  Molecules with C_N or C_Nh symmetry can absorb quanta of optical angular
momentum to generate twisted excitons with well-defined quasi-angular momenta
of their own. Angular momentum is conserved in such interactions at the level
of a paraxial approximation for the light beam. A sequence of absorption events
can thus be used to create a range of excitonic angular momenta. Subsequent
decay can produce radiation with a single angular momentum equal to that
accumulated. Such molecules can thus be viewed as mediators for changing the
angular momentum of light. This sidesteps the need to exploit nonlinear
light-matter interactions based on higher-order susceptibilities. A
tight-binding paradigm is used to verify angular momentum conservation and
demonstrate how it can be exploited to change the angular momentum of light.
The approach is then extended to a time-dependent density functional theory
setting where the key results are shown to hold in a many-body, multi-level
setting.
