Abstract

A vector-ray tracing (VRT) model is employed to simulate optical caustic structures [in terms of rainbow and hyperbolic umbilic (HU) fringes] in the secondary rainbow region of light scattering from oblate droplets. The changes of the rainbow fringe and HU fringe in response to shape deformation of oblate droplets are investigated and the curvature of the rainbow fringe is calculated. Then the location of cusp caustics is calculated from VRT simulations and compared with analytic solutions.

© 2013 Optical Society of America

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References

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  1. P. L. Marston and E. H. Trinh, Nature 312, 529 (1984).
    [CrossRef]
  2. J. F. Nye, Nature 312, 531 (1984).
    [CrossRef]
  3. P. L. Marston, Opt. Lett. 10, 588 (1985).
    [CrossRef]
  4. P. L. Marston, J. Acoust. Soc. Am. 81, 226 (1987).
    [CrossRef]
  5. P. L. Marston, C. E. Dean, and H. J. Simpson, “Light scattering from spheroidal drops: exploring optical catastrophes,” in Drops and Bubbles: American Institute of Physics Conference Proceedings, T. G. Wang, ed. (American Institute of Physics, 1989), Vol. 197, pp. 275–285.
  6. C. E. Dean and P. L. Marston, Appl. Opt. 30, 3443 (1991).
    [CrossRef]
  7. P. L. Marston, Phys. Acoust. 21, 1 (1992).
    [CrossRef]
  8. P. L. Marston, J. Quant. Spectosc. Radiat. Transfer 63, 341 (1999).
    [CrossRef]
  9. J. F. Nye, Proc. R. Soc. A 438, 397 (1992).
    [CrossRef]
  10. H. J. Simpson and P. L. Marston, Appl. Opt. 30, 3468 (1991).
    [CrossRef]
  11. G. Kaduchak, P. L. Marston, and H. J. Simpson, Appl. Opt. 33, 4691 (1994).
    [CrossRef]
  12. J. A. Lock and E. A. Hovenac, J. Opt. Soc. Am. A 8, 1541 (1991).
    [CrossRef]
  13. J. A. Lock and F. Xu, Appl. Opt. 49, 1288 (2010).
    [CrossRef]
  14. M. V. Berry and C. Upstill, Prog. Opt. 18, 257 (1980).
    [CrossRef]
  15. H. T. Yu, F. Xu, and C. Tropea, J. Quant. Spectosc. Radiat. Transfer 126, 105 (2013).
    [CrossRef]
  16. H. T. Yu, F. Xu, and C. Tropea, Opt. Express 21, 25761 (2013).
    [CrossRef]
  17. K. F. Ren, F. Onofri, C. Rozé, and T. Girasole, Opt. Lett. 36, 370 (2011).
    [CrossRef]
  18. G. Kaduchak and P. L. Marston, Appl. Opt. 33, 4697 (1994).
    [CrossRef]
  19. P. L. Marston and G. Kaduchak, Appl. Opt. 33, 4702 (1994).
    [CrossRef]
  20. D. S. Langley and P. L. Marston, Appl. Opt. 37, 1520 (1998).
    [CrossRef]

2013 (2)

H. T. Yu, F. Xu, and C. Tropea, J. Quant. Spectosc. Radiat. Transfer 126, 105 (2013).
[CrossRef]

H. T. Yu, F. Xu, and C. Tropea, Opt. Express 21, 25761 (2013).
[CrossRef]

2011 (1)

2010 (1)

1999 (1)

P. L. Marston, J. Quant. Spectosc. Radiat. Transfer 63, 341 (1999).
[CrossRef]

1998 (1)

1994 (3)

1992 (2)

J. F. Nye, Proc. R. Soc. A 438, 397 (1992).
[CrossRef]

P. L. Marston, Phys. Acoust. 21, 1 (1992).
[CrossRef]

1991 (3)

1987 (1)

P. L. Marston, J. Acoust. Soc. Am. 81, 226 (1987).
[CrossRef]

1985 (1)

1984 (2)

P. L. Marston and E. H. Trinh, Nature 312, 529 (1984).
[CrossRef]

J. F. Nye, Nature 312, 531 (1984).
[CrossRef]

1980 (1)

M. V. Berry and C. Upstill, Prog. Opt. 18, 257 (1980).
[CrossRef]

Berry, M. V.

M. V. Berry and C. Upstill, Prog. Opt. 18, 257 (1980).
[CrossRef]

Dean, C. E.

C. E. Dean and P. L. Marston, Appl. Opt. 30, 3443 (1991).
[CrossRef]

P. L. Marston, C. E. Dean, and H. J. Simpson, “Light scattering from spheroidal drops: exploring optical catastrophes,” in Drops and Bubbles: American Institute of Physics Conference Proceedings, T. G. Wang, ed. (American Institute of Physics, 1989), Vol. 197, pp. 275–285.

Girasole, T.

Hovenac, E. A.

Kaduchak, G.

Langley, D. S.

Lock, J. A.

Marston, P. L.

