Programmable Unitary Operations for Orbital Angular Momentum Encoded States

We have proposed and demonstrated a scalable and efficient scheme for programmable unitary operations in orbital angular momentum (OAM) domain. Based on matrix decomposition into diagonal and Fourier factors, arbitrary matrix operators can be implemented only by diagonal matrices alternately acting on orbital angular momentum domain and azimuthal angle domain, which are linked by Fourier transform. With numerical simulations, unitary matrices with dimensionality of 3*3 are designed and discussed for OAM domain. Meanwhile, the parallelism of our proposed scheme is also presented with two 3*3 matrices. Furthermore, as an alternative to verify our proposal, proof of principle experiments have been performed on path domain with the same matrix decomposition method, in which an average fidelity of 0.97 is evaluated through 80 experimental results with dimensionality of 3*3.