# Mean path length invariance in multiple light scattering

## TL;DR

This paper experimentally demonstrates that the average path length of light in a scattering medium remains constant despite changes in the medium's scattering properties, revealing a fundamental invariance in light transport.

## Contribution

The study provides the first experimental verification of the theoretical invariance of mean path length in multiple light scattering media across various scattering strengths.

## Key findings

- Mean path length remains constant despite varying scattering strength.
- Invariance observed over nearly two orders of magnitude in scattering properties.
- Results applicable to both ordered and disordered photonic systems.

## Abstract

Our everyday experience teaches us that the structure of a medium strongly influences how light propagates through it. A disordered medium, e.g., appears transparent or opaque, depending on whether its structure features a mean free path that is larger or smaller than the medium thickness. While the microstructure of the medium uniquely determines the shape of all penetrating light paths, recent theoretical insights indicate that the mean length of these paths is entirely independent of any structural medium property and thus also invariant with respect to a change in the mean free path. Here, we report an experiment that demonstrates this surprising property explicitly. Using colloidal solutions with varying concentration and particle size, we establish an invariance of the mean path length spanning nearly two orders of magnitude in scattering strength, from almost transparent to very opaque media. This very general, fundamental and counterintuitive result can be extended to a wide range of systems, however ordered, correlated or disordered, and has important consequences for many fields, including light trapping and harvesting for solar cells and more generally in photonic structure design.