Fundamental Bounds on the Polarizability of Macroscopic Scatterers

Abstract

Polarizability predicts how an object responds to an incident electromagnetic field, the interactions between small particles, or the optical forces exerted upon them. Polarizability is responsible for the effective-medium properties of artificial materials or metasurfaces. Despite significant progress in all these areas, it is unclear what the limits of the strength of such interactions are or, more specifically, what the upper bounds on the polarizability of a given spatial region that an unknown and designed particle would occupy are. This work connects the electromagnetic field description via an integral equation with a dual formulation of quadratic programming to derive fundamental bounds on components of all four polarizability tensors or on their specific combinations. In particular, the work establishes an intuitive visualization of what strong polarizability means and how strong it can be. The developed fundamental bound also answers which materials and domains are best for the given demands on polarizability. These findings establish a versatile platform that can accommodate a wide range of demands on polarizable bodies, providing an absolute measure of their performance against which the results of human-powered or automated design procedures can be compared.