Control and characterization of nano-structures with the symmetries of light

Light beams can be symmetric under different transformations: translations, rotations, mirror symmetries, duality transformations, etc. In this thesis, a systematic way of characterizing these symmetries is presented. Then, it is shown that light beams symmetric under different transformations can be used to control light-matter interactions at the nano-scale. Particular applications are developed, both theoretically and experimentally. Inducing a dual behaviour on a non-dual sample, the excitation of high multipolar order resonances and the measurement of circular dichroism using vortex beams are among them.