OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 15 — May. 20, 2009
  • pp: 2957–2965

Forward scattering light of droplets containing different size inclusions

Dakun Wu and Yanping Zhou  »View Author Affiliations

Applied Optics, Vol. 48, Issue 15, pp. 2957-2965 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (1363 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Scattering by a sphere with a different internal structure has drawn attention. The forward scattering light of a water droplet containing multiple different size carbon inclusions is calculated by the finite-difference time-domain method. Herein, distribution of these carbon inclusions conforms to Apollonian packing in a droplet. The space left over between carbon inclusions constructs a fractal, of which the fractal dimension D is expressed as D 1.305684 . The incident wave is in the y-direction polarization. The results show that the amplitude of the intensity fluctuations is not associated with the fractal dimension. Carbon inclusions only decrease the component y of electric field intensity at the place of inclusions. For a droplet containing multiple concentrated inclusions with different sizes, the amplitude of the intensity fluctuations is related with every space between inclusions. And the far field light intensity approaches the intensity caused by one carbon inclusion as space between inclusions becomes less and less. In order to know the effect of polarization direction, transmissibility versus θ(angle between the polarization direction of the incident wave used and the y-axis direction) is finally obtained. It can be seen that the transmissibility changes with θ conformably and reaches a minimum when θ = 30 ° . Transmissibility is equal for θ = 90 ° and θ = 0 ° .

© 2009 Optical Society of America

OCIS Codes
(290.2558) Scattering : Forward scattering

ToC Category:
Atmospheric and Oceanic Optics

Original Manuscript: December 12, 2008
Revised Manuscript: March 22, 2009
Manuscript Accepted: April 17, 2009
Published: May 18, 2009

