Inverse design of light-matter interactions

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 the Purcell factor of latter as an example, we use finite-difference time-domain techniques to demonstrate the ability of inverse design algorithms to go far beyond what can be achieved by intuition-based approaches, opening up a new route to their technological exploitation.