Abstract

We present numerical results concerning the properties of the electromagnetic field scattered by an infinite circular cylinder illuminated by a circular Gaussian beam. The cylinder is arbitrarily located and arbitrarily oriented with respect to the illuminating Gaussian beam. Numerical evaluations are provided within the framework of a rigorous electromagnetic theory, the generalized Lorenz–Mie theory, for infinite cylinders. This theory provides new insights that could not be obtained from older formulations, i.e., geometrical optics and plane-wave scattering. In particular, some emphasis is laid on the waveguiding effect and on the rainbow phenomenon whose fine structure is hardly predictable by use of geometrical optics.

© 1999 Optical Society of America

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    [CrossRef]
  3. H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 25, 5180–5190 (1996).
    [CrossRef]
  4. D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
    [CrossRef]
  5. N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler Anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).
  6. G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder, including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
    [CrossRef]
  7. G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995).
    [CrossRef]
  8. G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
    [CrossRef]
  9. G. Gouesbet, “Scattering of higher-order Gaussian beams by an infinite cylinder,” J. Opt. (Paris) 28, 45–65 (1997).
    [CrossRef]
  10. G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary-shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
    [CrossRef] [PubMed]
  11. 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]
  12. F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
    [CrossRef] [PubMed]
  13. J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. 33, 189–195 (1955).
  14. S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
    [CrossRef]
  15. S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
    [CrossRef]
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    [CrossRef]
  18. J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder. II. The interaction S-matrix and morphology dependent resonances,” J. Opt. Soc. Am. A 14, 653–661 (1997).
    [CrossRef]
  19. K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in the GLMT framework: formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
    [CrossRef]
  20. T. J. Bromwich, “Electromagnetic waves,” Phil. Mag. 38, 143–164 (1919).
    [CrossRef]
  21. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  22. G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
    [CrossRef] [PubMed]
  23. G. Gouesbet, K. F. Ren, G. Gréhan, “Rigorous justification of the cylindrical approximation to speed up computations in GLMT for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
    [CrossRef]
  24. G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation to speed up computations in the GLMT for cylinders, for arbitrary location and orientation of the scatterer,” Appl. Opt. (to be published).
  25. 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]
  26. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods, (World Scientific, Singapore, 1990), Chap. 2.
  27. S. Choudhary, L. Felsen, “Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking,” Proc. IEEE 62, 1530–1541 (1974).
    [CrossRef]
  28. C. W. Chan, W. K. Lee, “Measurement of a liquid refractive index by using high-order rainbows,” J. Opt. Soc. Am. B 13, 532–535 (1996).
    [CrossRef]
  29. C. L. Adler, J. A. Lock, B. R. Stone, C. J. Garcia, “High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder,” J. Opt. Soc. Am. A 14, 1305–1315 (1997).
    [CrossRef]
  30. J. A. Lock, C. L. Adler, “Debye-series analysis of the first-order rainbow produced in scattering of a diagonally incident plane wave by a circular cylinder,” J. Opt. Soc. Am. A 14, 1316–1328 (1997).
    [CrossRef]
  31. P. L. Marston, “Descartes glare points in scattering by icicles: color photographs and a tilted dielectric cylinder model of caustic and glare-point evolution,” Appl. Opt. 37, 1551–1556 (1998).
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  32. C. M. Mount, D. B. Thiessen, P. L. Marston, “Scattering observations for tilted transparent fibers: evolution of Airy caustics with cylinder tilt and the caustic merging transition,” Appl. Opt. 37, 1534–1539 (1998).
    [CrossRef]
  33. W. Möbius, “Zur Theorie des Regenbogens und ihrer experimentellen Prüfung,” Ann. Phys. (Leipzig) 4, 1498–1558 (1911).
  34. J. P. A. J. van Beeck, M. L. Riethmuller, “Surface integral method to quantify the droplet non-sphericity effect on rainbow thermometry,” presented at the AGARD Symposium on Advanced Aerodynamic Measurement Technology, Seattle, Wash., 22–25 September 1997.
  35. N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
    [CrossRef]
  36. S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fidrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, M. Maeda, ed., 23–26 August 1993.
  37. J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
    [CrossRef] [PubMed]
  38. F. Corbin, A. Garo, G. Gouesbet, G. Gréhan, “Réfractométrie d’arc-en-ciel: application au diagnostic de gouttes avec gradient d’indice,” presented at the 5ème Congrès Francophone de Vélocimétrie Laser, Rouen, France, 24–27 September 1996.
  39. C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers, presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.
  40. X. Han, Z. S. Wu, F. Corbin, G. Gréhan, K. F. Ren, G. Gouesbet, “Measurements of first and second rainbows of liquid jet and fiber” presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.
  41. 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]
  42. G. Gouesbet, L. Mees, G. Gréhan, “Partial wave description of shaped beams in elliptical cylinder coordinates,” J. Opt. Soc. Am. A 15, 3028–3038 (1998).
    [CrossRef]

