It is well known that concentric diffraction gratings are capable of beaming the spontaneous emission of large extended incoherent light sources (e.g. hot radiating surfaces and luminescent materials). Here, we reveal additional properties of such beams using layers of colloidal PbS nanocrystals coated onto metallic spiraling gratings as an example. We observe and explain with a simple model the formation of multiple beams when the spirals are deformed. We also point out an aspect of the light emission that does not seem to have been discussed so farnamely, that the polarization of the directional beams has a radial distribution. These findings are not restricted to our experimental configuration, suggesting a simple way to build incandescent and electroluminescent sources with non-trivial polarization states. The price to pay is an isotropic emission background due to the composite nature of the beams, which result from the incoherent superposition of a continuum of diffracted plasmons everywhere above the surface.