Multi-mode vector vortex beams generation enabled by a rotatable D²NN

In this work, we introduce a rotatable diffractive deep neural network (R-D²NN) architecture that enables the generation of multi-mode vector vortex beams (VVBs) through controlled rotation of its diffractive layers. This reconfigurable design allows a single physical device to transform an input Gaussian beam into diverse VVB outputs without the need for retraining. The system simultaneously produces orthogonally polarized optical fields carrying distinct orbital angular momentum (OAM) modes, which are coherently superposed to form target VVBs. The vectorial nature and topological charges of the generated beams are verified via Stokes parameter measurements. Numerical simulations demonstrate the generation of up to 16-mode VVBs with a mode purity exceeding 99% using five diffractive layers. Furthermore, we experimentally realize a proof-of-concept two-layer system using a single spatial light modulator (SLM) with two specific architectures, achieving an average mode purity of 85%. The proposed architecture provides a training-free, single-element solution for high-fidelity dynamic VVBs generation, promising for applications in advanced optical communications and sensing.