Eigenvalue distributions of correlated multichannel transfer matrices in strongly scattering systems

Abstract

We experimentally study the effects of correlations in the propagation of ultrasonic waves in water from a multielement source to a multielement detector through a strongly scattering system of randomly placed vertical rods. Due to the strong scattering, the wave transport in the sample is in the diffusive regime. The correlation between the waves is induced when the distance between transducer elements is within the coherence region of the scattered sound. We measure the multichannel transfer matrix $H$, each element of which represents the signal strength between the $m$ individual transmitters and $n$ receivers. The observed eigenvalue distribution of the matrix $H{H}^{†}$ clearly shows the effect of correlations between channels and can be interpreted using random matrix theory. These results are of practical importance in many areas, e.g., for evaluating the information transfer capacity of such a complex scattering system.