Optimizing Light Storage in Scattering Media with the Dwell-Time Operator

We prove that optimal control of light energy storage in disordered media can be reached by wave front 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 ℓ. We show that the distribution has a finite support with a maximal dwell time larger than the most likely value by a factor (L/ℓ)^{2}≫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, without any need for guide stars.