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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 14, Iss. 6 — Jun. 1, 1997
  • pp: 1305–1315

High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder

C. L. Adler, James A. Lock, Bradley R. Stone, and Claudio J. Garcia  »View Author Affiliations

JOSA A, Vol. 14, Issue 6, pp. 1305-1315 (1997)

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We examine scattering of a family of initially parallel diagonally incident rays by a dielectric circular cylinder and show that the interior and exterior caustics that occur are qualitatively identical to those produced at normal incidence. We find, however, that (1) varying the plane-wave tilt angle has the same effect on the caustics as varying the refractive index of the cylinder at normal incidence and (2) high-order interior caustics are visible because of larger internal-reflection Fresnel coefficients at diagonal incidence than at normal incidence. We also observe noncaustic ray trajectories produced by the sharp peaking of internal-reflection Fresnel coefficients at large ray impact parameters, as well as another class of internal caustics produced by scattering from inhomogeneities in our glass cylinder.

© 1997 Optical Society of America

Original Manuscript: July 12, 1996
Revised Manuscript: December 3, 1996
Manuscript Accepted: December 3, 1996
Published: June 1, 1997

C. L. Adler, James A. Lock, Bradley R. Stone, and Claudio 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)

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  1. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987), p. 222, Fig. 6.13.
  2. D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 26, 1348–1356 (1987). [CrossRef] [PubMed]
  3. K. Sassen, “Angular scattering and rainbow formation in pendant drops,” J. Opt. Soc. Am. 69, 1083–1089 (1979). [CrossRef]
  4. 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]
  5. J. D. Walker, “Multiple rainbows from single drops of water and other liquids,” Am. J. Phys. 44, 421–433 (1976). [CrossRef]
  6. J. D. Walker, “How to create and observe a dozen rainbows in a single drop of water,” Sci. Am. 237(1), 138–144 (1977). [CrossRef]
  7. J. D. Walker, “Mysteries of rainbows, notably their rare supernumerary arcs,” Sci. Am. 242(6), 174–184 (1980). [CrossRef]
  8. 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]
  9. J. A. Lock, “Theory of the observations made of high-order rainbows from a single water droplet,” Appl. Opt. 26, 5291–5298 (1987). [CrossRef] [PubMed]
  10. H. C. van de Hulst, R. T. Wang, “Glare points,” Appl. Opt. 30, 4755–4763 (1991). [CrossRef] [PubMed]
  11. C. F. Bohren, A. B. Fraser, “Newton’s zero-order rainbow: unobservable or nonexistent,” Am. J. Phys. 59, 325–326 (1991). [CrossRef]
  12. A. E. Shapiro, “Comment on Newton’s zero-order rainbow: unobservable or nonexistent,” Am. J. Phys. 60, 749–750 (1992). [CrossRef]
  13. J. A. Lock, T. A. McCollum, “Further thoughts on Newton’s zero-order rainbow,” Am. J. Phys. 62, 1082–1089 (1994). [CrossRef]
  14. V. Srivastava, M. A. Jarzembski, “Laser-induced stimulated Raman scattering in the forward direction of a droplet: comparison of Mie theory with geometrical optics,” Opt. Lett. 16, 126–128 (1991). [CrossRef] [PubMed]
  15. J. A. Lock, E. A. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1552 (1991). [CrossRef]
  16. H. M. Lai, P. T. Leung, K. L. Poon, K. Young, “Characterization of the internal energy density in Mie scattering,” J. Opt. Soc. Am. A 8, 1553–1558 (1991). [CrossRef]
  17. D. Q. Chowdhury, P. W. Barber, S. C. Hill, “Energy-density distribution inside large nonabsorbing spheres using Mie theory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992). [CrossRef] [PubMed]
