Abstract

The intensity of light scattered by a coated sphere illuminated with an off-axis Gaussian beam is calculated. Results are shown for different beam positions with respect to the sphere. As the beam is shifted further away from the surface of the sphere, the higher-Q morphology-dependent resonances become increasingly important in the backscatter spectra, and the angular scattering intensity becomes smoother.

The scattered intensity depends on the beam position, the refractive indices of the core and coat, the radius of the core, and the thickness of the coat. As the beam is moved further away from the sphere, the effect of the core on the scattering intensity decreases. When the incident Gaussian beam is focused outside of a particle with a relatively small core, the scattering spectra and angular scattering patterns become similar to those of a homogeneous sphere having the refractive index of the coat. These calculated results suggest that measurements of spectral scattering and angular scattering patterns for several Gaussian beam positions could be useful for the characterization of coated spheres.

© 1994 Optical Society of America

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References

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  1. G. Gousbet, G. Grehan, eds., Optical Particle Sizing: Theory and Practice (Plenum, New York, 1988), pp. 55–635.
  2. A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
    [CrossRef] [PubMed]
  3. P. Chýlek, V. Ramaswamy, A. Ashkin, J. M. Dziedzic, “Simultaneous determination of refractive index and size of spherical particles from light-scattering data,” Appl. Opt. 22, 2302–2307 (1983).
    [CrossRef] [PubMed]
  4. A. Naqwi, F. Durst, G. Kraft, “Sizing of submicrometer particles using a phase-Doppler system,” Appl. Opt. 33, 4903–4913 (1991).
    [CrossRef]
  5. K. H. Hesselbacher, K. Anders, A. Frohn, “Experimental investigation of Gaussian beam effects on the accuracy of a droplet-sizing method,” Appl. Opt. 33, 4930–4935 (1991).
    [CrossRef]
  6. D. S. Ro, T. S. Fahlen, H. C. Bryant, “Precision measurements of water droplet evaporation rates,” Appl. Opt. 7, 883–890 (1968).
    [CrossRef] [PubMed]
  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. K. H. Fung, I. N. Tang, H. R. Munkelwitz, “Study of condensational growth of water droplets by Mie resonance spectroscopy,” Appl. Opt. 26, 1282–1287 (1987).
    [CrossRef] [PubMed]
  9. T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
    [CrossRef]
  10. I. N. Tang, H. R. Munkelwitz, “Determination of vapor pressure from droplet evaporation kinetics,” J. Colloid Interface Sci. 141, 109–118 (1991).
    [CrossRef]
  11. S. Arnold, E. K. Murphy, G. Sageev, “Aerosol particle molecular spectroscopy,” Appl. Opt. 24, 1048–1053 (1985).
    [CrossRef] [PubMed]
  12. S. C. Hill, R. E. Benner, C. K. Rushforth, P. R. Conwell, “Sizing dielectric spheres and cylinders by aligning measured and computed structural resonance locations: algorithm for multiple orders,” Appl. Opt. 24, 2380–2390 (1985).
    [CrossRef] [PubMed]
  13. A. Ashkin, J. M. Dziedzic, R. M. Stolen, “Outer diameter measurements of low birefringence optical fibers by a new resonant backscatter technique,” Appl. Opt. 20, 2299–2303(1981).
    [CrossRef] [PubMed]
  14. A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
    [CrossRef]
  15. O. B. Toon, T. P. Ackerman, “Algorithm for the calculation of scattering by stratified spheres,” Appl. Opt. 20, 3657–3660 (1981).
    [CrossRef] [PubMed]
  16. R. L. Hightower, C. B. Richardson, “Resonant Mie scattering from a layered sphere,” Appl. Opt. 27, 4850–4855 (1988).
    [CrossRef] [PubMed]
  17. J. A. Lock, “Interference enhancement of the internal fields at structural scattering resonances of a coated sphere,” Appl. Opt. 29, 3180–3187 (1990).
    [CrossRef] [PubMed]
  18. K. A. Fuller, “Scattering of light by coated spheres,” Opt. Lett. 18, 257–259 (1993).
    [CrossRef] [PubMed]
  19. R. L. Hightower, C. B. Richardson, H. B. Lin, J. D. Eversole, A. J. Campillo, “Measurement of scattering of light from layered microspheres,” Opt. Lett. 13, 946–948 (1988).
    [CrossRef] [PubMed]
  20. A. K. Ray, A. Souyri, E. J. Davis, T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. 30, 3974–3983 (1991).
    [CrossRef] [PubMed]
  21. D.-S. Wang, P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190–1197 (1979).
    [CrossRef] [PubMed]
  22. B. R. Johnson, “Invariant imbedding T matrix approach to electromagnetic scattering,” Appl. Opt. 27, 4861–4873 (1988).
    [CrossRef] [PubMed]
  23. 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]
  24. 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]
  25. 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).
  26. K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
    [CrossRef] [PubMed]
  27. C. F. Bohren, D. R. Huffman, Absorption and Scattering by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 82–129.
  28. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 9, pp. 119–130.
  29. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chaps. 3 and 4, pp. 79–242.
    [CrossRef]
  30. 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]
  31. 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]
  32. 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]
  33. 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]
  34. 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 (Department of Electrical and Computer Engineering, Clarkson University, Potsdam, N.Y., 1993).
  35. A. Yariv, Optical Electronics, 4th ed. (Holt, Rinehart & Winston, New York, 1991), Chap. 2, pp. 88–94.

