Abstract

Relying on van de Hulst’s localization principle, a localized approximation to the generalized Lorenz-Mie theory is introduced. The validation of this simple approximation is obtained from numerical comparisons the Rayleigh-Gans theory. Other comparisons concerning scattering profiles are carried out first with theoretical data published in the literature and later with experimental measurements. Original results are given for coal particles as an example of the versatility of the method.

© 1986 Optical Society of America

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  1. G. Gouesbet, M. Ledoux, “Supermicronic and Submicronic Optical Sizing Including a Discussion of Densely Laden Flows,” Opt. Eng. 23, 631 (1984).
    [CrossRef]
  2. G. Gouesbet et al., “Laser Optical Sizing from 100 Å to 1 mm Diameter and from 0 to 1 kg/m3 Concentration,” AIAA paper 85–1083, AIAA Twentieth Thermophysics Conference, Williamsburg, VA (19–21 June 1985).
  3. W. M. Farmer, “Measurement of Particle Size, Number Density, and Velocity Using a Laser Interferometer,” Appl. Opt. 11, 2603 (1972).
    [CrossRef] [PubMed]
  4. O. Schwebel, G. Gouesbet, J. N. Le Toulouzan, R. Darrigo, “The G-Scheme of Approximations to the Thermal Diffusion Factors: Explicit Formulae,” in Proceedings, International Symposium on Plasma Chemistry, Zurich, 27 Aug.–1 Sept. (1979).
  5. G. Gouesbet, “Optical Sizing with Emphasis on Simultaneous Measurements of Velocities and Sizes of Particles Embedded in Flows,” in Proceedings, Fifteenth International Symposium on Heat and Mass Transfer, Dubrovnik. Yugoslavia, 5–9 Sept. 1983.
  6. A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156 (1970).
    [CrossRef]
  7. A. Ashkin, J. M. Dziedzic, “Optical Levitation by Radiation Pressure,” Appl. Phys. Lett. 19, 283 (1971).
    [CrossRef]
  8. A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
    [CrossRef] [PubMed]
  9. G. Roosen, C. Imbert, “The TEM01 Mode Laser Beam: A Powerful Tool for Optical Levitation of Various Types of Spheres,” Opt. Commun. 26, 432 (1978).
    [CrossRef]
  10. G. Roosen, F. de Saint Louvent, S. Slansky, “Etude de la pression radiation exercée sur une sphère creuse transparente par un faisceau cylindrique,” Opt. Commun. 24, 116 (1978).
    [CrossRef]
  11. G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. 8, 181 (1977).
    [CrossRef]
  12. G. Roosen, S. Slansky, “Influence of the Beam Divergence on the Exerted Force on a Sphere by a Laser Beam and Required Conditions for Stable Optical Levitation,” Opt. Commun. 29, 341 (1979).
    [CrossRef]
  13. G. Gréhan, G. Gouesbet, “Optical Levitation of a Single Particle to Study the Theory of the Quasi-Elastic Scattering of Light,” Appl. Opt. 19, 2485 (1980).
    [CrossRef] [PubMed]
  14. G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorenz-Mie,” J. Opt. 13, 97 (1982).
    [CrossRef]
  15. H. W. Kogelnik, T. Li, “Laser Beams and Resonators,” Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]
  16. M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to Paraxial Optics,” Phys. Rev. A 11, 1365 (1975).
    [CrossRef]
  17. L. W. Davis, “Theory of Electromagnetic Beams,” Phys. Rev. A 19, 1177 (1979).
    [CrossRef]
  18. G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using Bromwich Functions,” J. Opt. Paris 16, 83 (1985).
