Scattering matrices of two-dimensional complex acoustic media

Wave propagation in complex media has long been a captivating research topic with diverse applications. The accurate determination of scattering matrices (S-matrices) is crucial for the effective characterization of wave scattering phenomena in such media. This paper presents a detailed exposition of the formulation of S-matrices for two-dimensional acoustic complex media in a multimode waveguide, using channel and point bases. We explore the conversion relationships between these bases and the factors affecting their accuracy and reliability. The effectiveness of the proposed methods for extracting S-matrices is validated by numerical simulations on a complex medium consisting of randomly arranged cylinder scatterers. We successfully achieved acoustic wave focusing in both bases via wavefront shaping. We also reveal that the non-unitary characteristic of the conversion relations is linked to the absence of open channels in the point basis. Our results establish the theoretical and methodological foundation for further study of multiple-scattering phenomena in acoustics.