Inverse design of light-matter interactions in macroscopic QED

Inverse design represents a paradigm shift in the development of nanophotonic devices, where optimal geometries and materials are discovered by an algorithm rather than symmetry considerations or intuition. Here we present a very general formulation of inverse design that is applicable to atomic interactions in external environments, and derive from this some explicit formulae for optimisation of spontaneous decay rates, Casimir-Polder forces and resonant energy transfer. Using Purcell enhancement of the latter as a simple example, we employ finite-difference time-domain techniques in a proof-of-principle demonstration of our formula, finding enhancement of the rate many orders of magnitude larger than a selection of traditional designs.