Tailoring multiple scattering acoustic media with perfect transmission for non-Abelian braiding and beyond

Abstract

Multiple scattering of waves in complex media can be harnessed and tailored for diverse phenomena in sound and light. Despite the tremendous progress enabled by technologies such as time-reversal propagation and wavefront shaping, the full control of transmission matrix remains a significant challenge. In this work, we propose a multi-scattering-based approach to design reflectionless complex media with a unitary transmission matrix of arbitrary structures. As such, the perfect transmission of waves through such a medium performs a unitary operation. Based on this principle, we experimentally demonstrated braiding of multiple waveguide modes in an acoustic waveguide via multiple scattering and showed non-Abelian characteristics arising from the concatenation of distinct complex media. Furthermore, we show that the principle can be extended for realizing arbitrary unitary operations beyond braiding. Our scheme uses generalized Wigner-Smith operators to design the optimal acoustic complex media with near-arbitrary targeted functionalities. The scheme is generally applicable beyond acoustics, with broad implications to other wave types. Our results demonstrate unprecedented control over multiple-scattering waves and are relevant to applications that require precise control over propagation, such as multiplexed communications, wave-based logic operations, and computations.