1998 (4)

1997 (8)

C. L. Adler, J. A. Lock, B. R. Stone, C. J. Garcia, “High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder,” J. Opt. Soc. Am. A 14, 1305–1315 (1997).
[CrossRef]

J. A. Lock, C. L. Adler, “Debye-series analysis of the first-order rainbow produced in scattering of a diagonally incident plane wave by a circular cylinder,” J. Opt. Soc. Am. A 14, 1316–1328 (1997).
[CrossRef]

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler Anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

G. Gouesbet, “Scattering of higher-order Gaussian beams by an infinite cylinder,” J. Opt. (Paris) 28, 45–65 (1997).
[CrossRef]

G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary-shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
[CrossRef] [PubMed]

J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder. I. Parameterization of the incident beam and the far-zone scattered intensity,” J. Opt. Soc. Am. A 14, 640–652 (1997).
[CrossRef]

J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder. II. The interaction S-matrix and morphology dependent resonances,” J. Opt. Soc. Am. A 14, 653–661 (1997).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in the GLMT framework: formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

1996 (5)

J. A. Ferrari, E. M. Frins, “Interferometric method for fiber diameter determination,” Opt. Eng. 35, 1050–1053 (1996).
[CrossRef]

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 25, 5180–5190 (1996).
[CrossRef]

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
[CrossRef] [PubMed]

C. W. Chan, W. K. Lee, “Measurement of a liquid refractive index by using high-order rainbows,” J. Opt. Soc. Am. B 13, 532–535 (1996).
[CrossRef]

1995 (5)

1994 (1)

G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder, including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
[CrossRef]

1993 (1)

1990 (1)

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

1988 (1)

1984 (1)

1982 (2)

S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
[CrossRef]

S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
[CrossRef]

1979 (1)

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

1974 (1)

S. Choudhary, L. Felsen, “Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking,” Proc. IEEE 62, 1530–1541 (1974).
[CrossRef]

1973 (1)

H. M. Presby, “Refractive index and diameter measurements of unclad fibers,” Opt. Soc. Am. A 64, 280–284 (1973).

1955 (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. 33, 189–195 (1955).

1919 (1)

T. J. Bromwich, “Electromagnetic waves,” Phil. Mag. 38, 143–164 (1919).
[CrossRef]

1911 (1)

W. Möbius, “Zur Theorie des Regenbogens und ihrer experimentellen Prüfung,” Ann. Phys. (Leipzig) 4, 1498–1558 (1911).

Adler, C. L.

Allano, D.

Anders, K.

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

Bachalo, W. D.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fidrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, M. Maeda, ed., 23–26 August 1993.

Barber, P. W.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods, (World Scientific, Singapore, 1990), Chap. 2.

Belaid, S.

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

Bromwich, T. J.

T. J. Bromwich, “Electromagnetic waves,” Phil. Mag. 38, 143–164 (1919).
[CrossRef]

Buermann, D. H.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fidrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, M. Maeda, ed., 23–26 August 1993.

Chan, C. W.

Choudhary, S.

S. Choudhary, L. Felsen, “Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking,” Proc. IEEE 62, 1530–1541 (1974).
[CrossRef]

Corbin, C.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers, presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

Corbin, F.