    [CrossRef]
  19. 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 (1985).
    [CrossRef]
  20. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  21. G. Gouesbet, G. Gréhan, “Corrections for Mie Theory Given in “The Scattering of Light and Other Electromagnetic Radiations: Comments,” Appl. Opt. 23, 4462 (1984).
    [CrossRef]
  22. N. Morita, T. Tanaka, T. Yamasaki, Y. Nakanishi, “Scattering of a Beam Wave by a Spherical Object,” IEEE Trans. Antennas Propag. AP-16, 724 (1968).
    [CrossRef]
  23. W. C. Tsai, R. J. Pogorzelski, “Eigenfunction Solution of the Scattering of Beam Radiation Fields by Spherical Objects,” J. Opt. Soc. Am. 65, 1457 (1975).
    [CrossRef]
  24. W. G. Tam, R. Corriveau, “Scattering of Electromagnetic Beams by Spherical Objects,” J. Opt. Soc. Am. 68, 763 (1978).
    [CrossRef]
  25. C. W. Yeh, S. Colak, P. W. Barber, “Scattering of Sharply Focused Beams by Arbitrarily Shaped Dielectric Particles: an Exact Solution,” Appl. Opt. 21, 4426 (1982).
    [CrossRef] [PubMed]
  26. J. S. Kim, S. S. Lee, “Scattering of Laser Beams and the Optical Potential Well for a Homogeneous Sphere,” J. Opt. Soc. Am. 73, 303 (1983).
    [CrossRef]
  27. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  28. G. Gréhan, G. Gouesbet, “Mie Theory Calculations: New Progress, with Emphasis on Particle Sizing,” Appl. Opt. 18, 3489 (1979).
    [CrossRef] [PubMed]
  29. G. Gréhan, G. Gouesbet, C. Rabasse, “The Computer Program supermidi for Lorenz-Mie Theory and the Research of One-to-One Relationships for Particle Sizing,” in Proceedings, Symposium on Long Range and Short Range Optical Velocity Measurements, Institut Franco-Allemand de Saint-Louis, 15–18 Sept. 1980.
  30. W. Cherdron, F. Durst, G. Richter, “Computer Programs to Predict the Properties of Scattered Laser Radiation,” SFB 80/TM/121 (1978). Sonderforschungsbereich 80 “Ausbreitungsund Transportvorgänge in Strömungen”. Universtät-Karlsruhe.
  31. W. J. Lentz, “Generating Bessel Functions in Mie Scattering Calculations Using Continued Fractions,” Appl. Opt. 15, 668 (1976).
    [CrossRef] [PubMed]
  32. Lord Rayleigh, “On the Electromagnetic Theory of Light,” Philos. Mag. 12, 81 (1981).
  33. Lord Rayleigh, “The Incidence of Light upon a Transparent Sphere of Dimensions Comparable with the Wave-length,” Proc. R. Soc. London Ser. A 84, 25 (1910).
    [CrossRef]
  34. Lord Rayleigh, “On the Diffraction of Light by Spheres of Small Refractive Index,” Proc. R. Soc. London Ser. A 90, 219 (1914).
    [CrossRef]
  35. P. Debye, “Zerstreuung von Röntgenstrahlen,” Ann. Phys. Leipzig 46, 809 (1915).
    [CrossRef]
  36. R. Gans, “Strahlungsdiagramme ultramikroskopischer Teilchen,” Ann. Phys. Leipzig 76, 29 (1925).
    [CrossRef]
  37. G. Gouesbet, G. Gréhan, B. Maheu, “Single Scattering Characteristics of Volume Elements in Coal Clouds,” Appl. Opt. 22, 2038 (1983).
    [CrossRef] [PubMed]
  38. B. Maheu, J. N. Letoulouzan, G. Gouesbet, “Four-Flux Models to Solve the Scattering Transfer Equation in Terms of Lorenz-Mie Parameters,” Appl. Opt. 23, 3353 (1984).
    [CrossRef] [PubMed]
  39. P. Gougeon, J. N. Letoulouzan, G. Gouesbet, C. Thénard, “Optical Diagnosis in Multiple Scattering Media Using a Visible/Infrared Double Extinction Technique,” preparation.