1993 (2)

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]

1992 (3)

1991 (5)

1990 (2)

J. A. Lock, “Interference enhancement of the internal fields at structural scattering resonances of a coated sphere,” Appl. Opt. 29, 3180–3187 (1990).
[CrossRef] [PubMed]

T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
[CrossRef]

1989 (1)

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]

1988 (4)

1987 (1)

1985 (2)

1984 (1)

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]

1983 (1)

1981 (3)

1979 (1)

1968 (1)

1951 (1)

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Ackerman, T. P.

Aden, A. L.

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

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]

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]

Allen, T. M.

A. K. Ray, A. Souyri, E. J. Davis, T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. 30, 3974–3983 (1991).
[CrossRef] [PubMed]

T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
[CrossRef]

Anders, K.

Arnold, S.

Ashkin, A.

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]

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]

Benner, R. E.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 82–129.

Borghese, F.

Bryant, H. C.

Campillo, A. J.

Chang, R. K.

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]

Chowdhury, D. Q.

Chýlek, P.

Conwell, P. R.

Davis, E. J.

A. K. Ray, A. Souyri, E. J. Davis, T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. 30, 3974–3983 (1991).
[CrossRef] [PubMed]

T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
[CrossRef]

Denti, P.

Durst, F.

A. Naqwi, F. Durst, G. Kraft, “Sizing of submicrometer particles using a phase-Doppler system,” Appl. Opt. 33, 4903–4913 (1991).
[CrossRef]

Dziedzic, J. M.

Eversole, J. D.

Fahlen, T. S.

Frohn, A.

Fuller, K. A.

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

K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
[CrossRef] [PubMed]

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).

Fung, K. H.

Hesselbacher, K. H.

Hightower, R. L.

Hill, S. C.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 82–129.

Johnson, B. R.

Kerker, M.

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[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,” Ph.D. dissertation (Department of Electrical and Computer Engineering, Clarkson University, Potsdam, N.Y., 1993).

Kraft, G.

A. Naqwi, F. Durst, G. Kraft, “Sizing of submicrometer particles using a phase-Doppler system,” Appl. Opt. 33, 4903–4913 (1991).
[CrossRef]

Lin, H. B.

Lock, J. A.

J. A. Lock, “Interference enhancement of the internal fields at structural scattering resonances of a coated sphere,” Appl. Opt. 29, 3180–3187 (1990).
[CrossRef] [PubMed]

Long, M. B.

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]

Mazumder, M. M.

Munkelwitz, H. R.

I. N. Tang, H. R. Munkelwitz, “Determination of vapor pressure from droplet evaporation kinetics,” J. Colloid Interface Sci. 141, 109–118 (1991).
[CrossRef]

K. H. Fung, I. N. Tang, H. R. Munkelwitz, “Study of condensational growth of water droplets by Mie resonance spectroscopy,” Appl. Opt. 26, 1282–1287 (1987).
[CrossRef] [PubMed]

Murphy, E. K.

Naqwi, A.

