Decay Rate of Magnetic Dipoles near Non-magnetic Nanostructures

In this article, we propose a concise theoretical framework based on mixed field-susceptibilities to describe the decay of magnetic dipoles induced by non--magnetic nanostructures. This approach is first illustrated in simple cases in which analytical expressions of the decay rate can be obtained. We then show that a more refined numerical implementation of this formalism involving a volume discretization and the computation of a generalized propagator can predict the dynamics of magnetic dipoles in the vicinity of nanostructures of arbitrary geometries. We finally demonstrate the versatility of this numerical method by coupling it to an evolutionary optimization algorithm. In this way we predict a structure geometry which maximally promotes the decay of magnetic transitions with respect to electric emitters.