1985

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using Bromwich Functions,” J. Opt. Paris 16, 83 (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 (1985).
[CrossRef]

1984

1983

1982

1981

1980

1979

G. Gréhan, G. Gouesbet, “Mie Theory Calculations: New Progress, with Emphasis on Particle Sizing,” Appl. Opt. 18, 3489 (1979).
[CrossRef] [PubMed]

G. Roosen, S. Slansky, “Influence of the Beam Divergence on the Exerted Force on a Sphere by a Laser Beam and Required Conditions for Stable Optical Levitation,” Opt. Commun. 29, 341 (1979).
[CrossRef]

L. W. Davis, “Theory of Electromagnetic Beams,” Phys. Rev. A 19, 1177 (1979).
[CrossRef]

1978

G. Roosen, C. Imbert, “The TEM01 Mode Laser Beam: A Powerful Tool for Optical Levitation of Various Types of Spheres,” Opt. Commun. 26, 432 (1978).
[CrossRef]

G. Roosen, F. de Saint Louvent, S. Slansky, “Etude de la pression radiation exercée sur une sphère creuse transparente par un faisceau cylindrique,” Opt. Commun. 24, 116 (1978).
[CrossRef]

W. G. Tam, R. Corriveau, “Scattering of Electromagnetic Beams by Spherical Objects,” J. Opt. Soc. Am. 68, 763 (1978).
[CrossRef]

1977

G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. 8, 181 (1977).
[CrossRef]

1976

1975

1972

1971

A. Ashkin, J. M. Dziedzic, “Optical Levitation by Radiation Pressure,” Appl. Phys. Lett. 19, 283 (1971).
[CrossRef]

1970

A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

1968

N. Morita, T. Tanaka, T. Yamasaki, Y. Nakanishi, “Scattering of a Beam Wave by a Spherical Object,” IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

1966

1925

R. Gans, “Strahlungsdiagramme ultramikroskopischer Teilchen,” Ann. Phys. Leipzig 76, 29 (1925).
[CrossRef]

1915

P. Debye, “Zerstreuung von Röntgenstrahlen,” Ann. Phys. Leipzig 46, 809 (1915).
[CrossRef]

1914

Lord Rayleigh, “On the Diffraction of Light by Spheres of Small Refractive Index,” Proc. R. Soc. London Ser. A 90, 219 (1914).
[CrossRef]

1910

Lord Rayleigh, “The Incidence of Light upon a Transparent Sphere of Dimensions Comparable with the Wave-length,” Proc. R. Soc. London Ser. A 84, 25 (1910).
[CrossRef]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Optical Levitation by Radiation Pressure,” Appl. Phys. Lett. 19, 283 (1971).
[CrossRef]

A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156 (1970).
[CrossRef]

Barber, P. W.

Cherdron, W.

W. Cherdron, F. Durst, G. Richter, “Computer Programs to Predict the Properties of Scattered Laser Radiation,” SFB 80/TM/121 (1978). Sonderforschungsbereich 80 “Ausbreitungsund Transportvorgänge in Strömungen”. Universtät-Karlsruhe.

Colak, S.

Corriveau, R.

Darrigo, R.

O. Schwebel, G. Gouesbet, J. N. Le Toulouzan, R. Darrigo, “The G-Scheme of Approximations to the Thermal Diffusion Factors: Explicit Formulae,” in Proceedings, International Symposium on Plasma Chemistry, Zurich, 27 Aug.–1 Sept. (1979).

Davis, L. W.

L. W. Davis, “Theory of Electromagnetic Beams,” Phys. Rev. A 19, 1177 (1979).
[CrossRef]

de Saint Louvent, F.

G. Roosen, F. de Saint Louvent, S. Slansky, “Etude de la pression radiation exercée sur une sphère creuse transparente par un faisceau cylindrique,” Opt. Commun. 24, 116 (1978).
[CrossRef]

Debye, P.

P. Debye, “Zerstreuung von Röntgenstrahlen,” Ann. Phys. Leipzig 46, 809 (1915).
[CrossRef]

Delaunay, B.

G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. 8, 181 (1977).
[CrossRef]

Durst, F.

W. Cherdron, F. Durst, G. Richter, “Computer Programs to Predict the Properties of Scattered Laser Radiation,” SFB 80/TM/121 (1978). Sonderforschungsbereich 80 “Ausbreitungsund Transportvorgänge in Strömungen”. Universtät-Karlsruhe.

Dziedzic, J. M.

Farmer, W. M.

Gans, R.

R. Gans, “Strahlungsdiagramme ultramikroskopischer Teilchen,” Ann. Phys. Leipzig 76, 29 (1925).
[CrossRef]

Gouesbet, G.

