  This paper investigates the integration of beyond-diagonal reconfigurable
intelligent surfaces (BD-RISs) into cell-free massive multiple-input
multiple-output (CF-mMIMO) systems, focusing on applications involving
simultaneous wireless information and power transfer (SWIPT). The system
supports concurrently two user groups: information users (IUs) and energy users
(EUs). A BD-RIS is employed to enhance the wireless power transfer (WPT)
directed towards the EUs. To comprehensively evaluate the system's performance,
we present an analytical framework for the spectral efficiency (SE) of IUs and
the average harvested energy (HE) of EUs in the presence of spatial correlation
among the BD-RIS elements and for a non-linear energy harvesting circuit. Our
findings offer important insights into the transformative potential of BD-RIS,
setting the stage for the development of more efficient and effective SWIPT
networks. Finally, incorporating a heuristic scattering matrix design at the
BD-RIS results in a substantial improvement compared to the scenario with
random scattering matrix design.
