# Inverse Design of Perfectly Transmitting Eigenchannels in Scattering Media

## TL;DR

This paper presents a method to design waveguide shapes that produce perfectly transmitting eigenchannels in scattering media, enabling controlled light delivery and tailored energy distributions.

## Contribution

The authors develop an analytical model linking waveguide shape to eigenchannel intensity profiles and introduce an inverse design approach for perfect transmission.

## Key findings

- Analytical expression relating intensity profile to waveguide shape
- Successful inverse design of waveguides for desired energy distribution
- Prediction of eigenchannel profiles in disordered slabs

## Abstract

Light-matter interactions inside turbid medium can be controlled by tailoring the spatial distribution of energy density throughout the system. Wavefront shaping allows selective coupling of incident light to different transmission eigenchannels, producing dramatically different spatial intensity profiles. In contrast to the density of transmission eigenvalues that is dictated by the universal bimodal distribution, the spatial structures of the eigenchannels are not universal and depend on the confinement geometry of the system. Here, we develop and verify a model for the transmission eigenchannel with the corresponding eigenvalue close to unity. By projecting the original problem of two-dimensional diffusion in a homogeneous scattering medium onto a one-dimensional inhomogeneous diffusion, we obtain an analytical expression relating the intensity profile to the shape of the confining waveguide. Inverting this relationship enables the inverse design of the waveguide shape to achieve the desired energy distribution for the perfectly transmitting eigenchannel. Our approach also allows to predict the intensity profile of such channel in a disordered slab with open boundaries, pointing to the possibility of controllable delivery of light to different depths with local illumination.