OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 40, Iss. 9 — Mar. 20, 2001
  • pp: 1532–1547

Asymptotic Solutions for Optical Properties of Large Particles with Strong Absorption

Ping Yang, Bo-Cai Gao, Bryan A. Baum, Yong X. Hu, Warren J. Wiscombe, Michael I. Mishchenko, Dave M. Winker, and Shaima L. Nasiri  »View Author Affiliations

Applied Optics, Vol. 40, Issue 9, pp. 1532-1547 (2001)

View Full Text Article

Acrobat PDF (312 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The transverse wave condition is not applicable to the refracted electromagnetic wave within the context of geometrical optics when absorption is involved. Either the TM or the TE wave condition can be assumed for the wave to locally satisfy the electromagnetic boundary condition in a ray-tracing calculation. The assumed wave mode affects both the reflection and the refraction coefficients. As a result, nonunique solutions for these coefficients are inevitable. In this study the appropriate solutions for the Fresnel reflection–refraction coefficients are identified in light-scattering calculations based on the ray-tracing technique. In particular, a 3 × 2 refraction or transmission matrix is derived to account for the inhomogeneity of the refracted wave in an absorbing medium. An asymptotic solution that completely includes the effect of medium absorption on Fresnel coefficients is obtained for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations.

© 2001 Optical Society of America

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.1310) Atmospheric and oceanic optics : Atmospheric scattering
(010.3920) Atmospheric and oceanic optics : Meteorology
(280.1310) Remote sensing and sensors : Atmospheric scattering
(290.1090) Scattering : Aerosol and cloud effects
(290.5850) Scattering : Scattering, particles

Ping Yang, Bo-Cai Gao, Bryan A. Baum, Yong X. Hu, Warren J. Wiscombe, Michael I. Mishchenko, Dave M. Winker, and Shaima L. Nasiri, "Asymptotic Solutions for Optical Properties of Large Particles with Strong Absorption," Appl. Opt. 40, 1532-1547 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, San Diego, Calif., 1999).
  2. E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705–714 (1973).
  3. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for light calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994).
  4. P. Yang and K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996).
  5. W.-B. 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).
  6. G. Mie, “Beitrage zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
  7. S. Asano and M. Sato, “Light scattering by randomly oriented spheroidal particles,” Appl. Opt. 19, 962–974 (1980).
  8. V. G. Farafonov, N. V. Voshchinnikov, and V. V. Somsikov, “Light scattering by a core-mantle spheroidal particle,” Appl. Opt. 35, 5412–5426 (1996).
  9. M. I. Mishchenko, “Light scattering by randomly oriented axially symmetric particles,” J. Opt. Soc. Am. A 8, 871–882 (1991).
  10. M. I. Mishchenko, “Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength,” Appl. Opt. 32, 623–625 (1993).
  11. M. I. Mishchenko and A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 38, 1626–1629 (1999).
  12. Y. Takano and K. N. Liou, “Solar radiative transfer in cirrus clouds. I. Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
  13. A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
  14. J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. I. Diffraction and specular reflection. II. Transmission and cross-polarization effects,” Appl. Opt. 35, 500–531 (1996).
  15. K. Muinonen, K. Lumme, J. Peltoniemi, and W. M. Irvine, “Light scattering by randomly oriented crystals,” Appl. Opt. 28, 3051–3060 (1989).
  16. A. Arking and J. D. Childs, “Retrieval of cloud cover parameters from multispectral satellite images,” J. Clim. Appl. Meteorol. 24, 322–333 (1985).
  17. M. D. King, Y. J. Kaufman, W. P. Menzel, and D. Tanre, “Remote sensing of cloud, aerosol, and water vapor properties from the Moderate Resolution Imaging Spectrometer (MODIS),” IEEE Trans. Geosci. Remote Sens. 30, 2–26 (1992).
  18. W. L. Smith, H. E. Revercomb, R. O. Knuteson, F. A. Best, R. Dedecker, H. B. Howell, and H. M. Woolf, “Cirrus cloud properties derived from high spectral resolution infrared spectrometry during FIRE II. I. The high resolution interferometer sounder (HIS) systems,” J. Atmos. Sci. 52, 4238–4245 (1995).
  19. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  20. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).
  21. J. Zhang and L. Xu, “Light scattering by absorbing hexagonal ice crystals in cirrus clouds,” Appl. Opt. 34, 5867–5874 (1995).
  22. P. Yang and K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995).
  23. W. P. Arnott, Y. Y. Dong, and J. Hallett, “Extinction efficiency in the infrared (2–18 μm) of laboratory ice clouds: observations of scattering minima in the Christiansen bands of ice,” Appl. Opt. 34, 541–551 (1995).
  24. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  25. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  26. P. Yang and K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmosphere,” Contrib. Atmos. Phys. 71, 223–248 (1998).
  27. W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
  28. K. N. Liou and J. E. Hansen, “Intensity and polarization for single scattering by polydisperse spheres: a comparison of ray optics and Mie theory,” J. Atmos. Sci. 28, 995–1004 (1971).
  29. A. Macke, M. I. Mishchenko, K. Muinonen, and B. E. Carlson, “Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
  30. M. I. Mishchenko and A. Macke, “Incorporation of physical optics effect and computation of the Legendre expansion for ray-tracing phase functions involving δ-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
  31. P. Yang and K. N. Liou, “Light scattering by hexagonal ice crystals: solution by a ray-by-ray integration algorithm,” J. Opt. Soc. Am. A 14, 2278–2289 (1997).
  32. P. Minnis, K. N. Liou, and Y. Takano, “Inference of cirrus cloud properties using satellite-observed visible and infrared radiances. I. Parameterization of radiance fields,” J. Atmos. Sci. 50, 1279–1304 (1993).
  33. B. A. Baum, R. F. Arduini, B. A. Wielicki, P. Minnis, and S.-C. Tsay, “Multilevel cloud retrieval using multispectral HIRS and AVHRR data: nighttime oceanic analysis,” J. Geophys. Res. 99, 5499–5514 (1994).
  34. Q. Han, W. B. Rossow, J. Chou, K-S. Kuo, and R. M. Welch, “The effect of aspect ratio and surface roughness on satellite retrieval of ice-cloud properties,” J. Quant. Spectrosc. Radiat. Transfer 63, 559–583 (1999).
  35. M.-D. Chou, K-T. Lee, S.-C. Tsay, and Q. Fu, “Parameterization for cloud longwave scattering for use in atmosphere models,” J. Climate 12, 159–169 (1999).
  36. D. L. Mitchell, A. Macke, and Y. Liu, “Modeling cirrus clouds. II. Treatment of radiative properties,” J. Atmos. Sci. 53, 2967–2988 (1996).
  37. Q. Fu, P. Yang, and W. B. Sun, “An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models,” J. Climate 11, 2223–2237 (1998).
  38. T. C. Grenfell and S. G. Warren, “Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation,” J. Geophys. Res. 104, 31, 697–31, 709 (1999).
  39. D. L. Mitchell, “Parameterization of the Mie extinction and absorption coefficients for water clouds,” J. Atmos. Sci. 57, 1311–1326 (2000).
  40. A. J. Baran and S. Havemann, “Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory,” J. Quant. Spectrosc. Radiat. Transfer 63, 499–519 (1999).
  41. S. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
  42. Y. Takano and K. N. Liou, “Radiative transfer in cirrus clouds. II. Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
  43. K.-D. Rockwitz, “Scattering properties of horizontally oriented ice crystal columns in cirrus clouds,” Appl. Opt. 28, 4103–4110 (1989).

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