Off-axis phase modulation for SU(2) mode sorting

Multi-singularity structured beams carrying SU(2) modes offer significant potential for expanding communication capacity by leveraging their three orthogonal mode degrees of freedom (DoFs): central orbital angular momentum (OAM), sub-beam OAM, and coherent-state phase. Despite considerable advancements in the recognition of SU(2) modes, challenges remain in the sorting of these modes for signal demultiplexing, including multi-mode conversion and mode separation. In this work, we propose a novel, to the best of our knowledge, SU(2) mode sorting strategy based on off-axis phase modulation, which converts SU(2) modes into quasi-Gaussian modes with customized diffraction angles by combining conjugate phase and gradient phase modulation, thus sorting coaxially transmitted SU(2) modes to distinct spatial positions. We demonstrate the simultaneous sorting of 18 SU(2) modes (including three central OAM, three sub-beam OAM, and two coherent-state phases) with minimal cross talk, achieving levels below -13.8 dB. As a proof of concept, we have developed an SU(2) mode multiplexing communication link that successfully transmits 100 Gbit/s quadrature phase-shift keying (QPSK) signals with bit error rates (BERs) below 10^-5. Our approach provides flexibility in the spatial reallocation of SU(2) modes and holds promise for advancing multidimensional multiplexing communication and high-efficiency shift-keying (SK) communication.