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 (1985).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using Bromwich Functions,” J. Opt. Paris 16, 83 (1985).
[CrossRef]

G. Gouesbet, M. Ledoux, “Supermicronic and Submicronic Optical Sizing Including a Discussion of Densely Laden Flows,” Opt. Eng. 23, 631 (1984).
[CrossRef]

B. Maheu, J. N. Letoulouzan, G. Gouesbet, “Four-Flux Models to Solve the Scattering Transfer Equation in Terms of Lorenz-Mie Parameters,” Appl. Opt. 23, 3353 (1984).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, “Corrections for Mie Theory Given in “The Scattering of Light and Other Electromagnetic Radiations: Comments,” Appl. Opt. 23, 4462 (1984).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Single Scattering Characteristics of Volume Elements in Coal Clouds,” Appl. Opt. 22, 2038 (1983).
[CrossRef] [PubMed]

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

G. Gréhan, G. Gouesbet, “Optical Levitation of a Single Particle to Study the Theory of the Quasi-Elastic Scattering of Light,” Appl. Opt. 19, 2485 (1980).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, “Mie Theory Calculations: New Progress, with Emphasis on Particle Sizing,” Appl. Opt. 18, 3489 (1979).
[CrossRef] [PubMed]

G. Gouesbet et al., “Laser Optical Sizing from 100 Å to 1 mm Diameter and from 0 to 1 kg/m3 Concentration,” AIAA paper 85–1083, AIAA Twentieth Thermophysics Conference, Williamsburg, VA (19–21 June 1985).

P. Gougeon, J. N. Letoulouzan, G. Gouesbet, C. Thénard, “Optical Diagnosis in Multiple Scattering Media Using a Visible/Infrared Double Extinction Technique,” preparation.

G. Gréhan, G. Gouesbet, C. Rabasse, “The Computer Program supermidi for Lorenz-Mie Theory and the Research of One-to-One Relationships for Particle Sizing,” in Proceedings, Symposium on Long Range and Short Range Optical Velocity Measurements, Institut Franco-Allemand de Saint-Louis, 15–18 Sept. 1980.

G. Gouesbet, “Optical Sizing with Emphasis on Simultaneous Measurements of Velocities and Sizes of Particles Embedded in Flows,” in Proceedings, Fifteenth International Symposium on Heat and Mass Transfer, Dubrovnik. Yugoslavia, 5–9 Sept. 1983.

O. Schwebel, G. Gouesbet, J. N. Le Toulouzan, R. Darrigo, “The G-Scheme of Approximations to the Thermal Diffusion Factors: Explicit Formulae,” in Proceedings, International Symposium on Plasma Chemistry, Zurich, 27 Aug.–1 Sept. (1979).

Gougeon, P.

P. Gougeon, J. N. Letoulouzan, G. Gouesbet, C. Thénard, “Optical Diagnosis in Multiple Scattering Media Using a Visible/Infrared Double Extinction Technique,” preparation.

Gréhan, G.

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 (1985).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using Bromwich Functions,” J. Opt. Paris 16, 83 (1985).
[CrossRef]

G. Gouesbet, G. Gréhan, “Corrections for Mie Theory Given in “The Scattering of Light and Other Electromagnetic Radiations: Comments,” Appl. Opt. 23, 4462 (1984).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Single Scattering Characteristics of Volume Elements in Coal Clouds,” Appl. Opt. 22, 2038 (1983).
[CrossRef] [PubMed]

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

G. Gréhan, G. Gouesbet, “Optical Levitation of a Single Particle to Study the Theory of the Quasi-Elastic Scattering of Light,” Appl. Opt. 19, 2485 (1980).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, “Mie Theory Calculations: New Progress, with Emphasis on Particle Sizing,” Appl. Opt. 18, 3489 (1979).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, C. Rabasse, “The Computer Program supermidi for Lorenz-Mie Theory and the Research of One-to-One Relationships for Particle Sizing,” in Proceedings, Symposium on Long Range and Short Range Optical Velocity Measurements, Institut Franco-Allemand de Saint-Louis, 15–18 Sept. 1980.

Imbert, C.

G. Roosen, C. Imbert, “The TEM01 Mode Laser Beam: A Powerful Tool for Optical Levitation of Various Types of Spheres,” Opt. Commun. 26, 432 (1978).
[CrossRef]

G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. 8, 181 (1977).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Kim, J. S.

Kogelnik, H. W.

