Full characterization of the transmission properties of a multi-plane light converter

Multi-plane light conversion (MPLC) allows to perform arbitrary transformations on a finite set of spatial modes with no theoretical restriction to the quality of the transformation. Even though the number of shaped modes is in general small, the number of modes transmitted by an MPLC system is extremely large. In this paper, we aim to characterize the transmission properties of a multi-plane light converter inside and outside the design-modes subspace. We report the construction of the full transmission matrix of such systems. By performing singular value decompositions, we individuate ways to evaluate their efficiency in performing the design transformation. Moreover, we develop an analytical random matrix model that suggests that in the regime of a large number of shaped modes an MPLC system behaves like a random scattering medium with limited number of controlled channels.