 2
Fig. 2

Time dependence of the internal intensity at P1 (0.9a, 0°, 0°). The incident pulse is either a plane wave or a Gaussian beam focused at different locations. The incident frequency is on resonance with the TE58,1 MDR. The width of the incident pulse is τ0 = 0.5239 ns, and the resonant lifetime is τr = 0.2052 ns. The refractive index of the sphere is 1.36, and the radius is a ≈ 4μm for an incident wavelength of 0.532 μm. The beam position along the y axis is shown relative to the sphere radius a. The incident pulse is also shown, (a) Intensities shown on a linear scale, (b) same intensities as in (a) but on a log scale.

Fig. 3
Fig. 3

Time dependence of the internal intensity at P1(0.9a,0°,0°) of a sphere for the same cases as shown in Fig. 2 except that the incident pulse width is τ0 = 0.1746 ns, i.e., τ0 < τr.

Fig. 4
Fig. 4

Time dependence of the internal intensity at P1(0.9a,0°,0°) for the same set of parameters as in Fig. 3 except that the sphere is lossy, with a refractive index of m = 1.36 + i10−6.

Fig. 5
Fig. 5

Time dependence of the internal intensity at P1(0.9a, 0°, 0°), where the incident pulse is either a plane wave or a Gaussian beam focused at different locations. The incident field frequency is detuned by 5 linewidths from the TE58,1 MDR. All the other parameters are the same as in Fig. 2.

Fig. 6
Fig. 6

Time dependence of the internal intensity at P1(0.9a, 0°, 0°) for cases similar to those shown in Fig. 5 (N = 5), except that the incident pulse width is τ0 = 0.1746 ns.

Fig. 7
Fig. 7

Time dependence of the backscattered intensity at P2(500a, 180°, 0°), where the incident pulse is either a plane wave or a Gaussian pulse focused at different locations. All the parameters for the sphere and the incident pulse are the same as in Fig. 3.

Fig. 8
Fig. 8

Time dependence of the backscattered intensity at P2(500a, 180°, 0°) for the same cases shown in Fig. 7(a), except that the refractive index of the sphere is changed to m = 1.36 + il0−6.

Fig. 9
Fig. 9

Time dependence of the backscattered intensity at P2(500a, 180°, 0°) for the same cases shown in Fig. 7(a), except that the incident frequency is detuned 5 linewidths away from the TE58,1 resonance location.

Tables (2)

Equations (10)

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

E inc ( z , t ) = Ê inc ( z , t ) exp [ i Ω 0 ( t z / c ) ] i x ,
E ( r , t ) = 1 { E inc ( Ω ) E δ ( r , Ω ) } ,
E inc ( Ω ) = { Ê inc ( z , t ) exp [ i Ω 0 ( t z / c ) ] } z = 0 ,
E inc ( Ω ) = Ê inc ( Ω + Ω 0 ) .
E ( r , t ) = 1 { Ê inc ( Ω + Ω 0 ) E δ ( r , Ω ) } .
E i ( r , Ω ) = H m n D m n [ a e m n t M e m n 1 ( k r ) + a o m n t M o m n 1 ( k r ) + b e m n t N e m n 1 ( k r ) + b o m n t N o m n 1 ( k r ) ] .
E int ( r , Ω ) = H m n [ c e m n t M e m n 1 ( m k r ) + c o m n t M o m n 1 ( m k r ) + d e m n t N e m n 1 ( m k r ) + d o m n t N o m n 1 ( m k r ) ] .
E s ( r , Ω ) = H m n D m n [ f e m n t M e m n 3 ( k r ) + f o m n t M o m n 3 ( k r ) + g e m n t N e m n 3 ( k r ) + g o m n t N o m n 3 ( k r ) ] .
P t = c 16 E 0 2 ω 0 2 ,
Ω 0 = Ω r + N Δ Ω r ,

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