Dakun Wu and Yanping Zhou, "Forward scattering light of droplets containing different size inclusions," Appl. Opt. 48, 2957-2965 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. G. Videen, W. Sun, and Q. Fu, “Light scattering from irregular tetrahedral aggregates,” Opt. Commun. 156, 5-9 (1998). [CrossRef]
  2. E. Zubko, D. Petrov, Y. Shkuratov, and G. Videen, “Discrete dipole approximation simulations of scattering by particles with hierarchical structure,” Appl. Opt. 44, 6479-6485 (2005). [CrossRef]
  3. D. S. Wang and P. W. Barber, “Scattering by inhomogeneous nonspherical objects,” Appl. Opt. 18, 1190-1197 (1979). [CrossRef]
  4. D. S. Wang, “Light scattering by nonspherical multilayered particles,” Ph.D. dissertation (University of Utah, 1979).
  5. D. Q. Chowdhury, S. C. Hill, and P. W. Barber, “Morphology-dependent resonances in radially inhomogeneous spheres,” J. Opt. Soc. Am. A 8, 1702-1705 (1991). [CrossRef]
  6. P. Chylek, V. Srivastava, R. G. Pinnick, and R. T. Wang, “Scattering of electromagnetic waves by composite spherical particles: experiment and effective medium approximations,” Appl. Opt. 27, 2396-2404 (1988). [CrossRef]
  7. V. P. Drachev, W.-T. Kim, V. P. Safonov, V. A. Podolskiy, N. S. Zakovryashin, E. N. Khaliullin, V. M. Shalaev, and R. L. Armstrong, “Low-threshold lasing and broad-band multiphoton-excited light emission from Ag aggregate-adsorbate complexes in microcavity,” J. Mod. Opt. 49, 645-662 (2002). [CrossRef]
  8. K. A. Fuller, “Scattering of light by coated spheres,” Opt. Lett. 18, 257-259 (1993). [CrossRef]
  9. K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. III. Spheres containing arbitrarily located spherical inhomogeneities,” J. Opt. Soc. Am. A 12, 893-904 (1995). [CrossRef]
  10. D. W. Mackowski and P. D. Jones, “Theoretical investigation of particles having a directionally dependent absorption cross section,” J. Thermophys. Heat Transfer 9, 193-201 (1995). [CrossRef]
  11. J. G. Fikioris and N. K. Uzunoglu, “Scattering from an eccentrically stratified dielectric sphere,” J. Opt. Soc. Am. 69, 1359-1366 (1979). [CrossRef]
  12. F. Borghese, P. Denti, and R. Saija, “Optical properties of spheres containing a spherical eccentric inclusion,” J. Opt. Soc. Am. A 9, 1327-1335 (1992). [CrossRef]
  13. G. Videen, D. Ngo, P. Chylek, and R. G. Pinnick, “Light scattering from a sphere with an irregular inclusion,” J. Opt. Soc. Am. A 12, 922-928 (1995). [CrossRef]
  14. G. Videen, D. R. Prabhu, M. Davies, F. González, and F. Moreno, “Light scattering fluctuations of a soft spherical particle containing an inclusion,” Appl. Opt. 40, 4054-4057 (2001). [CrossRef]
  15. G. Videen, P. Pellegrino, D. Ngo, J. S. Videen, and R. G. Pinnick, “Light-scattering intensity fluctuations in microdroplets containing inclusions,” Appl. Opt. 36, 6115-6118 (1997). [CrossRef]
  16. F. Borghese, P. Denti, and R. Saija, “Optical properties of spheres containing several spherical inclusions,” Appl. Opt. 33, 484-493 (1994). [CrossRef]
  17. S. S. Mana and H. J. Herrmann, “Precise determination of the fractal dimensions of Apollonian packing and space-filling bearings,” J. Phys. A Math. Nucl. Gen. 24, L481-L490 (1991). [CrossRef]
  18. R. Descartes, Oeuvres de Descartes, C. Adam and P. Tannery, eds. (Cerf, 1901), Vol. IV, pp. 45-50.
  19. J. C. Lagarias, C. L. Mallows, and A. Wilks, “Beyond the Descartes circle theorem,” Am. Math. Monthly 109, 338-361(2002). [CrossRef]
  20. Y. Okada, T. Mukai, I. Mann, H. Nomura, T. Takeuchi, I. Sano, and S. Mukai, “Grouping and adding method for calculating light scattering by large fluffy aggregates,” J. Quant. Spectrosc. Radiat. Transfer 108, 65-80 (2007). [CrossRef]
  21. B. T. Draine, “The discrete dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848-872 (1988). [CrossRef]
  22. B. T. Draine and P. J. Flatau, “User guide to the discrete dipole approximation code DDSCAT 6.1” (2004), http://arxiv.org/abs/astro-ph/0409262.
  23. H. Okamoto, “Light scattering by clusters: the A1-term method,” Opt. Rev. 2, 407-412 (1995). [CrossRef]
  24. H. Okamoto and Y. Xu, “Light scattering by irregular interplanetary dust particles,” Earth Planets Space 50, 577-585(1998).
  25. D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13, 2266-2278 (1996). [CrossRef]
  26. M. I. Mishchenko and D. W. Mackowski, “Electromagnetic scattering by randomly oriented bispheres: comparison of theory and experiment and benchmark calculations,” J. Quant. Spectrosc. Radiat. Transfer 55, 683-694 (1996). [CrossRef]
  27. W. Sun, N. G. Loeb, and Q. Fu, “Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium,” Appl. Opt. 41, 5728-5743 (2002). [CrossRef]
  28. W. Sun, N. G. Loeb, G. Videen, and Q. Fu, “Examination of surface roughness on light scattering by long ice columns by use of a two-dimensional finite-difference time-domain algorithm,” Appl. Opt. 43, 1957-1964 (2004). [CrossRef]