F. Corbin, A. Garo, G. Gouesbet, G. Gréhan, “Réfractométrie d’arc-en-ciel: application au diagnostic de gouttes avec gradient d’indice,” presented at the 5ème Congrès Francophone de Vélocimétrie Laser, Rouen, France, 24–27 September 1996.

X. Han, Z. S. Wu, F. Corbin, G. Gréhan, K. F. Ren, G. Gouesbet, “Measurements of first and second rainbows of liquid jet and fiber” presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

Dändliker, R.

Davis, L. W.

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

Felsen, L.

S. Choudhary, L. Felsen, “Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking,” Proc. IEEE 62, 1530–1541 (1974).
[CrossRef]

Ferrari, J. A.

J. A. Ferrari, E. M. Frins, “Interferometric method for fiber diameter determination,” Opt. Eng. 35, 1050–1053 (1996).
[CrossRef]

Fidrich, M. J.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fidrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, M. Maeda, ed., 23–26 August 1993.

Frins, E. M.

J. A. Ferrari, E. M. Frins, “Interferometric method for fiber diameter determination,” Opt. Eng. 35, 1050–1053 (1996).
[CrossRef]

Frohn, A.

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

Garcia, C. J.

Garo, A.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers, presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

F. Corbin, A. Garo, G. Gouesbet, G. Gréhan, “Réfractométrie d’arc-en-ciel: application au diagnostic de gouttes avec gradient d’indice,” presented at the 5ème Congrès Francophone de Vélocimétrie Laser, Rouen, France, 24–27 September 1996.

Gauchet, N.

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler Anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

Girasole, T.

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler Anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

Gouesbet, G.

G. Gouesbet, K. F. Ren, G. Gréhan, “Rigorous justification of the cylindrical approximation to speed up computations in GLMT for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, “Partial wave description of shaped beams in elliptical cylinder coordinates,” J. Opt. Soc. Am. A 15, 3028–3038 (1998).
[CrossRef]

G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary-shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
[CrossRef] [PubMed]

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in the GLMT framework: formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler Anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

G. Gouesbet, “Scattering of higher-order Gaussian beams by an infinite cylinder,” J. Opt. (Paris) 28, 45–65 (1997).
[CrossRef]

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 25, 5180–5190 (1996).
[CrossRef]

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995).
[CrossRef]

G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
[CrossRef]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder, including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
[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]

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]

G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation to speed up computations in the GLMT for cylinders, for arbitrary location and orientation of the scatterer,” Appl. Opt. (to be published).

F. Corbin, A. Garo, G. Gouesbet, G. Gréhan, “Réfractométrie d’arc-en-ciel: application au diagnostic de gouttes avec gradient d’indice,” presented at the 5ème Congrès Francophone de Vélocimétrie Laser, Rouen, France, 24–27 September 1996.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers, presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

X. Han, Z. S. Wu, F. Corbin, G. Gréhan, K. F. Ren, G. Gouesbet, “Measurements of first and second rainbows of liquid jet and fiber” presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

Gréhan, G.

G. Gouesbet, K. F. Ren, G. Gréhan, “Rigorous justification of the cylindrical approximation to speed up computations in GLMT for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
[CrossRef]

G. Gouesbet, L. Mees, G. Gréhan, “Partial wave description of shaped beams in elliptical cylinder coordinates,” J. Opt. Soc. Am. A 15, 3028–3038 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in the GLMT framework: formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler Anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 25, 5180–5190 (1996).
[CrossRef]

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder, including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
[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]

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]

G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation to speed up computations in the GLMT for cylinders, for arbitrary location and orientation of the scatterer,” Appl. Opt. (to be published).

X. Han, Z. S. Wu, F. Corbin, G. Gréhan, K. F. Ren, G. Gouesbet, “Measurements of first and second rainbows of liquid jet and fiber” presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

F. Corbin, A. Garo, G. Gouesbet, G. Gréhan, “Réfractométrie d’arc-en-ciel: application au diagnostic de gouttes avec gradient d’indice,” presented at the 5ème Congrès Francophone de Vélocimétrie Laser, Rouen, France, 24–27 September 1996.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers, presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

Han, X.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers, presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

X. Han, Z. S. Wu, F. Corbin, G. Gréhan, K. F. Ren, G. Gouesbet, “Measurements of first and second rainbows of liquid jet and fiber” presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

Hill, S. C.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods, (World Scientific, Singapore, 1990), Chap. 2.

