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\section{Light scattering by infinite cylinders}


Let us consider the features of light scattering by infinite cylinders.
The direction, intensity and polarization of radiation scattered
by such particles depend on the orientation of the cylinder's axis
relative to both the direction of the incident radiation and
the orientation of the electric vector in it (the state of
polarization of the incident radiation).

If the angle between the direction of the incident radiation and
%the cylinder's axis is $\pi /2 - \alpha $,
the cylinder's axis is $\alpha $,
the scattered radiation lies on the conical surface
%(the angle at the top of the cone is $\pi  - 2\alpha$)
(the angle at the top of the cone is $2\alpha$)
and its intensity depends on the observation angle
$\Phi$  ($0^{\degr} \leq \Phi  \leq  \pi$).
The angle $\Phi$ is measured in the plane perpendicular to
the cylinder's axis from the forward direction.
The scattering angle $\Theta$ between the scattered and incident radiation
is connected with $\Phi$ by the relation
\be
%\cos \Theta  = \sin ^{2}\alpha  + \cos ^{2}\alpha \cdot \cos \Phi.
\cos \Theta  = \cos^{2}\alpha  + \sin^{2}\alpha \cdot \cos \Phi.
\ee
The angle $\Theta$ is always smaller than $\Phi$ and coincides with it
only in the cases of forward-transmitted radiation
$(\Theta=\Phi=0^{\degr})$ or the radiation incident perpendicular to
%cylinder's axis $(\alpha=0^{\degr}, \Theta  \equiv  \Phi)$.
cylinder's axis $(\alpha=90^{\degr}, \Theta  \equiv  \Phi)$.
In the last case, the scattered radiation forms the plane
perpendicular to the cylinder's axis.


The discussion of light scattering by infinite cylinders can be found
in the books of Kerker
(Kerker, M. {\em The scattering of light and  other  electromagnetic
radiation}, New York, Academic Press, 1969, 645pp.)
and  Bohren and Huffman (Bohren, C.F. and Huffman, D.R.
{\em Absorption and Scattering of
Light by Small Particles}, John Wiley and Sons, New York, 1983).
Some expressions and tables are given also by Wicramasinghe
(Wicramasinghe,  N.C.  {\em Light  scattering  functions  for  small
particles with  applications  in  astronomy},  Hilger,  1973,
510pp.).

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\rightline{N.V. Voshchinnikov}

\rightline{Jena/St.~Petersburg}

\rightline{May/September, 2002}

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