Abstract

The electric energy in a lossless or lossy spherical particle that is illuminated with a plane wave or a Gaussian beam is investigated. The analysis uses a combination of the plane-wave spectrum technique and the T-matrix method. Expressions for the electric energy in any mode as well as the total electric energy inside the particle are given. The amount of energy coupling into the particle for different beam illuminations is also investigated. The high-Q (low-order) resonant modes can dominate the electric energy inside a spherical particle many linewidths away from the resonance location, particularly if the beam is focused at the droplet edge or outside the droplet. If the sphere is lossy, low-order modes can still dominate the electric energy if the beam is focused far enough outside the sphere. As the absorption coefficient of the particle increases, the energy in a high-Q mode decreases much faster at the resonance frequency than it does at near or off-resonance frequencies. The effects of the absorption on the dominance of the internal fields by a high-Q mode decreases as the beam is shifted farther away from the particle. As the beam is shifted farther away from the particle the fraction of the incident energy coupled into the sphere at resonance first increases and then decreases. Although the coupled energy decreases as the beam is shifted farther from the sphere, most of that energy is in the lowest-order mode.

© 1994 Optical Society of America

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References

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  1. 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]
  2. 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]
  3. G. Chen, W. P. Acker, R. K. Chang, S. C. Hill, “Fine structures in the stimulated Raman scattering from single droplets,” Opt. Lett. 16, 117–119 (1991).
    [CrossRef] [PubMed]
  4. J.-C. Zhang, R. K. Chang, “Generation and suppression of stimulated Brillouin scattering in single liquid droplets,” J. Opt. Soc. Am B 6, 151–153 (1989).
    [CrossRef]
  5. 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]
  6. 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]
  7. 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]
  8. A. J. Campillo, J. D. Eversole, H-B. Lin, “Cavity quantum electrodynamics enhancement of stimulated emission in micro-droplets,” Phys. Rev. Lett. 67, 437–440 (1991).
    [CrossRef] [PubMed]
  9. 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]
  10. H. Chew, “Radiation lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38, 3410–3416 (1988).
    [CrossRef] [PubMed]
  11. 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.
  12. P. Chýlek, 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]
  13. D. S. Benincasa, P. W. Barber, Jain-Zhi Zhang, Wen-Feng 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]
  14. P. W. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
    [CrossRef] [PubMed]
  15. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990).
  16. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  17. J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
    [CrossRef]
  18. 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]
  19. J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
  20. S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
    [CrossRef]
  21. J. P. Barton, W. Ma, S. A. Schaub, D. R. Alexander, “Electromagnetic field for a beam incident on two adjacent spherical particles,” Appl. Opt. 30, 4706–4715 (1991).
    [CrossRef] [PubMed]
  22. G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
    [CrossRef] [PubMed]
  23. B. Maheu, G. Gréhen, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–25 (1987).
    [CrossRef] [PubMed]
  24. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  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, 1–9 (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,” Ph.D. dissertation (Clarkson University, Potsdam, N.Y., 1993).
  27. A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
    [CrossRef] [PubMed]
  28. 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]
  29. P. Chýlek, “Light scattering by small particles in an absorbing medium,” J. Opt. Soc. Am. 67, 561–563 (1977).
    [CrossRef]

1993 (2)

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]

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, 1–9 (1993).
[CrossRef]

1992 (2)

1991 (3)

1989 (6)

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. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
[CrossRef]

J.-C. Zhang, R. K. Chang, “Generation and suppression of stimulated Brillouin scattering in single liquid droplets,” J. Opt. Soc. Am B 6, 151–153 (1989).
[CrossRef]

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]

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]

1988 (3)

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

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

1987 (2)

1986 (1)

1985 (2)

1984 (1)

1981 (1)

1977 (1)

1975 (1)

Acker, W. P.

Alexander, D. R.

J. P. Barton, W. Ma, S. A. Schaub, D. R. Alexander, “Electromagnetic field for a beam incident on two adjacent spherical particles,” Appl. Opt. 30, 4706–4715 (1991).
[CrossRef] [PubMed]

S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
[CrossRef]

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. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[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]

Ashkin, A.

Barber, P. W.

Barton, J. P.

J. P. Barton, W. Ma, S. A. Schaub, D. R. Alexander, “Electromagnetic field for a beam incident on two adjacent spherical particles,” Appl. Opt. 30, 4706–4715 (1991).
[CrossRef] [PubMed]

J. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
[CrossRef]

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. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[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 electrodynamics enhancement of stimulated emission in micro-droplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Chang, R. K.

Chen, G.

Chew, H.

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

Chowdhury, D. Q.

Chýlek, P.

Dziedzic, J. M.

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 electrodynamics enhancement of stimulated emission in micro-droplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Gouesbet, G.

Gréhan, G.

Gréhen, G.

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]

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, 1–9 (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]

G. Chen, W. P. Acker, R. K. Chang, S. C. Hill, “Fine structures in the stimulated Raman scattering from single droplets,” Opt. Lett. 16, 117–119 (1991).
[CrossRef] [PubMed]

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).