Lax, M.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to Paraxial Optics,” Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Le Toulouzan, J. N.

O. Schwebel, G. Gouesbet, J. N. Le Toulouzan, R. Darrigo, “The G-Scheme of Approximations to the Thermal Diffusion Factors: Explicit Formulae,” in Proceedings, International Symposium on Plasma Chemistry, Zurich, 27 Aug.–1 Sept. (1979).

Ledoux, M.

G. Gouesbet, M. Ledoux, “Supermicronic and Submicronic Optical Sizing Including a Discussion of Densely Laden Flows,” Opt. Eng. 23, 631 (1984).
[CrossRef]

Lee, S. S.

Lentz, W. J.

Letoulouzan, J. N.

B. Maheu, J. N. Letoulouzan, G. Gouesbet, “Four-Flux Models to Solve the Scattering Transfer Equation in Terms of Lorenz-Mie Parameters,” Appl. Opt. 23, 3353 (1984).
[CrossRef] [PubMed]

P. Gougeon, J. N. Letoulouzan, G. Gouesbet, C. Thénard, “Optical Diagnosis in Multiple Scattering Media Using a Visible/Infrared Double Extinction Technique,” preparation.

Li, T.

Louisell, W. H.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to Paraxial Optics,” Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Maheu, B.

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using Bromwich Functions,” J. Opt. Paris 16, 83 (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 (1985).
[CrossRef]

B. Maheu, J. N. Letoulouzan, G. Gouesbet, “Four-Flux Models to Solve the Scattering Transfer Equation in Terms of Lorenz-Mie Parameters,” Appl. Opt. 23, 3353 (1984).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, B. Maheu, “Single Scattering Characteristics of Volume Elements in Coal Clouds,” Appl. Opt. 22, 2038 (1983).
[CrossRef] [PubMed]

McKnight, W. B.

M. Lax, W. H. Louisell, W. B. McKnight, “From Maxwell to Paraxial Optics,” Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Morita, N.

N. Morita, T. Tanaka, T. Yamasaki, Y. Nakanishi, “Scattering of a Beam Wave by a Spherical Object,” IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

Nakanishi, Y.

N. Morita, T. Tanaka, T. Yamasaki, Y. Nakanishi, “Scattering of a Beam Wave by a Spherical Object,” IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

Pogorzelski, R. J.

Rabasse, C.

G. Gréhan, G. Gouesbet, C. Rabasse, “The Computer Program supermidi for Lorenz-Mie Theory and the Research of One-to-One Relationships for Particle Sizing,” in Proceedings, Symposium on Long Range and Short Range Optical Velocity Measurements, Institut Franco-Allemand de Saint-Louis, 15–18 Sept. 1980.

Rayleigh, Lord

Lord Rayleigh, “On the Electromagnetic Theory of Light,” Philos. Mag. 12, 81 (1981).

Lord Rayleigh, “On the Diffraction of Light by Spheres of Small Refractive Index,” Proc. R. Soc. London Ser. A 90, 219 (1914).
[CrossRef]

Lord Rayleigh, “The Incidence of Light upon a Transparent Sphere of Dimensions Comparable with the Wave-length,” Proc. R. Soc. London Ser. A 84, 25 (1910).
[CrossRef]

Richter, G.

W. Cherdron, F. Durst, G. Richter, “Computer Programs to Predict the Properties of Scattered Laser Radiation,” SFB 80/TM/121 (1978). Sonderforschungsbereich 80 “Ausbreitungsund Transportvorgänge in Strömungen”. Universtät-Karlsruhe.

Roosen, G.

G. Roosen, S. Slansky, “Influence of the Beam Divergence on the Exerted Force on a Sphere by a Laser Beam and Required Conditions for Stable Optical Levitation,” Opt. Commun. 29, 341 (1979).
[CrossRef]

G. Roosen, C. Imbert, “The TEM01 Mode Laser Beam: A Powerful Tool for Optical Levitation of Various Types of Spheres,” Opt. Commun. 26, 432 (1978).
[CrossRef]

G. Roosen, F. de Saint Louvent, S. Slansky, “Etude de la pression radiation exercée sur une sphère creuse transparente par un faisceau cylindrique,” Opt. Commun. 24, 116 (1978).
[CrossRef]

G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. 8, 181 (1977).
[CrossRef]

Schwebel, O.

