OAM-basis transmission matrix in optics: a novel approach to manipulate light propagation through scattering media

Transmission matrix (TM) is an ideal theoretical model describing light propagation through scattering media. Until now, most of the present TMs utilize the eigenstates of spatial position as input and output bases. Thus, they describe the relationship between the spatial distributions of two light fields. Here, we demonstrate that wider relationships between the light fields could be described by a TM. As a significant example, we propose a generalized TM with the eigenstates of OAM as input bases - OAM-basis TM. With the measured OAM-basis TM, we achieved single-spot and multiple-spot focusing, verifying its availability in light propagation manipulation. The distinct eigenchannels property was also discussed. The OAM-basis TM has broadened the definition of TM. Meanwhile, it will open new perspectives for OAM-based communication, as well as the applications of wavefront shaping technology in biomedical photonics and optical communication.