P. L. Marston, J. Quant. Spectosc. Radiat. Transfer 63, 341 (1999).
[CrossRef]

D. S. Langley and P. L. Marston, Appl. Opt. 37, 1520 (1998).
[CrossRef]

P. L. Marston and G. Kaduchak, Appl. Opt. 33, 4702 (1994).
[CrossRef]

G. Kaduchak and P. L. Marston, Appl. Opt. 33, 4697 (1994).
[CrossRef]

G. Kaduchak, P. L. Marston, and H. J. Simpson, Appl. Opt. 33, 4691 (1994).
[CrossRef]

P. L. Marston, Phys. Acoust. 21, 1 (1992).
[CrossRef]

H. J. Simpson and P. L. Marston, Appl. Opt. 30, 3468 (1991).
[CrossRef]

C. E. Dean and P. L. Marston, Appl. Opt. 30, 3443 (1991).
[CrossRef]

P. L. Marston, J. Acoust. Soc. Am. 81, 226 (1987).
[CrossRef]

P. L. Marston, Opt. Lett. 10, 588 (1985).
[CrossRef]

P. L. Marston and E. H. Trinh, Nature 312, 529 (1984).
[CrossRef]

P. L. Marston, C. E. Dean, and H. J. Simpson, “Light scattering from spheroidal drops: exploring optical catastrophes,” in Drops and Bubbles: American Institute of Physics Conference Proceedings, T. G. Wang, ed. (American Institute of Physics, 1989), Vol. 197, pp. 275–285.

Nye, J. F.

J. F. Nye, Proc. R. Soc. A 438, 397 (1992).
[CrossRef]

J. F. Nye, Nature 312, 531 (1984).
[CrossRef]

Onofri, F.

Ren, K. F.

Rozé, C.

Simpson, H. J.

G. Kaduchak, P. L. Marston, and H. J. Simpson, Appl. Opt. 33, 4691 (1994).
[CrossRef]

H. J. Simpson and P. L. Marston, Appl. Opt. 30, 3468 (1991).
[CrossRef]

P. L. Marston, C. E. Dean, and H. J. Simpson, “Light scattering from spheroidal drops: exploring optical catastrophes,” in Drops and Bubbles: American Institute of Physics Conference Proceedings, T. G. Wang, ed. (American Institute of Physics, 1989), Vol. 197, pp. 275–285.

Trinh, E. H.

P. L. Marston and E. H. Trinh, Nature 312, 529 (1984).
[CrossRef]

Tropea, C.

H. T. Yu, F. Xu, and C. Tropea, J. Quant. Spectosc. Radiat. Transfer 126, 105 (2013).
[CrossRef]

H. T. Yu, F. Xu, and C. Tropea, Opt. Express 21, 25761 (2013).
[CrossRef]

Upstill, C.

M. V. Berry and C. Upstill, Prog. Opt. 18, 257 (1980).
[CrossRef]

Xu, F.

Yu, H. T.

H. T. Yu, F. Xu, and C. Tropea, Opt. Express 21, 25761 (2013).
[CrossRef]

H. T. Yu, F. Xu, and C. Tropea, J. Quant. Spectosc. Radiat. Transfer 126, 105 (2013).
[CrossRef]

Appl. Opt. (7)

J. Acoust. Soc. Am. (1)

P. L. Marston, J. Acoust. Soc. Am. 81, 226 (1987).
[CrossRef]

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

J. Quant. Spectosc. Radiat. Transfer (2)

P. L. Marston, J. Quant. Spectosc. Radiat. Transfer 63, 341 (1999).
[CrossRef]

H. T. Yu, F. Xu, and C. Tropea, J. Quant. Spectosc. Radiat. Transfer 126, 105 (2013).
[CrossRef]

Nature (2)

P. L. Marston and E. H. Trinh, Nature 312, 529 (1984).
[CrossRef]

J. F. Nye, Nature 312, 531 (1984).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Acoust. (1)

P. L. Marston, Phys. Acoust. 21, 1 (1992).
[CrossRef]

Proc. R. Soc. A (1)

J. F. Nye, Proc. R. Soc. A 438, 397 (1992).
[CrossRef]

Prog. Opt. (1)

M. V. Berry and C. Upstill, Prog. Opt. 18, 257 (1980).
[CrossRef]

Other (1)

P. L. Marston, C. E. Dean, and H. J. Simpson, “Light scattering from spheroidal drops: exploring optical catastrophes,” in Drops and Bubbles: American Institute of Physics Conference Proceedings, T. G. Wang, ed. (American Institute of Physics, 1989), Vol. 197, pp. 275–285.

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Figures (5)

Fig. 1.
Fig. 1.

Vector-ray tracing in an oblate droplet.

Fig. 2.
Fig. 2.

Definition of the scattering angles.

Fig. 3.
Fig. 3.

Evolution of the secondary rainbow fringe and HU fringe as the aspect ratio of an oblate water droplet increases.

Fig. 4.
Fig. 4.

Curvature of the secondary rainbow fringes calculated from VRT simulations for oblate water droplets with different aspect ratios.

Fig. 5.
Fig. 5.

Comparison of the cusp location calculated by VRT simulations and that by the analytical solutions for oblate water droplets with different aspect ratios.

Equations (4)

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

L01=1m[L0(L0·nA)nA][11m2+1m2(L0·nA)2]1/2nA,
L12=L012(L01·nB)nB,L23=L122(L12·nC)nC,L3=m[L23(L23·nD)nD]+[1m2+m2(L23·nD)2]1/2nD,
θ=cos1[ay/(ax2+ay2)1/2],
ϕ=cos1[(ax2+ay2)1/2/(ax2+ay2+az2)1/2].

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