  Recent research has shown that coupling between point scatterers in a
disordered medium by longitudinal electromagnetic fields is harmful for
Anderson localization of light. However, it has been unclear if this feature is
generic or specific for point scatterers. The present work demonstrates that
the intensity of longitudinal field outside a spherical dielectric scatterer
illuminated by monochromatic light exhibits a complicated, nonmonotonous
dependence on the scatterer size. Moreover, the intensity is reduced for a
hollow sphere, whereas one can adjust the parameters of a coated sphere to
obtain a relatively low longitudinal field together with a strong resonant
scattering efficiency. Therefore, random arrangements of structured (hollow or
coated) spheres may be promising three-dimensional disordered materials for
reaching Anderson localization of light.
