It has become of recent interest to complement electromagnetic responses in
intensity by the additional consideration of their polarizations. In order
to affect the latter, media have been considered that contain inclusions o
f randomly distributed and oriented short, thin wires (needles), whose pola
rized scattering amplitudes can modify the well-known polarization of surfa
ce reflections that is governed simply by the so-called Fresnel coefficient
s. In the present study, we analytically obtain, for the case of a multipli
city of perfectly conducting wires imbedded in a dielectric, the correspond
ing wave scattering amplitudes and their superposition with the specularly
surface-reflected wave amplitude when both are being generated by the same
incident wave. This allows a calculation of the total returned-wave polariz
ations which we express by the real Stokes parameters.