When waves travel through complex environments (such as acoustics), repeated scattering is usually a problem because it scrambles wavefronts and distorts the information they carry. As a result, most approaches seek to suppress or compensate for scattering. In this work, however, the researchers take the opposite approach and show that scattering itself can be harnessed to manipulate waves.

The challenge is to design a disordered medium so that multiple scattering produces a desired outcome. This is difficult because the scattering matrix, which describes how waves are transformed by the medium, depends sensitively on the positions of many individual scatterers. Finding a configuration that performs a target operation can therefore be like searching for a destination in a vast landscape. The researchers used a mathematical tool known as the generalized Wigner-Smith operator, which reveals how small changes in scatterer positions modify the scattering matrix. In effect, it acts as a local map of the design landscape, guiding the system toward target unitary transformations while maintaining near-perfect transmission.

The team demonstrated the concept using an acoustic waveguide containing eighty metallic cylinders. By carefully arranging the scatterers, they controlled how different waveguide modes were converted into one another, enabling operations known as braiding. Similar to weaving strands in a braid, braiding exchanges modes in a prescribed sequence. A particularly striking example is non-Abelian braiding, where changing the order of those exchanges produces different outcomes. Such order-dependent operations are of great interest in topological quantum computing and can also manipulate information encoded in classical waves. The researchers demonstrated this behavior experimentally using a compact multiple-scattering medium only a few wavelengths thick, avoiding the long structures required in previous wave-based braiding schemes.

The significance of the work extends well beyond braiding. The same design principle can realize a broad range of unitary transformations, suggesting that complex media can be programmed to process information carried by waves rather than simply transmit it. Although practical implementations will still face challenges such as loss, bandwidth, and fabrication constraints, the work offers a new way of thinking about disorder. Instead of treating scattering as an obstacle to overcome, researchers may be able to harness it as a resource to build compact, reconfigurable devices for communications, imaging, signal processing, and wave-based computation.

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Non-local and non-Hermitian acoustic metasurfaces by Xu Wang, Ruizhi Dong, Yong Li and Yun Jing (2023)