# Guiding waves through chaos: Universal bounds for targeted mode transport

## TL;DR

This paper introduces a new method to efficiently control wave energy transfer in chaotic environments without needing full knowledge of the medium.

## Contribution

A universal statistical framework for targeted mode transport is developed, enabling optimal wavefront shaping in complex systems.

## Key findings

- The TMT framework predicts eigenvalue distributions and identifies key parameters like coupling strength and absorption.
- Explicit bounds for optimal TMT wavefronts are derived, revealing phenomena like transmission gaps and reflectionless states.
- The theory is validated across multiple platforms, including microwave networks and reverberation chambers.

## Abstract

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.

A universal framework reveals governing laws for optimal wave focusing and maximal energy delivery in chaotic environments.