The average transmitted wave in random particulate materials

TL;DR

This paper provides experimental evidence for multiple effective wave propagations in random particulate materials, challenging traditional assumptions and linking extinction length to particle correlation length.

Contribution

It offers the first clear evidence of multiple effective waves in scalar wave propagation through isotropic particulate media, supported by high fidelity Monte-Carlo simulations.

Findings

Confirmed the existence of multiple effective waves in particulate materials

Proved the incident wave does not propagate within the material

Linked extinction length to particle correlation length

Abstract

Microwave remote sensing is significantly altered when passing through clouds or dense ice. This phenomenon isn't unique to microwaves; for instance, ultrasound is also disrupted when traversing through heterogeneous tissues. Understanding the average transmission in particle-filled environments is central to improve data extraction or even to create materials that can selectively block or absorb certain wave frequencies. Most methods that calculate the average transmitted field assume that it satisfies a wave equation with a complex effective wavenumber. However, recent theoretical work has predicted more than one effective wave propagating even in a material which is statistical isotropic and for scalar waves. In this work we provide the first clear evidence of these predicted multiple effective waves by using high fidelity Monte-Carlo simulations that do not make any statistical assumptions. To achieve this, we also had to fill in a missing link in the theory for particulate materials: we prove that the incident wave does not propagate within the material, which is usually taken as an assumption called the Ewald-Oseen extinction theorem. By proving this we conclude that the extinction length - the distance it takes for the incident wave to be extinct - is equal to the correlation length between the particles.