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A grand challenge in fundamental physics and practical applications is overcoming wave diffusion to deposit energy into a target region deep inside a diffusive system. While it is known that coherently controlling the incident wavefront allows diffraction-limited focusing inside a diffusive system, in many applications targets are significantly larger than such a focus and the maximum deliverable energy remains unknown. Here, we introduce the deposition matrix, which maps an input wavefront to its internal field distribution, and theoretically predict the ultimate limitations on energy deposition at any depth. For example, the maximum obtainable energy enhancement occurs at 3/4 a diffusive systems thickness: regardless of its scattering strength. Experimentally we measure the deposition matrix and excite its eigenstates to enhance/suppress the energy within an extended target region. Our theoretical analysis reveals that such enhancement/suppression results from both selective transmission eigenchannel excitation and constructive/destructive interference among these channels.
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 fundament
A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the syst
The newly emerging field of wave front shaping in complex media has recently seen enormous progress. The driving force behind these advances has been the experimental accessibility of the information stored in the scattering matrix of a disordered me
The optics of correlated disordered media is a fascinating research topic emerging at the interface between the physics of waves in complex media and nanophotonics. Inspired by photonic structures in nature and enabled by advances in nanofabrication
We review some recent (mostly ours) results on the Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magneto-active optical structures, (iii) graphene superlattices, and (i