O. Schwebel, G. Gouesbet, J. N. Le Toulouzan, R. Darrigo, “The G-Scheme of Approximations to the Thermal Diffusion Factors: Explicit Formulae,” in Proceedings, International Symposium on Plasma Chemistry, Zurich, 27 Aug.–1 Sept. (1979).

Slansky, S.

G. Roosen, S. Slansky, “Influence of the Beam Divergence on the Exerted Force on a Sphere by a Laser Beam and Required Conditions for Stable Optical Levitation,” Opt. Commun. 29, 341 (1979).
[CrossRef]

G. Roosen, F. de Saint Louvent, S. Slansky, “Etude de la pression radiation exercée sur une sphère creuse transparente par un faisceau cylindrique,” Opt. Commun. 24, 116 (1978).
[CrossRef]

Tam, W. G.

Tanaka, T.

N. Morita, T. Tanaka, T. Yamasaki, Y. Nakanishi, “Scattering of a Beam Wave by a Spherical Object,” IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

Thénard, C.

P. Gougeon, J. N. Letoulouzan, G. Gouesbet, C. Thénard, “Optical Diagnosis in Multiple Scattering Media Using a Visible/Infrared Double Extinction Technique,” preparation.

Tsai, W. C.

van de Hulst, H. C.

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

Yamasaki, T.

N. Morita, T. Tanaka, T. Yamasaki, Y. Nakanishi, “Scattering of a Beam Wave by a Spherical Object,” IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

Yeh, C. W.

Ann. Phys. Leipzig

P. Debye, “Zerstreuung von Röntgenstrahlen,” Ann. Phys. Leipzig 46, 809 (1915).
[CrossRef]

R. Gans, “Strahlungsdiagramme ultramikroskopischer Teilchen,” Ann. Phys. Leipzig 76, 29 (1925).
[CrossRef]

Appl. Opt.

G. Gouesbet, G. Gréhan, B. Maheu, “Single Scattering Characteristics of Volume Elements in Coal Clouds,” Appl. Opt. 22, 2038 (1983).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, “Optical Levitation of a Single Particle to Study the Theory of the Quasi-Elastic Scattering of Light,” Appl. Opt. 19, 2485 (1980).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, “Corrections for Mie Theory Given in “The Scattering of Light and Other Electromagnetic Radiations: Comments,” Appl. Opt. 23, 4462 (1984).
[CrossRef]

H. W. Kogelnik, T. Li, “Laser Beams and Resonators,” Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

W. M. Farmer, “Measurement of Particle Size, Number Density, and Velocity Using a Laser Interferometer,” Appl. Opt. 11, 2603 (1972).
[CrossRef] [PubMed]

W. J. Lentz, “Generating Bessel Functions in Mie Scattering Calculations Using Continued Fractions,” Appl. Opt. 15, 668 (1976).
[CrossRef] [PubMed]

G. Gréhan, G. Gouesbet, “Mie Theory Calculations: New Progress, with Emphasis on Particle Sizing,” Appl. Opt. 18, 3489 (1979).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
[CrossRef] [PubMed]

C. W. Yeh, S. Colak, P. W. Barber, “Scattering of Sharply Focused Beams by Arbitrarily Shaped Dielectric Particles: an Exact Solution,” Appl. Opt. 21, 4426 (1982).
[CrossRef] [PubMed]

B. Maheu, J. N. Letoulouzan, G. Gouesbet, “Four-Flux Models to Solve the Scattering Transfer Equation in Terms of Lorenz-Mie Parameters,” Appl. Opt. 23, 3353 (1984).
[CrossRef] [PubMed]

Appl. Phys. Lett.

A. Ashkin, J. M. Dziedzic, “Optical Levitation by Radiation Pressure,” Appl. Phys. Lett. 19, 283 (1971).
[CrossRef]

IEEE Trans. Antennas Propag.

