# $\mathbb{T}$-operator bounds on angle-integrated absorption and thermal radiation for arbitrary objects

## TL;DR

This paper establishes fundamental bounds on the angle-integrated absorption and thermal radiation of arbitrary objects using the scattering T-operator, capturing the transition from volume to area scaling in different regimes.

## Contribution

It introduces a unified theoretical framework for bounds on absorption and radiation that incorporates material, geometric, and passivity constraints using the T-operator.

## Key findings

- Bounds accurately reflect the transition from volume to area scaling.
- Comparison with prior limits shows improved accuracy.
- Topology optimization results approach the theoretical bounds.

## Abstract

We derive fundamental per-channel bounds on angle-integrated absorption and thermal radiation for arbitrary bodies---for any given material susceptibility and bounding region---that simultaneously encode both the per-volume limit on polarization set by passivity and geometric constraints on radiative efficiencies set by finite object sizes through the scattering $\mathbb{T}$-operator. We then analyze these bounds in two practical settings, comparing against prior limits as well as near optimal structures discovered through topology optimization. Principally, we show that the bounds properly capture the physically observed transition from the volume scaling of absorptivity seen in deeply subwavelength objects (nanoparticle radius or thin film thickness) to the area scaling of absorptivity seen in ray optics (blackbody limits).