  Structured light are custom light fields where the phase, polarization, and
intensity vary with position. It has been used for nanotweezers, nanoscale
imaging, and quantum information technology, but its role in exciting optical
transitions in materials has been little examined so far. Here we use group
theory to derive the optical selection rules for nanosystems that get excited
by structured light. If the size of the nanostructure is comparable to the
light wavelength, it will sample the full beam profile during excitation with
profound consequences on optical excitations. Using nanooligomers as model
nanosystems, we show that structured light excites optical transitions that are
forbidden for linearly polarized or unpolarized light. Such dipole forbidden
modes have longer lifetimes and narrower resonances than dipole allowed
transitions. We derive symmetry-adapted eigenmodes for nanooligomers containing
up to six monomers. Our study includes tables with selection rules for
cylindrical vector beams, for beams with orbital angular momentum, and for
field retardation along the propagation direction. We discuss multi-photon
processes of nonlinear optics in addition to one-photon absorption. Structured
light will unlock a broad range of excitations in nanooligomers and other
nanostructures that are currently inaccessible to optical studies.