N. Morita, T. Tanaka, T. Yamasaki, Y. Nakanishi, “Scattering of a Beam Wave by a Spherical Object,” IEEE Trans. Antennas Propag. AP-16, 724 (1968).
[CrossRef]

J. Opt.

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

G. Roosen, B. Delaunay, C. Imbert, “Etude de la pression de radiation exercée par un faisceau lumineux sur une sphère réfringente,” J. Opt. 8, 181 (1977).
[CrossRef]

J. Opt. Paris

G. Gouesbet, G. Gréhan, B. Maheu, “Scattering of a Gaussian Beam by a Mie Scatter Center Using Bromwich Functions,” J. Opt. Paris 16, 83 (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 (1985).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

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[CrossRef]

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[CrossRef]

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[CrossRef]

Opt. Eng.

G. Gouesbet, M. Ledoux, “Supermicronic and Submicronic Optical Sizing Including a Discussion of Densely Laden Flows,” Opt. Eng. 23, 631 (1984).
[CrossRef]

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[CrossRef]

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[CrossRef]

Other

P. Gougeon, J. N. Letoulouzan, G. Gouesbet, C. Thénard, “Optical Diagnosis in Multiple Scattering Media Using a Visible/Infrared Double Extinction Technique,” preparation.

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W. Cherdron, F. Durst, G. Richter, “Computer Programs to Predict the Properties of Scattered Laser Radiation,” SFB 80/TM/121 (1978). Sonderforschungsbereich 80 “Ausbreitungsund Transportvorgänge in Strömungen”. Universtät-Karlsruhe.

G. Gouesbet et al., “Laser Optical Sizing from 100 Å to 1 mm Diameter and from 0 to 1 kg/m3 Concentration,” AIAA paper 85–1083, AIAA Twentieth Thermophysics Conference, Williamsburg, VA (19–21 June 1985).

O. Schwebel, G. Gouesbet, J. N. Le Toulouzan, R. Darrigo, “The G-Scheme of Approximations to the Thermal Diffusion Factors: Explicit Formulae,” in Proceedings, International Symposium on Plasma Chemistry, Zurich, 27 Aug.–1 Sept. (1979).

G. Gouesbet, “Optical Sizing with Emphasis on Simultaneous Measurements of Velocities and Sizes of Particles Embedded in Flows,” in Proceedings, Fifteenth International Symposium on Heat and Mass Transfer, Dubrovnik. Yugoslavia, 5–9 Sept. 1983.

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Figures (14)

Fig. 1
Fig. 1

Geometry of the scattering problem: Mie scatter center illuminated by an axisymmetric beam with Gaussian amplitude distribution.

Fig. 2
Fig. 2

Comparison of the GLMT (localized approximation) with Rayleigh-Gans: m = 1.001; λ = 0.5145 μm; d = 4 μm; α = 24.4; w0 = 5 μm.

Fig. 3
Fig. 3

Comparison of the GLMT (localized approximation) with Rayleigh-Gans: m = 1.001; λ = 0.5145 μm; d = 4 μm; α = 24.4; w0 = 0.5 μm.

Fig. 4
Fig. 4

Comparison of the GLMT (localized approximation) with Tsai and Pogorzelski Eθ polarization: m = 1.5–103i; λ = 0.5145 μm; d = 1.5076 μm; α = 9.2056; w0 = 1.029 μm.

Fig. 5
Fig. 5

Comparison of the GLMT (localized approximation) with Tsai and Pogorzelski Eφ polarization: m = 1.5–103i; λ = 0.5145 μm; d = 1.5076 μm; α = 9.2056; w0 = 1.029 μm.

Fig. 6
Fig. 6

Comparison of the GLMT (localized approximation) with Tsai and Pogorzelski Eθ polarization: m = 1.5–103i; λ = 0.5145 μm; d = 3.087 μm; α = 18.8496; w0 = 2.058 μm.

Fig. 7
Fig. 7

Comparison of the GLMT (localized approximation) with Tsai and Pogorzelski Eφ polarization: m = 1.5–103i; λ = 0.5145 μm; d = 3.087 μm; α = 18.8496; w0 = 2.058 μm.

Fig. 8
Fig. 8

Comparison of the GLMT (localized approximation) with Tsai and Pogorzelski Eθ polarization: m = 1.5–103i; λ = 0.5145 μm; d = 3.087 μm; α = 18.8496; w0 = 1.029 μm.

Fig. 9
Fig. 9

Comparison of the GLMT (localized approximation) with Tsai and Pogorzelski Eφ polarization: m = 1.5–103i; λ = 0.5145 μm; d = 3.087 μm; α = 18.8496; w0 = 1.029 μm.

