Skip to main content
SpringerLink
Log in

Light scattering by hexagonal ice crystal in the Wentzel–Kramers–Brillouin approximation

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

The Wentzel–Kramers–Brillouin (WKB) method is applied for hexagonal ice crystal. A closed form expression of the form factor is derived for an hexagonal ice crystal. The other approximations, such as the Rayleigh–Gans–Debye approximation (RGD) and the anomalous diffraction (AD), are deducted as particular cases from our formula. Furthermore, the coefficient of extinction is also given. This study is made for two special cases of the incidence (flat incident and edge-on incidence). To illustrate our analytical results, some numerical examples are analyzed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  • Belafhal, A., Ibnchaikh, M., Nassim, K.: Scattering amplitude of absorbing and non absorbing spheroidal particles in the WKB approximation. J. Quant. Spectrosc. Radiat. Transf. 72, 385–402 (2002)

    Article  ADS  Google Scholar 

  • Chylek, P., Klett, J.D.: Extinction cross sections of nonspherical particles in the anomalous diffraction approximation. J. Opt. Soc. Am. 8, 274–281 (1991)

    Article  ADS  Google Scholar 

  • Eremin, Y.A., Ivakhnenko, V.I.: Modeling of light scattering by nonspherical inhomogeneous particles. J. Quant. Spectrosc. Radiat. Transf. 60, 475–482 (1998)

    Article  ADS  Google Scholar 

  • Fan, X., Zheng, W., Singh, D.J.: Light scattering and surface plasmons on small spherical particles. Light Sci. Appl. 3, 179–192 (2014)

    Article  Google Scholar 

  • Fast, F.G.: Calculation of the light differential scattering cross section of optically soft and convex bodies. Opt. Commun. 313, 394–400 (2014)

    Article  Google Scholar 

  • Ishimaru, A.: Wave Propagation and Scattering in Random Media Volume I-Single Scattering and Transport Theory, pp. 9–40. Academic Press, New York (1978)

    Book  Google Scholar 

  • Klett, J.D., Sutherland, R.A.: Approximate methods for modeling the scattering properties of nonspherical particles: evaluation of the Wentzel–Kramers–Brillouin method. Appl. Opt. 31, 373–386 (1992)

    Article  ADS  Google Scholar 

  • Mishchenko, M.I., Tishkovets, V.P., Travis, L.D., Cairns, B., Dlugach, J.M., Liu, L., Rosenbush, V.K., Kiselev, N.N.: Electromagnetic scattering by a morphologically complex object: fundamental concepts and common misconceptions. J. Quant. Spectrosc. Radiat. Transf. 112, 671–692 (2011)

    Article  ADS  Google Scholar 

  • Shapovalov, K.A.: Light scattering of cylindrical particles in Rayleigh–Gans–Debye approximation. Randomly oriented particles. Atmos. Oceanic. Opt. 17, 627–629 (2004)

    Google Scholar 

  • Shapovalov, K.A.: Light scattering by particles of toroidal shape in the Rayleigh–Gans–Debye approximation. Opt. Spectrosc. 110, 806–810 (2011)

    Article  ADS  Google Scholar 

  • Shepelevich, N.V., Prostakova, I.V., Lopatin, V.N.: Extrema in the light scattering indicatrix of a homogeneous spheroid. J. Quant. Spectrosc. Radiat. Transf. 63, 353–367 (1999)

    Article  ADS  MATH  Google Scholar 

  • Sun, W., Fu, Q.: Anomalous diffraction theory for arbitrary oriented hexagonal crystals. J. Quant. Spectrosc. Radiat. Transf. 63, 727–737 (1999)

    Article  ADS  Google Scholar 

  • Takano, Y., Asano, S.: Fraunhofer Diffraction by ice crystals suspended in the atmosphere. J. Meteorol. Soc. Jpn. 61, 289–300 (1983)

    ADS  Google Scholar 

  • van de Hulst, H.C.: Light Scattering by Small Particles. Wiley, New York (1957)

    Google Scholar 

  • Yang, P., Liou, K. N.: Light scattering and absorption by nonspherical ice crystals. Light Scattering Reviews, pp. 32–73. (2006)

Download references

Author information

Authors and Affiliations

  1. Laboratory of Physics of Condensed Matter, Department of Physics, Faculty of Sciences, Chouaïb Doukkali University, B.P 20, 24000, El Jadida, Morocco

    M. Ibn Chaikh & R. Lamsoudi

  2. Laboratory of Nuclear, Atomic and Molecular Physics, Department of Physics, Faculty of Sciences, Chouaïb Doukkali University, B.P 20, 24000, El Jadida, Morocco

    A. Belafhal

Authors
  1. M. Ibn Chaikh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Lamsoudi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Belafhal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Belafhal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ibn Chaikh, M., Lamsoudi, R. & Belafhal, A. Light scattering by hexagonal ice crystal in the Wentzel–Kramers–Brillouin approximation. Opt Quant Electron 48, 466 (2016). https://doi.org/10.1007/s11082-016-0738-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-016-0738-0

Keywords

Search

Navigation