OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 28 — Oct. 1, 2011
  • pp: F29–F38

Time domain analysis of scattering by a water droplet

Philip Laven  »View Author Affiliations

Applied Optics, Vol. 50, Issue 28, pp. F29-F38 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (1204 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Rainbows, coronas and glories are caused by the scattering of sunlight from water droplets in the atmosphere. Although these optical phenomena are seen fairly frequently, even scientifically minded people sometimes struggle to provide explanations for their formation. This paper offers explanations of these phenomena based on numerical computations of the scattering of a 5 fs pulse of red light by a spherical droplet of water. The results reveal the intricate details of the various scattering mechanisms, some of which are essentially undetectable except in the time domain.

© 2011 Optical Society of America

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(240.6690) Optics at surfaces : Surface waves
(290.4020) Scattering : Mie theory
(320.2250) Ultrafast optics : Femtosecond phenomena

Original Manuscript: May 23, 2011
Revised Manuscript: July 21, 2011
Manuscript Accepted: July 21, 2011
Published: August 23, 2011

Virtual Issues
Vol. 6, Iss. 11 Virtual Journal for Biomedical Optics

Philip Laven, "Time domain analysis of scattering by a water droplet," Appl. Opt. 50, F29-F38 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. P. Debye, “Das elektromagnetische Feld um einen Zylinder und die Theorie des Regenbogens,” Phys. Z. 9, 775–778(1908).
  2. B. Van der Pol and H. Bremmer, “The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to radiotelegraphy and the theory of the rainbow,” Philos. Mag. 24, 825–864(1937).
  3. E. A. Hovenac and J. A. Lock, “Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series,” J. Opt. Soc. Am. A 9, 781–795(1992). [CrossRef]
  4. E. E. M. Khaled, D. Q. Chowdhury, S. C. Hill, and P. W. Barber, “Internal and scattered time-dependent intensity of a dielectric sphere illuminated with a pulsed Gaussian beam,” J. Opt. Soc. Am. A 11, 2065–2071 (1994). [CrossRef]
  5. K. S. Schifrin and I. G. Zolotov, “Quasi-stationary scattering of electromagnetic pulses by spherical particles,” Appl. Opt. 33, 7798–7804 (1994). [CrossRef]
  6. L. Méès, G. Gouesbet, and G. Gréhan, “Scattering of laser pulses (plane wave and focused Gaussian beam) by spheres,” Appl. Opt. 40, 2546–2550 (2001). [CrossRef]
  7. L. Méès, G. Gréhan, and G. Gouesbet, “Time-resolved scattering diagrams for a sphere illuminated by plane wave and focused short pulses,” Opt. Commun. 194, 59–65 (2001). [CrossRef]
  8. Y. P. Han, L. Méès, K. F. Ren, G. Gréhan, Z. S. Wu, and G. Gouesbet, “Far scattered field from a spheroid under a femtosecond pulsed illumination in a generalized Lorenz-Mie theory framework,” Opt. Commun. 231, 71–77 (2004). [CrossRef]
  9. H. Bech and A. Leder, “Particle sizing by ultrashort laser pulses—numerical simulation,” Optik 115, 205–217 (2004). [CrossRef]
  10. H. Bech and A. Leder, “Particle sizing by time-resolved Mie calculations—A numerical study,” Optik 117, 40–47 (2006). [CrossRef]
  11. C. Calba, C. Rozé, T. Girasole, and L. Méès, “Monte Carlo simulation of the interaction between an ultra-short pulse and a strongly scattering medium: The case of large particles,” Opt. Commun. 265, 373–382 (2006). [CrossRef]
  12. S. Bakić, C. Heinisch, N. Damaschke, T. Tschudi, and C. Tropea, “Time integrated detection of femtosecond laser pulses scattered by small droplets,” Appl. Opt. 47, 523–530(2008). [CrossRef] [PubMed]
  13. S. Bakić, F. Xu, N. Damaschke, and C. Tropea, “Feasibility of extending rainbow refractometry to small particles using femtosecond laser pulses,” Part. Part. Syst. Charact. 26, 34–40 (2009). [CrossRef]
  14. P. Laven, “Separating diffraction from scattering: the million dollar challenge,” J. Nanophoton. 4, 041593 (2010). [CrossRef]
  15. J. A. Lock and P. Laven, “Mie scattering in the time domain. Part 2. The role of diffraction,” J. Opt. Soc. Am. A 28, 1096–1106 (2011). [CrossRef]
  16. J. B. Keller, “A geometrical theory of diffraction,” in Calculus of Variations and Its Applications, L.M.Graves, ed., Proceedings of Symposia in Applied Mathematics (McGraw-Hill, 1958), Vol.  3, pp. 27–52.
  17. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116–130 (1962). [CrossRef] [PubMed]
  18. J. A. Lock and P. Laven, “Mie scattering in the time domain. Part I. The role of surface waves,” J. Opt. Soc. Am. A 28, 1086–1095 (2011). [CrossRef]
  19. H. M. Nussenzveig, “High-frequency scattering by a transparent sphere. I. Direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969). [CrossRef]
  20. P. Laven, “How are glories formed?” Appl. Opt. 44, 5675–5683 (2005). [CrossRef] [PubMed]
  21. P. Laven, “Effects of refractive index on glories,” Appl. Opt. 47, H133–H142 (2008). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited