Hierarchical Mean-Field $\mathbb{T}$ Operator Bounds on Electromagnetic Scattering: Upper Bounds on Near-Field Radiative Purcell Enhancement

We show how the central equality of scattering theory, the definition of the \mathbb{T}operator, can be used to generate hierarchies of mean-field constraints that act as natural complements to the standard electromagnetic design problem of optimizing some objective with respect to structural degrees of freedom. Proof-of-concept application to the problem of maximizing radiative Purcell enhancement for a dipolar current source in the vicinity...