Abstract

The forward scattering of a Gaussian laser beam by a spherical particle located along the beam axis is analyzed with the generalized Lorenz–Mie theory (GLMT) and with diffraction theory. Forward-scattering and near-forward-scattering profiles from electrodynamically levitated droplets, 51.6 μm in diameter, are also presented and compared with GLMT-based predictions. The total intensity in the forward direction, formed by the superposition of the incident and the scattered fields, is found to correlate with the particle-extinction cross section, the particle diameter, and the beam width. Based on comparison with the GLMT, the diffraction solution is accurate when beam widths that are approximately greater than or equal to the particle diameter are considered and when large particles that have an extinction efficiency near the asymptotic value of 2 are considered. However, diffraction fails to describe the forward intensity for more tightly focused beams. The experimental observations, which are in good agreement with GLMT-based predictions, reveal that the total intensity profile about the forward direction is quite sensitive to particle axial position within a Gaussian beam. These finite beam effects are significant when the ratio of the beam to the particle diameter is less than approximately 5:1. For larger beam-to-particle-diameter ratios, the total field in the forward direction is dominated by the incident beam.

© 1995 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  32. G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
    [CrossRef] [PubMed]
  33. F. Slimani, G. Gréhan, G. Gouesbet, D. Allano, “Near-field Lorenz–Mie theory and its application to microholography,” Appl. Opt. 23, 4140–4148 (1984).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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1994 (1)

1993 (3)

J. A. Lock, Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle,” J. Opt. Soc. Am. A 10, 693–706 (1993).
[CrossRef]

J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Laser sheet scattering from spherical particles,” Part. Part. Syst. Char. 10, 146–151 (1993).
[CrossRef]

1992 (3)

E. J. Davis, “Microchemical engineering: the physics and chemistry of the microparticle,” Adv. Chem. Eng. 18, 1–95 (1992).
[CrossRef]

G. Gréhan, G. Gouesbet, F. Guilloteau, J. P. Chevaillier, “Comparison of the diffraction theory and the generalized Lorenz–Mie theory for a sphere arbitrarily located into a laser beam,” Opt. Commun. 90, 1–6 (1992).
[CrossRef]

F. Guilloteau, G. Gréhan, G. Gouesbet, “Optical levitation experiments to assess the validity of the GLMT,” Appl. Opt. 31, 2942–2951 (1992).
[CrossRef] [PubMed]

1991 (1)

1990 (2)

1989 (1)

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]

1988 (4)

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
[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]

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

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

1985 (3)

E. J. Davis, “Electrodynamic balance stability characteristics and applications to the study of aerocolloidal particles,” Langmuir 1, 379–387 (1985).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. (Paris) 16, 83–93 (1985).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “The order of approximation in a theory of the scattering of a Gaussian beam by a Mie scatter center,” J. Opt. (Paris) 16, 239–247 (1985).
[CrossRef]

1984 (1)

1982 (1)

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

1981 (1)

1980 (1)

1979 (1)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

1978 (1)

1977 (1)

1975 (1)

1974 (1)

E. J. Davis, E. Chorbajian, “The measurement of evaporation rates of submicron aerosol droplets,” Indust. Eng. Chem. Fundam. 13, 272–277 (1974).
[CrossRef]

1968 (1)

N. Morita, T. Tanaka, T. Yamasaki, Y. Nahanishi, “Scattering of a beam wave by a spherical object,” IEEE Trans. Antennas Propag. AP-16, 724–727 (1968).
[CrossRef]

1966 (1)

H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[CrossRef]

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

1890 (1)

L. Lorenz, “Lysbevaegelsen i og uden for en half plane lysbölger belyst Kulge,” Vidensk. Selk. Skr. 6, 1–62 (1890).

Alexander, D. R.

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]

Allano, D.

Barton, J. P.

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]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 3, p. 57.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small ParticlesWiley, New York, 1983), Chap. 4, p. 118.

Casperson, L. W.

Chen, S. H.

Chevaillier, J. P.

G. Gréhan, G. Gouesbet, F. Guilloteau, J. P. Chevaillier, “Comparison of the diffraction theory and the generalized Lorenz–Mie theory for a sphere arbitrarily located into a laser beam,” Opt. Commun. 90, 1–6 (1992).
[CrossRef]

J. P. Chevaillier, J. Fabre, G. Gréhan, G. Gouesbet, “Comparison of diffraction theory and generalized Lorenz–Mie theory for a sphere located on the axis of a laser beam,” Appl. Opt. 29, 1293–1298 (1990).
[CrossRef] [PubMed]

Chorbajian, E.

