  We theoretically explore the optical properties of a circular array of
quantum dots. This structure, that we call a circular emitter array (CEA), can
exchange optical angular momentum via the emission and absorption of circularly
polarised light as well as light carrying orbital angular momentum. Analytical
expressions are derived for both interband and intraband transition rates and
selection rules are determined. Only the key properties of the quantum dots are
considering when modelling the CEA. This extends the applicability of our model
to CEAs composed of a variety of quantum dots. Finally design principles for
the tuning of the specific optical properties of the CEA are determined. This
opens up the prospect of the designing a metamaterial, consisting of a surface
of CEAs, that upconverts optical angular momentum.
