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

TL;DR

This paper introduces hierarchical mean-field bounds based on the $ ext{T}$ operator in scattering theory to establish tighter limits on electromagnetic near-field radiative enhancement, with implications for sensing and quantum tech.

Contribution

It develops a novel hierarchy of mean-field constraints from the $ ext{T}$ operator, providing more accurate bounds on radiative Purcell enhancement than existing methods.

Findings

Performance bounds are often more than an order of magnitude tighter.

The bounds reveal the limitations of current models with different domain and field scales.

Method can be extended to other wave physics domains.

Abstract

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 of a structured medium, an effect central to many sensing and quantum technologies, yields performance bounds that are frequently more than an order of magnitude tighter than all current frameworks, highlighting the irreality of these models in the presence of differing domain and field-localization length scales. Closely related to domain decomposition and multi-grid methods, similar constructions are possible in any branch of wave physics, paving the way for systematic evaluations of fundamental limits beyond electromagnetism.