Ibrahim, K. M.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fidrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, M. Maeda, ed., 23–26 August 1993.

Kozaki, S.

S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
[CrossRef]

S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
[CrossRef]

Krattiger, B.

Lebrun, D.

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

Lee, W. K.

Lock, J. A.

Maheu, B.

Marston, P. L.

Mees, L.

G. Gouesbet, L. Mees, G. Gréhan, “Partial wave description of shaped beams in elliptical cylinder coordinates,” J. Opt. Soc. Am. A 15, 3028–3038 (1998).
[CrossRef]

G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation to speed up computations in the GLMT for cylinders, for arbitrary location and orientation of the scatterer,” Appl. Opt. (to be published).

Mignon, H.

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 25, 5180–5190 (1996).
[CrossRef]

Möbius, W.

W. Möbius, “Zur Theorie des Regenbogens und ihrer experimentellen Prüfung,” Ann. Phys. (Leipzig) 4, 1498–1558 (1911).

Mount, C. M.

Onofri, F.

Özkul, C.

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

Presby, H. M.

H. M. Presby, “Refractive index and diameter measurements of unclad fibers,” Opt. Soc. Am. A 64, 280–284 (1973).

Ren, K. F.

G. Gouesbet, K. F. Ren, G. Gréhan, “Rigorous justification of the cylindrical approximation to speed up computations in GLMT for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in the GLMT framework: formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler Anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation to speed up computations in the GLMT for cylinders, for arbitrary location and orientation of the scatterer,” Appl. Opt. (to be published).

X. Han, Z. S. Wu, F. Corbin, G. Gréhan, K. F. Ren, G. Gouesbet, “Measurements of first and second rainbows of liquid jet and fiber” presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers, presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

Riethmuller, M. L.

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, M. L. Riethmuller, “Surface integral method to quantify the droplet non-sphericity effect on rainbow thermometry,” presented at the AGARD Symposium on Advanced Aerodynamic Measurement Technology, Seattle, Wash., 22–25 September 1997.

Roth, N.

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

Sankar, S. V.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fidrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, M. Maeda, ed., 23–26 August 1993.

Slimani, F.

Souli, N.

Stone, B. R.

Thiessen, D. B.

Tropea, C.

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 25, 5180–5190 (1996).
[CrossRef]

van Beeck, J. P. A. J.

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
[CrossRef] [PubMed]

J. P. A. J. van Beeck, M. L. Riethmuller, “Surface integral method to quantify the droplet non-sphericity effect on rainbow thermometry,” presented at the AGARD Symposium on Advanced Aerodynamic Measurement Technology, Seattle, Wash., 22–25 September 1997.

Wait, J. R.

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. 33, 189–195 (1955).

Wu, Z. S.

X. Han, Z. S. Wu, F. Corbin, G. Gréhan, K. F. Ren, G. Gouesbet, “Measurements of first and second rainbows of liquid jet and fiber” presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers, presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

Xu, T. H.

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 25, 5180–5190 (1996).
[CrossRef]

Zimmermann, E.

Ann. Phys. (Leipzig) (1)

W. Möbius, “Zur Theorie des Regenbogens und ihrer experimentellen Prüfung,” Ann. Phys. (Leipzig) 4, 1498–1558 (1911).

Appl. Opt. (8)

P. L. Marston, “Descartes glare points in scattering by icicles: color photographs and a tilted dielectric cylinder model of caustic and glare-point evolution,” Appl. Opt. 37, 1551–1556 (1998).
[CrossRef]

C. M. Mount, D. B. Thiessen, P. L. Marston, “Scattering observations for tilted transparent fibers: evolution of Airy caustics with cylinder tilt and the caustic merging transition,” Appl. Opt. 37, 1534–1539 (1998).
[CrossRef]

G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary-shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
[CrossRef] [PubMed]

