Controlling wave propagation in complex environments is a central challenge across wireless communications, imaging, and acoustics, where multiple scattering and interference obscure direct transmission paths. Coherent wavefront shaping enables precise energy delivery but typically requires full knowledge of the medium. Here, we introduce a universal statistical framework for targeted mode transport (TMT) that circumvents this limitation and validate it on various platforms including microwave networks, two-dimensional chaotic cavities, and three-dimensional reverberation chambers. TMT quantifies the efficiency of transferring energy between specified input and output channels in multimode wave-chaotic systems. We develop a diagrammatic theory that predicts the eigenvalue distribution of the TMT operator and identifies the macroscopic parameters-coupling strength, absorption, and channel control-that govern performance. The theory provides explicit bounds for optimal TMT wavefronts and captures phenomena like statistical transmission gaps and reflectionless states. These findings establish design principles for energy delivery and information transfer in complex environments, with broad implications for adaptive signal processing and wave-based technologies.
Wang et al. (Wed,) studied this question.