  As discovered by Philip Anderson in 1958, strong disorder can block
propagation of waves and lead to the localization of wave-like excitations in
space. Anderson localization of light is particularly exciting in view of its
possible applications for random lasing or quantum information processing. We
show that, surprisingly, Anderson localization of light cannot be achieved in a
random three-dimensional ensemble of point scattering centers that is the
simplest and widespread model to study the multiple scattering of waves.
Localization is recovered if the vector character of light is neglected. This
shows that, at least for point scatterers, the polarization of light plays an
important role in the Anderson localization problem.