F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

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]

H. Mignon, G. Gréhan, G. Gouesbet, T. H. Xu, C. Tropea, “Measurement of cylindrical particles with phase Doppler anemometry,” Appl. Opt. 25, 5180–5190 (1996).
[CrossRef]

J. P. A. J. van Beeck, M. L. Riethmuller, “Rainbow phenomena applied to the measurement of droplet size and velocity and to the detection of nonsphericity,” Appl. Opt. 35, 2259–2266 (1996).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propag. (1)

S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
[CrossRef]

J. Appl. Phys. (1)

S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
[CrossRef]

J. Laser Appl. (1)

N. Roth, K. Anders, A. Frohn, “Simultaneous measurement of temperature and size of droplets in the micrometer range,” J. Laser Appl. 2, 37–42 (1990).
[CrossRef]

J. Opt. (Paris) (2)

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt. (Paris) 26, 225–239 (1995).
[CrossRef]

G. Gouesbet, “Scattering of higher-order Gaussian beams by an infinite cylinder,” J. Opt. (Paris) 28, 45–65 (1997).
[CrossRef]

J. Opt. Soc. Am. A (10)

C. L. Adler, J. A. Lock, B. R. Stone, C. J. Garcia, “High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder,” J. Opt. Soc. Am. A 14, 1305–1315 (1997).
[CrossRef]

J. A. Lock, C. L. Adler, “Debye-series analysis of the first-order rainbow produced in scattering of a diagonally incident plane wave by a circular cylinder,” J. Opt. Soc. Am. A 14, 1316–1328 (1997).
[CrossRef]

G. Gouesbet, K. F. Ren, G. Gréhan, “Rigorous justification of the cylindrical approximation to speed up computations in GLMT for cylinders,” J. Opt. Soc. Am. A 15, 511–523 (1998).
[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]

E. Zimmermann, R. Dändliker, N. Souli, B. Krattiger, “Scattering of an off-axis Gaussian beam by a dielectric cylinder compared with a rigorous electromagnetic approach,” J. Opt. Soc. Am. A 12, 398–403 (1995).
[CrossRef]

J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder. I. Parameterization of the incident beam and the far-zone scattered intensity,” J. Opt. Soc. Am. A 14, 640–652 (1997).
[CrossRef]

J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder. II. The interaction S-matrix and morphology dependent resonances,” J. Opt. Soc. Am. A 14, 653–661 (1997).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in the GLMT framework: formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

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]

G. Gouesbet, L. Mees, G. Gréhan, “Partial wave description of shaped beams in elliptical cylinder coordinates,” J. Opt. Soc. Am. A 15, 3028–3038 (1998).
[CrossRef]

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

J. Phys. (1)

J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” J. Phys. 33, 189–195 (1955).

Opt. Diagnost. Eng. (1)

N. Gauchet, T. Girasole, K. F. Ren, G. Gréhan, G. Gouesbet, “Application of generalized Lorenz–Mie theory for cylinders to cylindrical characterization by phase-Doppler Anemometry,” Opt. Diagnost. Eng. 2, 1–10 (1997).

Opt. Eng. (2)

D. Lebrun, S. Belaid, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorenz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

J. A. Ferrari, E. M. Frins, “Interferometric method for fiber diameter determination,” Opt. Eng. 35, 1050–1053 (1996).
[CrossRef]

Opt. Soc. Am. A (1)

H. M. Presby, “Refractive index and diameter measurements of unclad fibers,” Opt. Soc. Am. A 64, 280–284 (1973).

Part. Part. Syst. Charact. (2)

G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder, including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
[CrossRef]

G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
[CrossRef]

Phil. Mag. (1)

T. J. Bromwich, “Electromagnetic waves,” Phil. Mag. 38, 143–164 (1919).
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L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[CrossRef]

Proc. IEEE (1)

S. Choudhary, L. Felsen, “Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking,” Proc. IEEE 62, 1530–1541 (1974).
[CrossRef]

Other (7)

J. P. A. J. van Beeck, M. L. Riethmuller, “Surface integral method to quantify the droplet non-sphericity effect on rainbow thermometry,” presented at the AGARD Symposium on Advanced Aerodynamic Measurement Technology, Seattle, Wash., 22–25 September 1997.