Fig. 10
Fig. 10

Comparison of the GLMT (localized approximation) with Yeh et al.: m = 1.1; λ = 0.5145 μm; d = 0.81885 μm; α = 5; w0 = 0.61414 μm.

Fig. 11
Fig. 11

Scattering pattern for different beam radii: Eθ polarization: m = 1.5; = 0.5145 μm; d = 29.479 μm; a = 171.

Fig. 12
Fig. 12

Comparison between the GLMT (localized approximation) and experiment: Eθ polarization: m = 1.5; λ = 0.5145 μm; d = 29.479 μm; α = 171.

Fig. 13
Fig. 13

Scattering profile of coal particles for different beam radii: Eθ polarization: m = 1.999–0.6i; λ = 0.5145 μm; d = 16.377 μm; α = 100.

Fig. 14
Fig. 14

Scattering profile of coal particles for different beam radii: Eφ polarization: m = 1.999–0.6i; λ = 0.5145 μm; d = 16.377 μm; α = 100.

Equations (21)

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I θ = λ 2 4 π 2 r 2 S 2 2 cos 2 φ ,
I φ = λ 2 4 π 2 r 2 S 2 2 sin 2 φ ,
S 1 = n = 1 2 n + 1 n ( n + 1 ) g n [ a n π n ( cos θ ) + b n τ n ( cos θ ) ] ,
S 2 = n = 1 2 n + 1 n ( n + 1 ) g n [ a n π n ( cos θ ) + b n π n ( cos θ ) ] ,
tan γ = Re ( S 1 ) Im ( S 2 ) - Re ( S 1 ) Im ( S 2 ) Re ( S 1 ) Re ( S 2 ) - Im ( S 1 ) Im ( S 2 ) .
C sca = λ 2 2 π n = 1 ( 2 n + 1 ) ( a n 2 + b n 2 ) g 2 ,
C ext = λ 2 2 π Re n = 1 ( 2 n + 1 ) ( a n + b n ) g n 2 .
C pr = λ 2 2 π Re [ [ n = 1 ( 2 n + 1 ) a n + b n 2 g n 2 - n = 1 2 n + 1 n ( n + 1 ) a n * b n g n 2 - n = 1 n ( n + 2 ) n + 1 ( a n a n + 1 * + b n b n + 1 * ) g n g n + 1 * ]
g n = 2 n + 1 π n ( n + 1 ) · 1 ( - 1 ) i n n 0 π 0 i k r sin 2 θ · f · exp ( - i k r cos θ ) × ψ n 1 ( k r ) P n 1 ( cos θ ) d θ d ( k r ) ,
f ( r sin θ , r cos θ ) = ψ 0 ( 1 - 2 Q l r cos θ ) ,
Q = 1 ( i + 2 z / l ) .
A n = exp { - [ ( n + 1 2 λ ) 2 π ω 0 ] } .
g n = A n = exp { - [ ( n + 1 2 ) λ 2 π w 0 ] 2 } ;
δ = k d m - m e 1 ,
m - m e 1 ,
E ( r , θ , φ ) = E 0 exp ( - r 2 sin 2 θ w 0 2 ) ,
d a = 3 π r 0 λ 2 m 2 - 1 m 2 + 2 E ( r , θ , φ ) sin ( OP , E ) d v .
r 0 = 1 , φ 0 = π / 2 , ( OP , E ) = ( OP , Ox ) = π / 2.
d a = π ( m 2 - 1 ) λ 2 E 0 exp ( - r 2 sin 2 θ w 0 2 ) r 2 sin θ d r d θ d φ .
2 π δ λ = - ( 2 π λ ) ( 2 sin θ 0 2 ) · ( r cos θ 0 2 ) ( sin θ sin φ - tan θ 0 2 cos θ ) .
A ( θ 0 ) = 0 d / 2 0 π 0 2 π π ( m 2 - 1 ) λ 2 E 0 exp ( - r 2 sin 2 θ w 0 2 ) × sin 2 π [ t T + r sin θ 0 λ × ( sin θ sin φ - tan θ 0 2 · cos ) } r 2 sin θ d r d θ d φ .

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