Abstract

The scattering of light by obliquely illuminated circular dielectric cylinders was previously demonstrated to be enhanced by a merger of Airy caustics at a critical tilt angle. [Appl. Opt. 37, 1534 (1998)]. A related enhancement is demonstrated here for backward and near-backward scattering for cylinders cut with a flat end perpendicular to the cylinder’s axis. It is expected that merged caustics will enhance the backscattering by clouds of randomly oriented circular cylinders that have appropriately flat ends.

© 2003 Optical Society of America

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References

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  1. 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).
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    [CrossRef]
  3. 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]
  4. 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]
  5. L. Mees, K. F. Ren, G. Grehan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999).
    [CrossRef]
  6. J. A. Lock, C. L. Adler, E. A. Hovenac, “Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis,” J. Opt. Soc. Am. 17, 1846–1856 (2000).
    [CrossRef]
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  8. F. J. Blonigen, P. L. Marston, “Backscattering enhancements for tilted solid plastic cylinders in water due to the caustic merging transition: observations and theory,” J. Acoust. Soc. Am. 107, 689–698 (2000).
    [CrossRef] [PubMed]
  9. D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995).
  10. W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).
  11. K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: Applications to climate research,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), Chap. 15, pp. 417–449.
    [CrossRef]
  12. K. Sassen, W. P. Arnott, J. M. Barnett, S. Aulenbach, “Can cirrus clouds produce glories?” Appl. Opt. 37, 1427–1433 (1998).
    [CrossRef]
  13. D. S. Langley, P. L. Marston, “Glory in optical backscattering from air bubbles,” Phys. Rev. Lett. 47, 913–916 (1981).
    [CrossRef]
  14. P. L. Marston, “Geometrical and catastrophe optics methods in scattering,” in Physical Acoustics, A. D. Pierce, R. N. Thurston, eds. (Academic, Boston, Mass., 1992), Vol. 21, pp. 1–234.
  15. R. T. Wang, H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106–117 (1991).
    [CrossRef] [PubMed]
  16. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, 1992).
    [CrossRef]
  17. Y. Takano, M. Tanaka, “Phase matrix and cross sections for single scattering by circular cylinders: a comparison of ray optics and wave theory,” Appl. Opt. 19, 2781–2793 (1980).
    [CrossRef] [PubMed]
  18. F. Kuik, J. F. Dehaan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
    [CrossRef] [PubMed]
  19. M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
    [CrossRef] [PubMed]
  20. M. I. Mishchenko, K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309–312 (1998).
    [CrossRef]
  21. Y. G. Liu, W. P. Arnott, J. Hallett, “Anomalous diffraction theory for arbitrarily oriented finite circular cylinders and comparison with exact T-matrix results,” Appl. Opt. 37, 5019–5030 (1998).
    [CrossRef]

2000 (2)

J. A. Lock, C. L. Adler, E. A. Hovenac, “Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis,” J. Opt. Soc. Am. 17, 1846–1856 (2000).
[CrossRef]

F. J. Blonigen, P. L. Marston, “Backscattering enhancements for tilted solid plastic cylinders in water due to the caustic merging transition: observations and theory,” J. Acoust. Soc. Am. 107, 689–698 (2000).
[CrossRef] [PubMed]

1999 (1)

1998 (5)

1997 (2)

1996 (1)

1994 (1)

1991 (1)

1981 (1)

D. S. Langley, P. L. Marston, “Glory in optical backscattering from air bubbles,” Phys. Rev. Lett. 47, 913–916 (1981).
[CrossRef]

1980 (1)

Adler, C. L.

Arnott, W. P.

Aulenbach, S.

Barnett, J. M.

Blonigen, F. J.

F. J. Blonigen, P. L. Marston, “Backscattering enhancements for tilted solid plastic cylinders in water due to the caustic merging transition: observations and theory,” J. Acoust. Soc. Am. 107, 689–698 (2000).
[CrossRef] [PubMed]

Dehaan, J. F.

Garcia, C. J.

Gouesbet, G.

Grehan, G.

Hallett, J.

Hovenac, E. A.