A. Naqwi, F. Durst, G. Kraft, “Sizing of submicrometer particles using a phase-Doppler system,” Appl. Opt. 33, 4903–4913 (1991).
[CrossRef]

Ramaswamy, V.

Ray, A. K.

Richardson, C. B.

Ro, D. S.

Rushforth, C. K.

Sageev, G.

Saija, R.

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]

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]

Sindoni, O. I.

Souyri, A.

Stolen, R. M.

Taflin, D. C.

T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
[CrossRef]

Tang, I. N.

I. N. Tang, H. R. Munkelwitz, “Determination of vapor pressure from droplet evaporation kinetics,” J. Colloid Interface Sci. 141, 109–118 (1991).
[CrossRef]

K. H. Fung, I. N. Tang, H. R. Munkelwitz, “Study of condensational growth of water droplets by Mie resonance spectroscopy,” Appl. Opt. 26, 1282–1287 (1987).
[CrossRef] [PubMed]

Toon, O. B.

Tzeng, H.-M.

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]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 9, pp. 119–130.

Wall, K. F.

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]

Wang, D.-S.

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Holt, Rinehart & Winston, New York, 1991), Chap. 2, pp. 88–94.

Appl. Opt. (1)

J. A. Lock, “Interference enhancement of the internal fields at structural scattering resonances of a coated sphere,” Appl. Opt. 29, 3180–3187 (1990).
[CrossRef] [PubMed]

Appl. Opt. (16)

K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30, 4716–4731 (1991).
[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]

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

P. Chýlek, V. Ramaswamy, A. Ashkin, J. M. Dziedzic, “Simultaneous determination of refractive index and size of spherical particles from light-scattering data,” Appl. Opt. 22, 2302–2307 (1983).
[CrossRef] [PubMed]

A. Naqwi, F. Durst, G. Kraft, “Sizing of submicrometer particles using a phase-Doppler system,” Appl. Opt. 33, 4903–4913 (1991).
[CrossRef]

K. H. Hesselbacher, K. Anders, A. Frohn, “Experimental investigation of Gaussian beam effects on the accuracy of a droplet-sizing method,” Appl. Opt. 33, 4930–4935 (1991).
[CrossRef]

D. S. Ro, T. S. Fahlen, H. C. Bryant, “Precision measurements of water droplet evaporation rates,” Appl. Opt. 7, 883–890 (1968).
[CrossRef] [PubMed]

S. Arnold, E. K. Murphy, G. Sageev, “Aerosol particle molecular spectroscopy,” Appl. Opt. 24, 1048–1053 (1985).
[CrossRef] [PubMed]

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

A. Ashkin, J. M. Dziedzic, R. M. Stolen, “Outer diameter measurements of low birefringence optical fibers by a new resonant backscatter technique,” Appl. Opt. 20, 2299–2303(1981).
[CrossRef] [PubMed]

K. H. Fung, I. N. Tang, H. R. Munkelwitz, “Study of condensational growth of water droplets by Mie resonance spectroscopy,” Appl. Opt. 26, 1282–1287 (1987).
[CrossRef] [PubMed]

O. B. Toon, T. P. Ackerman, “Algorithm for the calculation of scattering by stratified spheres,” Appl. Opt. 20, 3657–3660 (1981).
[CrossRef] [PubMed]

R. L. Hightower, C. B. Richardson, “Resonant Mie scattering from a layered sphere,” Appl. Opt. 27, 4850–4855 (1988).
[CrossRef] [PubMed]

A. K. Ray, A. Souyri, E. J. Davis, T. M. Allen, “Precision of light scattering techniques for measuring optical parameters of microspheres,” Appl. Opt. 30, 3974–3983 (1991).
[CrossRef] [PubMed]

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

B. R. Johnson, “Invariant imbedding T matrix approach to electromagnetic scattering,” Appl. Opt. 27, 4861–4873 (1988).
[CrossRef] [PubMed]

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]

Ind. Eng. Chem. Res. (1)

T. M. Allen, D. C. Taflin, E. J. Davis, “Determination of activity coefficients via microdroplet evaporation experiments,” Ind. Eng. Chem. Res. 29, 682–690 (1990).
[CrossRef]

