Transmission matrix assisted beam shaping through a multi-mode multi-core fiber

We present a transmission matrix (TM)-based approach for shaping the output beam of a multi-mode multi-core fiber (MM-MCF). By treating the MM-MCF as a particular scattering medium, we first measure its pixel-basis TM, which is then used to generate focal spots at different positions across multiple output cores. Furthermore, we convert the pixel-basis TM into the fiber’s eigenmode-basis TM and subsequently diagonalize the matrix. The diagonalization process enables the extraction of misalignments and fiber parameters. Based on these parameters and the quasi-diagonalized eigenmode-basis TM, we construct a pixel-to-eigenmode hybrid TM. This hybrid TM facilitates an accurate mapping from the input mode basis to the output fiber's eigenmode basis. Finally, we demonstrate the simultaneous generation of different-order eigenmodes at the output cores of the MM-MCF.