Perturbative light–matter interactions; from first principles to inverse design

Our experience of the world around us is governed almost entirely by light–matter interactions. At the most fundamental level, such interactions are described by quantum electrodynamics (QED), a well-established theory that has stood up to decades of experimental testing to remarkable degrees of precision. However, the complexity of real systems almost always means that the quantum electrodynamical equations describing a given scenario are often infeasible or impractical to solve. Thus, a sequence of approximations and idealisations are made, in order to build up from the simple case of an isolated electron interacting with a gauge field leading to the deceptively simple laws governing reflection and refraction at mirrors and lenses. This review provides a pedagogical overview of this journey, concentrating on cases where external boundary conditions can be used as a control method. Beginning from the fundamental Lagrangian, topics include gauge freedom, perturbative macroscopic QED descriptions of spontaneous decay, Casimir–Polder forces, resonant energy transfer, interatomic Coulombic decay, all of which are described in terms of the dyadic Green’s tensor that solves the Helmholtz equation. We discuss in detail how to calculate this tensor in practical situations before outlining new techniques in the design and optimisation of perturbative light–matter interactions, highlighting some recent advances in free-form, unconstrained inverse design of optical devices. Finally, an outlook towards the frontiers in the interaction of quantum light with matter is given, including its interface with chemical reactivity via polaritonic chemistry and quantum chemistry via quantum electrodynamical density functional theory (QEDFT).