  The discovery of orbital angular momentum (OAM) in light established a new
degree of freedom by which to control not only its flow but also its
interaction with matter. Here, we show that by shaping extremely sub-wavelength
polariton modes, for example by imbuing plasmon and phonon polariton with OAM,
we engineer which transitions are allowed or forbidden in electronic systems
such as atoms, molecules, and artificial atoms. Crucial to the feasibility of
these engineered selection rules is the access to conventionally forbidden
transitions afforded by sub-wavelength polaritons. We also find that the
position of the absorbing atom provides a surprisingly rich parameter for
controlling which absorption processes dominate over others. Additional
tunability can be achieved by altering the polaritonic properties of the
substrate, for example by tuning the carrier density in graphene, potentially
enabling electronic control over selection rules. Our findings are best suited
to OAM-carrying polaritonic modes that can be created in graphene, monolayer
conductors, thin metallic films, and thin films of polar dielectrics such as
boron nitride. By building on these findings we foresee the complete
engineering of spectroscopic selection rules through the many degrees of
freedom in the shape of optical fields.