Hsieh, Wen-Feng

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, 1–9 (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,” Ph.D. dissertation (Clarkson University, Potsdam, N.Y., 1993).

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 electrodynamics enhancement of stimulated emission in micro-droplets,” Phys. Rev. Lett. 67, 437–440 (1991).
[CrossRef] [PubMed]

Long, M. B.

Ma, W.

Maheu, B.

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. Chýlek, 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.

Schaub, S. A.

J. P. Barton, W. Ma, S. A. Schaub, D. R. Alexander, “Electromagnetic field for a beam incident on two adjacent spherical particles,” Appl. Opt. 30, 4706–4715 (1991).
[CrossRef] [PubMed]

S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
[CrossRef]

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. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

Snow, J. R.

Tzeng, H. M.

van de Hulst, H. C.

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

Wall, K. F.

Yeh, C.

Zhang, J.-C.

J.-C. Zhang, R. K. Chang, “Generation and suppression of stimulated Brillouin scattering in single liquid droplets,” J. Opt. Soc. Am B 6, 151–153 (1989).
[CrossRef]

Zhang, Jain-Zhi

Appl. Opt. (9)

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]

P. Chýlek, 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]

D. S. Benincasa, P. W. Barber, Jain-Zhi Zhang, Wen-Feng 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]

P. W. Barber, C. Yeh, “Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies,” Appl. Opt. 14, 2864–2872 (1975).
[CrossRef] [PubMed]

J. P. Barton, W. Ma, S. A. Schaub, D. R. Alexander, “Electromagnetic field for a beam incident on two adjacent spherical particles,” Appl. Opt. 30, 4706–4715 (1991).
[CrossRef] [PubMed]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatter centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef] [PubMed]

B. Maheu, G. Gréhen, G. Gouesbet, “Generalized Lorenz-Mie theory: first exact values and comparisons with the localized approximation,” Appl. Opt. 26, 23–25 (1987).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
[CrossRef] [PubMed]

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]

Appl. Phys. Lett. (1)

S. A. Schaub, J. P. Barton, D. R. Alexander, “Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam,” Appl. Phys. Lett. 55, 2709–2711 (1989).
[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, 1–9 (1993).
[CrossRef]

J. Appl. Phys. (3)

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal and near-surface electromagnetic fields for a spherical particle irradiated by a focused laser beam,” J. Appl. Phys. 64, 1632–1639 (1988).
[CrossRef]

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. P. Barton, D. R. Alexander, “Fifth-order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. Opt. Soc. Am B (1)

J.-C. Zhang, R. K. Chang, “Generation and suppression of stimulated Brillouin scattering in single liquid droplets,” J. Opt. Soc. Am B 6, 151–153 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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

Opt. Lett. (4)

Phys. Rev. A (1)

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

Phys. Rev. A. (1)

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]

Phys. Rev. Lett. (1)

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

Other (4)

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).

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

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

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Figures (7)

Fig. 1
Fig. 1

Spherical particle of radius a centered at the origin of a right-handed Cartesian coordinate system. The spherical coordinate system (r, θ, ϕ) is also shown. The incident Gaussian beam has a spot size ω0. The beam focal point x 0, y 0, z 0.

Fig. 2
Fig. 2

Fraction of the electric energy in the TE69,1 mode inside a sphere as a function of the size parameter and the location y 0 of the incident Gaussian beam. The refractive index of the lossless sphere is m = 1.36. The amplitude of the electric field of the plane wave is unity and is polarized in the x direction. The incident Gaussian beam is polarized in the xz plane, and the electric-field amplitude at the beam’s focal point is unity. In all cases the wave propagates in the z direction. The beam focal point is located at x 0 = 0, y 0 = variable, z 0 = 0, and ω0 = 2 μm, in all the cases.

Fig. 3
Fig. 3

Fraction of the electric energy in the TE69,1 mode inside a sphere as a function of size parameter. All the parameters are the same as in Fig. 2 except that the refractive index of the sphere is changed to m = 1.36 + j10−4 (lossy sphere).

Fig. 4
Fig. 4

Normalized averaged electric energy density inside a sphere as a function of size parameter for plane-wave and different Gaussian beam illumination positions. The refractive index of the sphere is m = 1.36 (lossless sphere) and m = 1.36 + j10−4 (lossy sphere). All the parameters of the beam are the same as in Fig. 2. (a) On-axis, (b) y 0/a = 1.0, (c) y 0/a = 1.23, (d) y 0/a = 1.5, and (e) plane-wave illumination.

Fig. 5
Fig. 5

Sum of internal electric-field expansion coefficients (∑ m |c m , n , l |2) as a function of size parameter for different Gaussian beam illumination positions. The refractive index is m = 1.36 (lossless sphere). All the parameters of the beam are the same as in Fig. 2. (a) On-axis, (b) y 0/a = 1.0, (c) y 0/a = 1.23, and (d) y 0/a = 1.5.

