# Universal Validity Ranges of Diffusion Theory for Light and Other Electromagnetic Waves

## TL;DR

This paper establishes the precise limits of diffusion theory's validity for electromagnetic waves, showing where it fails and quantifying the errors in inferred scattering properties outside these ranges.

## Contribution

It provides universal, quantitative bounds on scattering parameters for which diffusion theory remains physically valid, addressing a long-standing gap in understanding its applicability.

## Key findings

- Diffusion theory fails for strong forward scattering and absorption.
- Applying diffusion theory outside validity ranges causes up to tenfold errors in scattering parameters.
- The results impact atmospheric sciences, biophysics, lighting, and wave localization studies.

## Abstract

The well-known diffusion theory describes propagation of light and electromagnetic waves in complex media. While diffusion theory is known to fail both for predominant forward scattering or strong absorption, its precise range of validity has never been established. Therefore we present precise, universal limits on the scattering properties, beyond which diffusion theory yields unphysical negative energy density and negative incident flux. When applying diffusion theory to samples outside validity ranges to {\it infer} scattering properties from transmission and reflection, the resulting transport parameters deviate by up to an order of magnitude compared to the true ones. These discrepancies are relevant to atmospheric and climate sciences, biophysics and health sciences, white LEDs and lighting, and Anderson localization of waves.