# Optimizing light storage in scattering media with the dwell-time operator

## TL;DR

This paper introduces a dwell-time operator derived from the scattering matrix to optimize light energy storage in disordered media, revealing eigenstates that deposit more energy than open channels and enabling energy storage in complex targets.

## Contribution

It develops a novel dwell-time operator from the scattering matrix and characterizes its eigenvalue distribution, advancing control of light storage in scattering media.

## Key findings

- Eigenvalue distribution has finite support with a maximum dwell-time much larger than the typical value.
- Highest dwell-time eigenstates deposit more energy than open channels.
- Dwell-time operator can be used to store energy in resonant targets within complex media.

## Abstract

We prove that optimal control of light energy storage in disordered media can be reached by wavefront shaping. For this purpose, we build an operator for dwell-times from the scattering matrix, and characterize its full eigenvalue distribution both numerically and analytically in the diffusive regime, where the thickness $L$ of the medium is much larger than the mean free path $\ell$. We show that the distribution has a finite support with a maximal dwell-time larger than the most likely value by a factor $(L/\ell)^2\gg 1 $. This reveals that the highest dwell-time eigenstates deposit more energy than the open channels of the medium. Finally, we show that the dwell-time operator can be used to store energy in resonant targets buried in complex media.