E. J. Davis, E. Chorbajian, “The measurement of evaporation rates of submicron aerosol droplets,” Indust. Eng. Chem. Fundam. 13, 272–277 (1974).
[CrossRef]

Corriveau, R.

Davis, E. J.

E. J. Davis, “Microchemical engineering: the physics and chemistry of the microparticle,” Adv. Chem. Eng. 18, 1–95 (1992).
[CrossRef]

E. J. Davis, “Electrodynamic balance stability characteristics and applications to the study of aerocolloidal particles,” Langmuir 1, 379–387 (1985).
[CrossRef]

E. J. Davis, E. Chorbajian, “The measurement of evaporation rates of submicron aerosol droplets,” Indust. Eng. Chem. Fundam. 13, 272–277 (1974).
[CrossRef]

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Fabre, J.

Glantschnig, W. J.

Gouesbet, G.

J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz–Mie theory. I: On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Laser sheet scattering from spherical particles,” Part. Part. Syst. Char. 10, 146–151 (1993).
[CrossRef]

F. Guilloteau, G. Gréhan, G. Gouesbet, “Optical levitation experiments to assess the validity of the GLMT,” Appl. Opt. 31, 2942–2951 (1992).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, F. Guilloteau, J. P. Chevaillier, “Comparison of the diffraction theory and the generalized Lorenz–Mie theory for a sphere arbitrarily located into a laser beam,” Opt. Commun. 90, 1–6 (1992).
[CrossRef]

J. P. Chevaillier, J. Fabre, G. Gréhan, G. Gouesbet, “Comparison of diffraction theory and generalized Lorenz–Mie theory for a sphere located on the axis of a laser beam,” Appl. Opt. 29, 1293–1298 (1990).
[CrossRef] [PubMed]

G. Gréhan, F. Guilloteau, G. Gouesbet, “GLMT-validations: the off-axis case,” Part. Part. Syst. Char. 7, 248–249 (1990).
[CrossRef]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

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

G. Gouesbet, B. Maheu, G. Gréhan, “The order of approximation in a theory of the scattering of a Gaussian beam by a Mie scatter center,” J. Opt. (Paris) 16, 239–247 (1985).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. (Paris) 16, 83–93 (1985).
[CrossRef]

F. Slimani, G. Gréhan, G. Gouesbet, D. Allano, “Near-field Lorenz–Mie theory and its application to microholography,” Appl. Opt. 23, 4140–4148 (1984).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

G. Gréhan, G. Gouesbet, “Optical levitation of a single particle to study the theory of quasi-elastic scattering of light,” Appl. Opt. 19, 2485–2487 (1980).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light-scattering calculations,” Appl. Opt. (to be published).

Gréhan, G.

K. F. Ren, G. Gréhan, G. Gouesbet, “Laser sheet scattering from spherical particles,” Part. Part. Syst. Char. 10, 146–151 (1993).
[CrossRef]

F. Guilloteau, G. Gréhan, G. Gouesbet, “Optical levitation experiments to assess the validity of the GLMT,” Appl. Opt. 31, 2942–2951 (1992).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, F. Guilloteau, J. P. Chevaillier, “Comparison of the diffraction theory and the generalized Lorenz–Mie theory for a sphere arbitrarily located into a laser beam,” Opt. Commun. 90, 1–6 (1992).
[CrossRef]

J. P. Chevaillier, J. Fabre, G. Gréhan, G. Gouesbet, “Comparison of diffraction theory and generalized Lorenz–Mie theory for a sphere located on the axis of a laser beam,” Appl. Opt. 29, 1293–1298 (1990).
[CrossRef] [PubMed]

G. Gréhan, F. Guilloteau, G. Gouesbet, “GLMT-validations: the off-axis case,” Part. Part. Syst. Char. 7, 248–249 (1990).
[CrossRef]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

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

G. Gouesbet, B. Maheu, G. Gréhan, “The order of approximation in a theory of the scattering of a Gaussian beam by a Mie scatter center,” J. Opt. (Paris) 16, 239–247 (1985).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. (Paris) 16, 83–93 (1985).
[CrossRef]

F. Slimani, G. Gréhan, G. Gouesbet, D. Allano, “Near-field Lorenz–Mie theory and its application to microholography,” Appl. Opt. 23, 4140–4148 (1984).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

G. Gréhan, G. Gouesbet, “Optical levitation of a single particle to study the theory of quasi-elastic scattering of light,” Appl. Opt. 19, 2485–2487 (1980).
[CrossRef] [PubMed]

J. T. Hodges, G. Gréhan, C. Presser, H. G. Semerjian, “Elastic scattering from spheres under non plane-wave illumination,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1862, 294–308 (1993).

