On the density of states and extinction mean free path of waves in random media: Dispersion relations and sum rules

TL;DR

This paper derives fundamental dispersion relations and sum rules linking the density of states and extinction mean free path in wave propagation through random media, aiding analysis and design of complex materials.

Contribution

It establishes a general theoretical framework connecting density of states and mean free path via causality and Kramers-Kronig relations, applicable to complex media.

Findings

Derived dispersion relations between density of states and mean free path.

Established a frequency sum rule constraining these quantities.

Provided a general theoretical basis for analyzing wave transport in complex systems.

Abstract

We establish a fundamental relationship between the averaged density of states and the extinction mean free path of wave propagating in random media. From the principle of causality and the Kramers-Kronig relations, we show that both quantities are connected by dispersion relations and are constrained by a frequency sum rule. The results are valid under very general conditions and should be helpful in the analysis of measurements of wave transport through complex systems and in the design of randomly or periodically structured materials with specific transport properties.