  18. M. A. Jarzembski, V. Srivastava, “Electromagnetic field enhancement in small liquid droplets using geometrical optics,” Appl. Opt. 28, 4962–4965 (1989). [CrossRef] [PubMed]
  19. J.-G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, “Observations of Descartes ring stimulated Raman scattering in micrometer-sized water droplets,” Opt. Lett. 16, 1310–1312 (1991). [CrossRef] [PubMed]
  20. P. Chylek, M. A. Jarzembski, N. Y. Chou, R. G. Pinnick, “Effect of size and material of liquid spherical particles on laser-induced breakdown,” Appl. Phys. Lett. 49, 1475–1477 (1986). [CrossRef]
  21. R. G. Pinnick, P. Chylek, M. Jarzembski, E. Creegan, V. Srivastava, G. Fernandez, J. D. Pendleton, A. Biswas, “Aerosol-induced laser breakdown thresholds: wavelength dependence,” Appl. Opt. 27, 987–996 (1988). [CrossRef] [PubMed]
  22. J. F. Nye, “Rainbow scattering from spheroidal drops—an explanation of the hyperbolic umbilic foci,” Nature (London) 312, 531–532 (1984). [CrossRef]
  23. J. F. Nye, “Rainbows from ellipsoidal water drops,” Proc. R. Soc. London, Ser. A 438, 397–417 (1992). [CrossRef]
  24. P. L. Marston, E. H. Trinh, “Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops,” Nature (London) 312, 529–531 (1984). [CrossRef]
  25. P. L. Marston, “Cusp diffraction catastrophe from spheroids: generalized rainbows and inverse scattering,” Opt. Lett. 10, 588–590 (1985). [CrossRef] [PubMed]
  26. H. J. Simpson, P. L. Marston, “Scattering of white light from levitated oblate water drops near rainbows and other diffraction catastrophes,” Appl. Opt. 30, 3468–3473, 3547 (1991). [CrossRef] [PubMed]
  27. G. Kaduchak, P. L. Marston, H. J. Simpson, “E6 diffraction catastrophe of the primary rainbow of oblate water drops: observations with white-light and laser illumination,” Appl. Opt. 33, 4691–4696 (1994). [CrossRef] [PubMed]
  28. G. Kaduchak, P. L. Marston, “Hyperbolic umbilic and E6 diffraction catastrophes associated with the secondary rainbow of oblate water drops: observations with laser illumination,” Appl. Opt. 33, 4697–4701 (1994). [CrossRef] [PubMed]
  29. P. L. Marston, G. Kaduchak, “Generalized rainbows and unfolded glories of oblate drops: organization for multiple internal reflections and extension of cusps into Alexander’s dark band,” Appl. Opt. 33, 4702–4713 (1994). [CrossRef] [PubMed]
  30. J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. II. Transmission and cross-polarization effects,” Appl. Opt. 35, 515–531 (1996). [CrossRef] [PubMed]
  31. J. F. Owen, R. K. Chang, P. W. Barber, “Internal electric field distributions of a dielectric cylinder at resonance wavelengths,” Opt. Lett. 6, 540–542 (1981). [CrossRef] [PubMed]
  32. A. Steinhardt, L. Fukshansky, “Geometrical optics approach to the intensity distribution infinite cylindrical media,” Appl. Opt. 26, 3778–3789 (1987). [CrossRef] [PubMed]
  33. 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]
  34. J. B. Keller, H. B. Keller, “Determination of reflected and transmitted fields by geometrical optics,” J. Opt. Soc. Am. 40, 48–52 (1950). [CrossRef]
  35. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), p. 264, Fig. 6.3.
  36. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 200, Fig. 8.4.
  37. 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]
  38. The glass cylinder was provided, polished, and frosted by Ferguson’s Cut Glass Originals, 4292 Pearl Road, Cleveland, Ohio 44109.
  39. G. P. Können, “Appearance of supernumeraries of the secondary rainbow in rain showers,” J. Opt. Soc. Am. A 4, 810–816 (1987). [CrossRef]

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