Fig. 6
Fig. 6

Sum of internal electric-field expansion coefficients (∑ m |c m , n , l |2) as a function of size parameter for different Gaussian-beam-illumination positions. All the parameters are the same as in Fig. 5, except the refractive index of the sphere is changed to m = 1.36 + 10−4 (lossy sphere). (a) On-axis, (b) y 0/a = 1.0, (c) y 0/a = 1.23, and (d) y 0/a = 1.5.

Fig. 7
Fig. 7

Peak electric energy density inside the sphere normalized by the peak electric energy density of the incident beam. The curves are for different focal point positions y 0/a.

Tables (2)

Tables Icon

Table 2 MDR’s and Their Characteristics in Figs. 2 and 3

Equations (17)

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

W e = 0 m 2 2 V E int ( r , θ , ϕ ) · [ E int ( r , θ , ϕ ) ] * d v = 0 m 2 2 V E int ( r , θ , ϕ ) 2 d v ,
E int = H m n c e m n t M e m n ( m k r ) + c o m n t M o m n ( m k r ) + d e m n t N e m n ( m k r ) + d o m n t N omn ( m k r ) ,
W e = 0 m 2 H 2 2 V { m n [ c e m n t 2 M e m n ( m k r ) 2 + c o m n t 2 M o m n ( m k r ) 2 + d e m n t 2 N e m n ( m k r ) 2 + d o m n t 2 N o m n ( m k r ) 2 ] } d v ,
W e = 0 m 2 H 2 2 m n { c e m n t 2 V M e m n ( m k r ) 2 d v + c o m n t 2 V M o m n ( m k r ) 2 d v + d e m n t 2 V N e m n ( m k r ) 2 d v + d o m n t 2 V N o m n ( m k r ) 2 d v } .
V M e m n ( m k r ) 2 d v = π a 3 [ j n 2 ( m k a ) - j n + 1 ( m k a ) j n - 1 ( m k a ) ] [ n ( n + 1 ) 2 n + 1 ] × { 2 m = 0 ( n + m ) ! ( n - m ) ! m 1 ,
V M o m n ( m k r ) 2 d v = π a 3 [ j n 2 ( m k a ) - j n + 1 ( m k a ) j n - 1 ( m k a ) ] [ n ( n + 1 ) 2 n + 1 ] × { 0 m = 0 ( n + m ) ! ( n - m ) ! m 1 ,
V N e m n ( m k r ) 2 d v = π a 3 { - 2 n ( m k a ) 2 j n 2 ( m k a ) + j n - 1 2 ( m k a ) - j n ( m k a ) j n - 2 ( m k a ) } [ ( n + 1 ) 2 n + 1 ] × { 2 m = 0 ( n + m ) ! ( n - m ) ! m 1 ,
V N o m n ( m k r ) 2 d v = π a 3 { - 2 n ( m k a ) 2 j n 2 ( m k a ) + j n - 1 2 ( m k a ) - j n ( m k a ) j n - 2 ( m k a ) } [ ( n + 1 ) 2 n + 1 ] × { 0 m = 0 ( n + m ) ! ( n - m ) ! m 1 ,
W e = W e E + W e M ,
W e E = 0 m 2 H 2 π a 3 2 m n [ j n 2 ( m k a ) - j n + 1 ( m k a ) j n - 1 ( m k a ) ] [ n ( n + 1 ) 2 n + 1 ] × { 2 c e m n t 2 m = 0 [ c e m n t 2 + c e m n t 2 ] [ ( n + m ) ! ( n - m ) ! ] m 1 ,
W e M = ( 0 m 2 H 2 π a 3 2 ) m n [ - 2 n ( m k a ) 2 j n 2 ( m k a ) + j n - 1 2 ( m k a ) - j n ( m k a ) j n - 2 ( m k a ) ] [ n ( n + 1 ) 2 n - 1 ] × { 2 d e m n t 2 m = 0 [ d e m n t 2 + d o m n t 2 ] [ ( n + m ) ! ( n - m ) ! ] m 1 .
R n e = D n W e ,
D n 0 m 2 H 2 π a 3 2 [ j n 2 ( m k a ) - j n + 1 ( m k a ) j n - 1 ( m k a ) ] × [ n ( n + 1 ) 2 n + 1 ] × m { 2 c e m n t 2 m = 0 [ c e m n t 2 + c o m n t 2 ] [ ( n + m ) ! ( n - m ) ! ] m 1 .
R n h = G n W e ,
G n = 0 m 2 H 2 π a 3 2 [ - 2 n ( m k a ) 2 j n 2 ( m k a ) + j n - 1 2 ( m k a ) - j n ( m k a ) j n - 2 ( m k a ) ] [ n ( n + 1 ) 2 n + 1 ] × m { 2 d e m n t 2 m = 0 [ d e m n t 2 + d o m n t 2 ] [ ( n + m ) ! ( n - m ) ! ] m 1 .
W norm = int E max int 2 0 E 0 2 = m 2 E max int 2 E 0 .
w e = ( W e / V ) ( 1 / 2 0 ) v E 0 2 d v ,

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