Hierarchical mean-field<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="double-struck">T</mml:mi></mml:math>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...