J. A. Lock, C. L. Adler, E. A. Hovenac, “Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis,” J. Opt. Soc. Am. 17, 1846–1856 (2000).
[CrossRef]

Hovenier, J. W.

Kuik, F.

Langley, D. S.

D. S. Langley, P. L. Marston, “Glory in optical backscattering from air bubbles,” Phys. Rev. Lett. 47, 913–916 (1981).
[CrossRef]

Liou, K. N.

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: Applications to climate research,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), Chap. 15, pp. 417–449.
[CrossRef]

Liu, Y. G.

Livingston, W.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995).

Lock, J. A.

Lynch, D. K.

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995).

Macke, A.

Marston, P. L.

F. J. Blonigen, P. L. Marston, “Backscattering enhancements for tilted solid plastic cylinders in water due to the caustic merging transition: observations and theory,” J. Acoust. Soc. Am. 107, 689–698 (2000).
[CrossRef] [PubMed]

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]

D. S. Langley, P. L. Marston, “Glory in optical backscattering from air bubbles,” Phys. Rev. Lett. 47, 913–916 (1981).
[CrossRef]

P. L. Marston, “Geometrical and catastrophe optics methods in scattering,” in Physical Acoustics, A. D. Pierce, R. N. Thurston, eds. (Academic, Boston, Mass., 1992), Vol. 21, pp. 1–234.

P. L. Marston, “Optical caustics and related phenomena,” in On Minnaert’s Shoulders: Twenty Years of Light and Color Conferences, C. L. Adler, ed., Vol. 1 of Classic Reprints on CD-ROM (Optical Society of America, Washington, D.C., 2000).

Mees, L.

Mishchenko, M. I.

M. I. Mishchenko, K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309–312 (1998).
[CrossRef]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

Mount, C. M.

Nussenzveig, H. M.

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, 1992).
[CrossRef]

Ren, K. F.

Sassen, K.

K. Sassen, W. P. Arnott, J. M. Barnett, S. Aulenbach, “Can cirrus clouds produce glories?” Appl. Opt. 37, 1427–1433 (1998).
[CrossRef]

M. I. Mishchenko, K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309–312 (1998).
[CrossRef]

Stone, B. R.

Takano, Y.

Y. Takano, M. Tanaka, “Phase matrix and cross sections for single scattering by circular cylinders: a comparison of ray optics and wave theory,” Appl. Opt. 19, 2781–2793 (1980).
[CrossRef] [PubMed]

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: Applications to climate research,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), Chap. 15, pp. 417–449.
[CrossRef]

Tanaka, M.

Tape, W.

W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).

Thiessen, D. B.

Travis, L. D.

van de Hulst, H. C.

Wang, R. T.

Yang, P.

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: Applications to climate research,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), Chap. 15, pp. 417–449.
[CrossRef]

Appl. Opt. (9)

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]

L. Mees, K. F. Ren, G. Grehan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation: numerical results,” Appl. Opt. 38, 1867–1876 (1999).
[CrossRef]

K. Sassen, W. P. Arnott, J. M. Barnett, S. Aulenbach, “Can cirrus clouds produce glories?” Appl. Opt. 37, 1427–1433 (1998).
[CrossRef]

Y. Takano, M. Tanaka, “Phase matrix and cross sections for single scattering by circular cylinders: a comparison of ray optics and wave theory,” Appl. Opt. 19, 2781–2793 (1980).
[CrossRef] [PubMed]

F. Kuik, J. F. Dehaan, J. W. Hovenier, “Single scattering of light by circular cylinders,” Appl. Opt. 33, 4906–4918 (1994).
[CrossRef] [PubMed]

M. I. Mishchenko, L. D. Travis, A. Macke, “Scattering of light by polydisperse, randomly oriented, finite circular cylinders,” Appl. Opt. 35, 4927–4940 (1996).
[CrossRef] [PubMed]

R. T. Wang, H. C. van de Hulst, “Rainbows: Mie computations and the Airy approximation,” Appl. Opt. 30, 106–117 (1991).
[CrossRef] [PubMed]

