Emission of twisted light from quantum dot arrays with a discrete rotational symmetry

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.