OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 42, Iss. 9 — Mar. 20, 2003
  • pp: 1710–1720

Improved recursive algorithm for light scattering by a multilayered sphere

Wen Yang  »View Author Affiliations

Applied Optics, Vol. 42, Issue 9, pp. 1710-1720 (2003)

View Full Text Article

Enhanced HTML    Acrobat PDF (208 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An improved recurrence algorithm to calculate the scattering field of a multilayered sphere is developed. The internal and external electromagnetic fields are expressed as a superposition of inward and outward waves. The alternative yet equivalent expansions of fields are proposed by use of the first kind of Bessel function and the first kind of Hankel function instead of the first and the second kinds of Bessel function. The final recursive expressions are similar in form to those of Mie theory for a homogeneous sphere and are proved to be more concise and convenient than earlier forms. The new algorithm avoids the numerical difficulties, which give rise to significant errors encountered in practice by previous methods, especially for large, highly absorbing thin shells. Various calculations and tests show that this algorithm is efficient, numerically stable, and accurate for a large range of size parameters and refractive indices.

© 2003 Optical Society of America

OCIS Codes
(010.1110) Atmospheric and oceanic optics : Aerosols
(290.1310) Scattering : Atmospheric scattering
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles

Original Manuscript: June 8, 2002
Revised Manuscript: November 8, 2002
Published: March 20, 2003

Wen Yang, "Improved recursive algorithm for light scattering by a multilayered sphere," Appl. Opt. 42, 1710-1720 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  2. P. Chylek, V. Ramaswamy, R. J. Cheng, “Effect of graphitic carbon on the albedo of clouds,” J. Atmos. Sci. 41, 3076–3084 (1984). [CrossRef]
  3. J. V. Martins, P. Artaxo, C. Liousse, J. S. Reid, P. V. Hobbs, Y. J. Kaufman, “Effects of black carbon content, particle size, and mixing on the light absorption by aerosols from biomass burning in Brazil,” J. Geophys. Res. 103, 32041–32050 (1998). [CrossRef]
  4. G. W. Kattawar, D. A. Hood, “Electromagnetic scattering from a spherical polydispersion of coated spheres,” Appl. Opt. 15, 1996–1999 (1976). [CrossRef] [PubMed]
  5. A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951). [CrossRef]
  6. R. W. Fenn, H. Oser, “Scattering properties of concentric soot-water spheres for visible and infrared light,” Appl. Opt. 4, 1504–1509 (1965). [CrossRef]
  7. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  8. O. B. Toon, T. P. Ackerman, “Algorithms for the calculation of scattering by stratified spheres,” Appl. Opt. 20, 3657–3660 (1981). [CrossRef] [PubMed]
  9. R. Bhandari, “Scattering coefficients for a multilayered sphere: analytic expressions and algorithms,” Appl. Opt. 24, 1960–1967 (1985). [CrossRef] [PubMed]
  10. Z. S. Wu, Y. P. Wang, “Electromagnetic scattering for multilayered sphere: recursive algorithms,” Radio Sci. 26, 1393–1401 (1991). [CrossRef]
  11. Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, G. Grehan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered sphere,” Appl. Opt. 36, 5188–5198 (1997). [CrossRef] [PubMed]
  12. B. R. Johnson, “Light scattering by a multilayer sphere,” Appl. Opt. 35, 3286–3296 (1996). [CrossRef] [PubMed]
  13. D. W. Mackowski, R. A. Altenkirch, M. P. Menguc, “Internal absorption cross sections in a stratified sphere,” Appl. Opt. 29, 1551–1559 (1990). [CrossRef] [PubMed]
  14. L. Kai, P. Massoli, “Scattering of electromagnetic-plane waves by radially inhomogeneous spheres: a finely stratified sphere model,” Appl. Opt. 33, 501–511 (1994). [CrossRef] [PubMed]
  15. K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. III. Spheres containing arbitrary located spherical inhomogeneities,” J. Opt. Soc. Am. A 12, 893–904 (1995). [CrossRef]
  16. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980). [CrossRef] [PubMed]
  17. R. Bhandari, “Tiny core or thin layer as a perturbation in scattering by a single-layered sphere,” J. Opt. Soc. Am. A 3, 319–328 (1987). [CrossRef]
  18. W. F. Espenscheid, E. Willis, E. Matijevic, M. Kerker, “Aerosol studies by light scattering. IV. Preparation and particle size distribution of aerosol consisting of concentric spheres,” J. Colloid Sci. 20, 501–521 (1965). [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