J. Appl. Phys. (1)

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. Appl. Phys. (2)

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. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

J. Colloid Interface Sci. (1)

I. N. Tang, H. R. Munkelwitz, “Determination of vapor pressure from droplet evaporation kinetics,” J. Colloid Interface Sci. 141, 109–118 (1991).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

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]

Opt. Lett. (2)

Other (7)

G. Gousbet, G. Grehan, eds., Optical Particle Sizing: Theory and Practice (Plenum, New York, 1988), pp. 55–635.

C. F. Bohren, D. R. Huffman, Absorption and Scattering by Small Particles (Wiley, New York, 1983), Chap. 4, pp. 82–129.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 9, pp. 119–130.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chaps. 3 and 4, pp. 79–242.
[CrossRef]

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 (Department of Electrical and Computer Engineering, Clarkson University, Potsdam, N.Y., 1993).

A. Yariv, Optical Electronics, 4th ed. (Holt, Rinehart & Winston, New York, 1991), Chap. 2, pp. 88–94.

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).

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Figures (3)

Fig. 1
Fig. 1

Spherical particle centered at the origin of a right-handed Cartesian-coordinate system (x, y, z). The spherical coordinate system (r, θ, ϕ) is shown. The sphere is either a homogeneous sphere with a radius a or a coated sphere with a coat and a core of radii rs and rc, respectively. The sphere is illuminated with a plane wave or a Gaussian beam. The intensity of the plane wave is E0 = 1. The beam has a spot size of w0 μm. The maximum field intensity at the beam’s focal point is 1. The beam’s focal point is at (x0, y0, z0). The incident waves propagate in the z direction.

Fig. 2
Fig. 2

Backscatter intensity of a homogeneous sphere (dashed curves) and a coated sphere (solid curves) as a function of the size parameter for Gaussian beam and plane wave illumination. The refractive index of the homogeneous sphere is m = 1.36. The coat of the coated sphere has a refractive index ms = 1.36 and its radius at each size parameter is rs. The refractive index of the core is mc = 1.5 and its radius is rc. The ratio of the core’s radius to the coat’s radius is R = rc/rs. The spot size of the beam is w0 = 1 μm and the beam’s focal point for all the cases is at x0 = 0 and z0 = 0. The wavelength of the incident wave is λ = 0.532 μm for all cases in Figs. 2 and 3. The results are calculated at p1(500ā, 180°, 0°), ā = 2.93357 μm (the radius of the sphere corresponding to TE41,1 MDR). (a) on-axis Gaussian beam, y0 = 0, and R = 0.7, (b)y0/ā = 0.5 and R = 0.7, (c)y0/ā = 1.0 and R = 0.7, (d)y0/ā = 1.0 and R = 0.82, (e) y0/ā = 1.5 and R = 0.7, (f) y0/ā = 1.5 and R = 0.82, and (g) plane wave illumination with R = 0.7.

Fig. 3
Fig. 3

Angular scattering intensity of a homogeneous sphere of m = 1.36 (dashed curves) and a coated sphere of ms = 1.36 and mc = 1.5 (solid curves) as a function of the spherical coordinate angle θ for a plane wave and a Gaussian beam illumination. All the parameters of the incident beam are the same as in the case of Fig. 2. The results are calculated at p1(500ā, θ°, 0°) for a sphere of size parameter x = 34.6469129 corresponding to the TE41,1 MDR with Q = 7.87 × 103. (a) on-axis Gaussian beam and R = 0.7, (b) y0/ā = 0.5 and R = 0.7, (c) y0/ā = 1.0 and R = 0.7, (d) y0/ā = 1.0 and R = 0.82, (e) y0/ā = 1.5 and R = 0.7, and (f) y0/ā = 1.5 and R = 0.82.

Equations (6)

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

E i ( k r ) = 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 s ( k r ) = 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 ) ] ,
f e m n t = [ T 11 ] a e m n t , f o m n t = [ T 22 ] a o m n t , g e m n t = [ T 33 ] b e m n t , g o m n t = [ T 44 ] b o m n t ,
[ T 11 ] = [ T 22 ] = ( b n ) * , [ T 33 ] = [ T 44 ] = ( a n ) * ,
Δ f = c 4 m a ,
Δ x = π 2 m .

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