G. Gouesbet, K. F. Ren, L. Mees, G. Gréhan, “The cylindrical localized approximation to speed up computations in the GLMT for cylinders, for arbitrary location and orientation of the scatterer,” Appl. Opt. (to be published).

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods, (World Scientific, Singapore, 1990), Chap. 2.

S. V. Sankar, K. M. Ibrahim, D. H. Buermann, M. J. Fidrich, W. D. Bachalo, “An integrated phase Doppler/rainbow refractometer system for simultaneous measurement of droplet size, velocity, and refractive index,” presented at the Third International Congress on Optical Particle Sizing, M. Maeda, ed., 23–26 August 1993.

F. Corbin, A. Garo, G. Gouesbet, G. Gréhan, “Réfractométrie d’arc-en-ciel: application au diagnostic de gouttes avec gradient d’indice,” presented at the 5ème Congrès Francophone de Vélocimétrie Laser, Rouen, France, 24–27 September 1996.

C. Corbin, X. Han, Z. S. Wu, K. F. Ren, G. Gréhan, A. Garo, G. Gouesbet, “Rainbow refractometry: applications to nonhomogeneous scatterers, presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

X. Han, Z. S. Wu, F. Corbin, G. Gréhan, K. F. Ren, G. Gouesbet, “Measurements of first and second rainbows of liquid jet and fiber” presented at the Third International Conference on Fluid Dynamic Measurement and Its Applications, Beijing, China, 14–17 October 1997.

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Figures (17)

Fig. 1
Fig. 1

Cartesian-coordinate systems for beam description.

Fig. 2
Fig. 2

Coordinate systems for rotated off-axis beam description.

Fig. 3
Fig. 3

Observation geometry.

Fig. 4
Fig. 4

Schematic of the scattering of rays.

Fig. 5
Fig. 5

Map of the scattering pattern for a 16-µm Gaussian beam (wavelength, 0.5027 µm) illuminating a 60-µm glass fiber: on-axis case.

Fig. 6
Fig. 6

Light scattered in the backward direction.

Fig. 7
Fig. 7

Light scattered in the forward direction.

Fig. 8
Fig. 8

Forward scattering for a refractive index of 1.3363 - x × i.

Fig. 9
Fig. 9

Scattering pattern for the scattering of a 16-µm Gaussian beam illuminating a 60-µm glass fiber: off-axis case.

Fig. 10
Fig. 10

Schematic of paths of rays for an off-axis incident beam.

Fig. 11
Fig. 11

Scattering pattern for a 60-µm glass fiber perpendicularly illuminated by a plane wave and Gaussian beams.

Fig. 12
Fig. 12

Scattered intensity by a 60-µm glass fiber illuminated by tilted Gaussian beams. Incident angle, π/4.

Fig. 13
Fig. 13

Scattered intensity by a 60-µm glass fiber illuminated by tilted Gaussian beams. Incident angle, π/8.

Fig. 14
Fig. 14

Scattered intensity by a 60-µm glass fiber illuminated by tilted Gaussian beams. Incident angle, 3π/8.

Fig. 15
Fig. 15

Scattered intensity by a 60-µm glass fiber illuminated by tilted Gaussian beams versus φ. Incident angle, π/8; the coordinate kz, -2500.

Fig. 16
Fig. 16

Rainbow diagram: A1, primary peak; A2, A3, supernumerary peaks.

Fig. 17
Fig. 17

Comparison of the rainbow shift that is due to ellipticity or orientation of the fiber predicted from Airy theory with an effective index, from GLMT with an effective index, from GLMT for an oriented fiber, and from Möbius theory.

Tables (2)

Tables Icon

Table 1 Beam Waist Diameter Equal to 16 µm

Tables Icon

Table 2 Angular Location θi of the Main Rainbow and of the Supernumerary Peaks for Two Gaussian Beam Diameters

Equations (2)

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

dld=1M2-sin2π/2-ΓM21/2,
M=M2-cos2 Γ1/2sin Γ.

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