arXiv:2604.11763v1 Announce Type: new Abstract: Arbitrary manipulation of light across multiple physical dimensions is essential for harnessing its parallelism in fundamental research and advanced applications, such as optical interconnects, computing, imaging, sensing, and quantum networks. However, creating a universal device capable of arbitrary operations of multidimensional optical beams has been challenging, primarily due to their complex mutual interferences and dynamic transmission characteristics. In this study, we experimentally demonstrate a self-configuring integrated photonic processor designed for the arbitrary manipulations of multiple optical waves over their spatial and polarization dimensions. Despite the random nature of the input speckle, the photonic processor relies on an optical singular-value decomposition engine to sort all orthogonal input beams and implement arbitrary processing over both spatial and polarization dimensions precisely. Notably, the photonic processor can be self programmed in situ, enabling versatile functionalities such as beam shaping, optical switching, and reconfigurable optical add-drop multiplexing. Our findings advance the manipulation of multidimensional optical beams through a scalable, CMOS-compatible integration approach, paving the way for fully exploiting the parallelism of light in various applications.