Computational bounds to light-matter interactions via local conservation laws

TL;DR

This paper introduces a computational framework leveraging local conservation laws to establish bounds on light-matter interactions, enabling efficient determination of scatterer size and scattering properties across bandwidths.

Contribution

It presents a novel iterative method for deriving bounds from polarization-current formulations, applicable to diverse optical problems including Fourier transforms and scattering limits.

Findings

Bound on minimum scatterer size for a given operator

Bounds on far-field scattering over arbitrary bandwidths

Rapid convergence of the iterative constraint enforcement

Abstract

We develop a computational framework for identifying bounds to light-matter interactions, originating from polarization-current-based formulations of local conservation laws embedded in Maxwell's equations. We propose an iterative method for imposing only the maximally violated constraints, enabling rapid convergence to global bounds. Our framework can identify bounds to the minimum size of any scatterer that encodes a specific linear operator, given only its material properties, as we demonstrate for the optical computation of a discrete Fourier transform. It further resolves bounds on far-field scattering properties over any arbitrary bandwidth, where previous bounds diverge.