Analytic framework for understanding the competing multiple light scattering processes

In many complex physical phenomena such as wave propagation in scattering media, the process of interest often cannot be easily distinguished from other processes because only the total combined process is accessible. This makes it difficult to extract the precise knowledge of each subprocess. Here, we derive an analytic expression describing the way the eigenchannel coupling of the total process distributes its energy to the individual subprocesses, with only partial information on each subprocess such as the average eigenvalue 〈τ〉 and enhancement factor η. We found that the ratio of (η - 1)〈τ〉 between two subprocesses is a critical parameter determining the preferable subprocess in the energy coupling. This work provides a new analytic framework for understanding the effect of wavefront shaping in the control of wave propagation in disordered media.