Energy density distribution of shaped waves inside scattering media mapped onto a complete set of diffusion modes

TL;DR

This paper demonstrates that the energy density distribution of optimally shaped waves in scattering media can be accurately described using only the lowest eigenfunctions of the diffusion equation, simplifying analysis and applications.

Contribution

It introduces a method to approximate the energy density distribution with minimal eigenfunctions, significantly reducing computational complexity and improving understanding of wave behavior in scattering media.

Findings

Energy density closely matches the fundamental eigenfunction.

Total internal energy is underestimated by only 2% when using the fundamental eigenfunction.

Spatial distribution of shaped energy density is highly similar to the fundamental eigenfunction.

Abstract

We show that the spatial distribution of the energy density of optimally shaped waves inside a scattering medium can be described by considering only a few of the lowest eigenfunctions of the diffusion equation. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtained the energy density inside a quasi-1D disordered waveguide by numerical calculation of the joined scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density obtained, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results from our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.