  29. P. Yang and K. N. Liou, “Finite difference time domain method for light scattering by nonspherical and inhomogeneous particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, and J. D. Travis, eds. (Academic, 2000). pp. 173-221.
  30. T. Mukai, H. Ishimoto, T. Kozasa, J. Blum, and J. M. Greenberg, “Radiation pressure forces of fluffy porous grains,” Astron. Astrophys. 262, 315-320 (1992).
  31. P. Chylek and V. Srivastava, “Dielectric constant of a composite inhomogeneous medium,” Phys. Rev. B 27, 5098-106(1983). [CrossRef]
  32. A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780-2788 (1993). [CrossRef]
  33. K. Muinonen, T. Nousiainen, P. Fast, K. Lumme, and J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577-601 (1996). [CrossRef]
  34. Y. Okada, A. M. Nakamura, and T. Mukai, “Light scattering by particulate media of irregularly shaped particles: laboratory measurements and numerical simulations,” J. Quant. Spectrosc. Radiat. Transfer 100, 295-304 (2006). [CrossRef]
  35. T. Mukai and Y. Okada, “Optical properties of large aggregates,” in Dust in Planetary Systems Workshop, H. Kruger and A. Graps, eds. (ESA Publications, 2007), paper SP-643.
  36. M. J. Wolff, G. C.Clayton, P. G. Martin, and R. E. Schulte-Ladbeck, “Modeling composite and fluffy grains: the effects of porosity,” Astrophys. J. 423, 412-425 (1994). [CrossRef]
  37. M. J. Wolff, G. C. Clayton, and S. J.Gibson, “Modeling composite and fluffy grain. II. Porosity and phase functions,” Astrophys. J. 503, 815-830 (1998). [CrossRef]
  38. N. V. Voshchinnikov and S. S.Mathis, “Calculating cross sections of composite interstellar grains,” Astrophys. J. 526, 257-264 (1999). [CrossRef]
  39. N. V. Voshchinnikov, V. B. Il'in , and Th. Henning, “Modelling the optical properties of composite and porous interstellar grains,” Astron. Astrophys. 429, 371-381 (2005). [CrossRef]
  40. N. V. Voshchinnikov, V. B. Il'in , Th. Henning, and D. N. Dubkova, “Dust extinction and absorption: the challenge of porous grains,” Astron. Astrophys. 445, 167-177(2006). [CrossRef]
  41. M. Koehler and I. Mann, “Light-scattering models applied to circumstellar dust properties,” J. Quant. Spectrosc. Radiat. Transfer 89, 453-460 (2004). [CrossRef]
  42. J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385-420(1904). [CrossRef]
  43. D. Bruggeman, “Calculation of various physics constants in heterogeneous substances. I. Dielectricity constants and conductivity of mixed bodies from isotropic substances,” Ann. Phys. 24, 636-664 (1935). [CrossRef]
  44. G. A. Niklaason, C. G. Granqvist, and O. Hunderi, “Effective medium models for the optical properties of inhomogeneous materials,” Appl. Opt. 20, 26-30 (1981). [CrossRef]
  45. M. Kocifaj and G. Videen, “Optical behavior of composite carbonaceous aerosols: DDA and EMT approaches,” J. Quant. Spectrosc. Radiat. Transfer 109, 1404-1416 (2008). [CrossRef]
  46. L. Kolokolova and B. Å. S. Gustafsonm, “Scattering by inhomogeneous particles: microwave analog experiments and comparison to effective medium theories,” J. Quant. Spectrosc. Radiat. Transfer 70, 611-625 (2001). [CrossRef]
  47. A. Taflove and S. C.Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method , Artech House Antennas and Propagation Library Series (Artech House, 2005).
  48. Y. Okada, T. Mukai, I. Mann, H. Nomura, T. Takeuchi, I. Sano, and S. Mukai, “Grouping and adding method for calculating light scattering by large fluffy aggregates,” J. Quant. Spectrosc. Radiat. Transfer 108, 65-80 (2007). [CrossRef]
  49. M. A. Yurkin, A. G. Hoekstral, R. S. Brock, and J. Q. Lu, “Systematic comparison of the discrete dipole approximation and the finite difference time domain method,” Opt. Express 15, 17902-17911 (2007). [CrossRef]
  50. M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an overview and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106, 558-589 (2007). [CrossRef]
  51. W. Sun and Q. Fu, “Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices,” Appl. Opt. 39, 5569-5578 (2000). [CrossRef]
  52. W. Sun, Q. Fu, and Z. Chen, “Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition,” Appl. Opt. 38, 3141-3151 (1999). [CrossRef]
  53. M. J. Cryan, D. C. L. Wong, I. J. Craddock, S. Yu, J. Rorison, and C. J. Railton, “Analysis of losses in 2D photonic crystal membrane waveguides using the 3D FDTD method,” in Proceedings of 6th International Conference on Transparent Optical Networks 2004 (IEEE, 2004), Vol. B2.3, pp.109-112.
  54. R. Jaenicke, “Properties of atmospheric aerosols,” in Landold-Bornstein: Numerical Data and Functional Relationships in Science and Technology (Springer, 1988). Vol. 4b, p. 417.

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

OSA is a member of CrossRef.

CrossCheck Deposited