Sorting light’s radial momentum and orbital angular momentum with a parabolalike lens

Both orbital angular momentum and radial momentum describe the transverse momentum of a light field. Efficient discrimination between and sorting of the two kinds of momentum lie at the heart of further applications. Here, we propose a parabolalike lens that can transform the orbital angular momentum and radial momentum into different positions in the parabolas. We experimentally characterize the performance of our implementation by separating individual angular and radial momenta as well as multiple superposition states. The reported scheme can achieve two kinds of transverse momentum identification and thus can provide a possible way to complete the characterization of the full transverse momentum of an optical field. The proposed device can readily be used in multiplexing and demultiplexing of optical information, and, in principle, achieve unit efficiency, and thus may be suitable for applications that involve quantum states of light.