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light-scattering calculations,” Appl. Opt. (to be published).

Guilloteau, F.

F. Guilloteau, G. Gréhan, G. Gouesbet, “Optical levitation experiments to assess the validity of the GLMT,” Appl. Opt. 31, 2942–2951 (1992).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, F. Guilloteau, J. P. Chevaillier, “Comparison of the diffraction theory and the generalized Lorenz–Mie theory for a sphere arbitrarily located into a laser beam,” Opt. Commun. 90, 1–6 (1992).
[CrossRef]

G. Gréhan, F. Guilloteau, G. Gouesbet, “GLMT-validations: the off-axis case,” Part. Part. Syst. Char. 7, 248–249 (1990).
[CrossRef]

Hamelin, P.

P. Hamelin, “Application de la diffusion lumineuse à la métrologie des particules en écoulement diphasique dispersé,” Ph.D. dissertation (l’Institut National Polytechnique de Toulouse, Toulouse, France, 1986).

Hecht, E.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974), Chap. 11, p. 397.

Hodges, J. T.

J. T. Hodges, G. Gréhan, C. Presser, H. G. Semerjian, “Elastic scattering from spheres under non plane-wave illumination,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1862, 294–308 (1993).

Hovenac, E. A.

J. A. Lock, E. A. Hovenac, “Diffraction of a Gaussian beam by a spherical obstacle,” Am. J. Phys. 61, 698–707 (1993).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 3, p. 57.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small ParticlesWiley, New York, 1983), Chap. 4, p. 118.

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, San Diego, Calif., 1969), Chap. 3, p. 27.

Kogelnik, H.

H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[CrossRef]

Li, T.

H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[CrossRef]

Lock, J. A.

Lorenz, L.

L. Lorenz, “Lysbevaegelsen i og uden for en half plane lysbölger belyst Kulge,” Vidensk. Selk. Skr. 6, 1–62 (1890).

Maheu, B.

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz–Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt. (Paris) 19, 59–67 (1988).
[CrossRef]

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

G. Gouesbet, G. Gréhan, B. Maheu, “Computations of the gn coefficients in the generalized Lorenz–Mie theory using three different methods,” Appl. Opt. 27, 4874–4883 (1988).
[CrossRef] [PubMed]

G. Gouesbet, B. Maheu, G. Gréhan, “The order of approximation in a theory of the scattering of a Gaussian beam by a Mie scatter center,” J. Opt. (Paris) 16, 239–247 (1985).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian beam by a Mie scatter center using a Bromwich formalism,” J. Opt. (Paris) 16, 83–93 (1985).
[CrossRef]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Morita, N.

N. Morita, T. Tanaka, T. Yamasaki, Y. Nahanishi, “Scattering of a beam wave by a spherical object,” IEEE Trans. Antennas Propag. AP-16, 724–727 (1968).
[CrossRef]

Nahanishi, Y.

N. Morita, T. Tanaka, T. Yamasaki, Y. Nahanishi, “Scattering of a beam wave by a spherical object,” IEEE Trans. Antennas Propag. AP-16, 724–727 (1968).
[CrossRef]

Pogorzelski, R. J.

Presser, C.

J. T. Hodges, G. Gréhan, C. Presser, H. G. Semerjian, “Elastic scattering from spheres under non plane-wave illumination,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1862, 294–308 (1993).

Ren, K. F.

K. F. Ren, G. Gréhan, G. Gouesbet, “Laser sheet scattering from spherical particles,” Part. Part. Syst. Char. 10, 146–151 (1993).
[CrossRef]

Schaub, S. A.

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H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 13, p. 231.

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H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 13, p. 231.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), Chap. 3, p. 57.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974), Chap. 11, p. 397.

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light-scattering calculations,” Appl. Opt. (to be published).

J. T. Hodges, G. Gréhan, C. Presser, H. G. Semerjian, “Elastic scattering from spheres under non plane-wave illumination,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed. Proc. Soc. Photo-Opt. Instrum. Eng.1862, 294–308 (1993).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small ParticlesWiley, New York, 1983), Chap. 4, p. 118.

P. Hamelin, “Application de la diffusion lumineuse à la métrologie des particules en écoulement diphasique dispersé,” Ph.D. dissertation (l’Institut National Polytechnique de Toulouse, Toulouse, France, 1986).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 9, p. 114.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, San Diego, Calif., 1969), Chap. 3, p. 27.

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