  The polarization of the light scattered by an optically dense, random
solution of dielectric nanoparticles shows peculiar properties when the
scatterers exhibit strong electric and magnetic polarizabilities. While the
distribution of the scattering intensity in these systems shows the typical
irregular speckle patterns, the helicity of the incident light can be fully
conserved when the electric and magnetic polarizabilities of the scatterers are
equal. We show that the multiple scattering of helical beams by a random
dispersion of "dual" dipolar nano-spheres leads to a speckle pattern exhibiting
a perfect isotropic constant polarization, a situation that could be useful in
coherent control of light as well as in lasing in random media.