Y. G. Liu, W. P. Arnott, J. Hallett, “Anomalous diffraction theory for arbitrarily oriented finite circular cylinders and comparison with exact T-matrix results,” Appl. Opt. 37, 5019–5030 (1998).
[CrossRef]

Geophys. Res. Lett. (1)

M. I. Mishchenko, K. Sassen, “Depolarization of lidar returns by small ice crystals: an application to contrails,” Geophys. Res. Lett. 25, 309–312 (1998).
[CrossRef]

J. Acoust. Soc. Am. (1)

F. J. Blonigen, P. L. Marston, “Backscattering enhancements for tilted solid plastic cylinders in water due to the caustic merging transition: observations and theory,” J. Acoust. Soc. Am. 107, 689–698 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. A. Lock, C. L. Adler, E. A. Hovenac, “Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis,” J. Opt. Soc. Am. 17, 1846–1856 (2000).
[CrossRef]

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

Phys. Rev. Lett. (1)

D. S. Langley, P. L. Marston, “Glory in optical backscattering from air bubbles,” Phys. Rev. Lett. 47, 913–916 (1981).
[CrossRef]

Other (6)

P. L. Marston, “Geometrical and catastrophe optics methods in scattering,” in Physical Acoustics, A. D. Pierce, R. N. Thurston, eds. (Academic, Boston, Mass., 1992), Vol. 21, pp. 1–234.

P. L. Marston, “Optical caustics and related phenomena,” in On Minnaert’s Shoulders: Twenty Years of Light and Color Conferences, C. L. Adler, ed., Vol. 1 of Classic Reprints on CD-ROM (Optical Society of America, Washington, D.C., 2000).

D. K. Lynch, W. Livingston, Color and Light in Nature (Cambridge U. Press, Cambridge, 1995).

W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).

K. N. Liou, Y. Takano, P. Yang, “Light scattering and radiative transfer in ice crystal clouds: Applications to climate research,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), Chap. 15, pp. 417–449.
[CrossRef]

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, 1992).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Geometry of the truncated circular cylinder considered. The ends of the cylinder are perpendicular to the symmetry axis. The wave vector of the illumination is tilted by an angle γ relative to the ends of the cylinder. The actual angle of incidence is i for an illuminated surface point U (where the local cylinder normal is N). The angle of incidence projected onto the base plane is φ, which is smaller than i.

Fig. 2
Fig. 2

Rays confined to the meridional plane of the cylinder that contribute to the backscattering after the fewest number of reflections. The rays shown are reversible. From Ref. 8, only the region within a distance d = 4a(tan γ)/n′ contributes to the backscattering for the process considered, where n′ is given by Eq. (2). Rays can be backscattered after additional internal reflections; however, the contributions from those rays are relatively weak near tilts given by Eq. (1). This is a consequence of the curvature of the outgoing wave fronts associated with the extra reflections. Angle of refraction ϑ is discussed in Section 5 below.

Fig. 3
Fig. 3

Experimental configuration for viewing the backscattering from the end of a small tilted cylinder (not drawn to scale). A lens is placed in front of the CCD camera with the CCD array at the focal plane. The backscattering region was also viewed by eye through a telescope. The illumination is horizontal, and the axis of the cylinder is tilted from the vertical by an amount γ by a goniometer. The goniometer measures the rotation about a horizontal axis that is perpendicular to the incident wave vector.

Fig. 4
Fig. 4

CCD strip records of the near-backward scattering for the value of γ displayed at the left. The strips are shifted vertically in proportion to tilt deviation γ c - γ. The evolution as a function of tilt for the calculated Descartes condition is shown as white curves on the right and left sides of the pattern. This evolution was calculated as explained in Section 3. The horizontal scale shows a 1° deviation in the backscattering angle. The CCD camera has been saturated near the brightest region of two of the records.

Equations (5)

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

γc=arccosn2-1/31/2,
nγ, n=n2-sin2 γ1/2/cos γ  n,
cos2 φD=n2-1/3,
w=2kra2/33 sin φD-1/3cos φDθ-θD,
ψθ, γ=arccosmˆ·mˆb=arccoscos θ sin2 γ+cos2 γ.

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