Orbital angular momentum (OAM), emerging as an inherently high-dimensional property of photons, has boosted information capacity in optical communications. However, the potential of OAM in optical computing remains almost unexplored. Here, we present a highly efficient optical computing protocol for complex vector convolution with the superposition of high-dimensional OAM eigenmodes. We used two cascaded spatial light modulators to prepare suitable OAM superpositions to encode two complex vectors. Then, a deep-learning strategy is devised to decode the complex OAM spectrum, thus accomplishing the optical convolution task. In our experiment, we succeed in demonstrating 7-, 9-, and 11-dimensional complex vector convolutions, in which an average proximity better than 95% and a mean relative error <6 % are achieved. Our present scheme can be extended to incorporate other degrees of freedom for a more versatile optical computing in the high-dimensional Hilbert space.
Based on our constructed robust π/2 mode converter, we report a concise yet high-efficient experiment to realize the detection of high-order orbital angular momentum (OAM). The π/2 mode converter that consists of a pair of cylindrical lens is actually not new. However, our experiment show clearly its excellent robustness, as we have detected the high-order OAM numbers up to ℓ = 150 carried by standard Laguerre-Gaussian (LG) modes. The observed patterns of two-dimensional optical lattices indicate that the radial index p of LG beams can be straightforwardly inferred as well. Our demonstration has potential in both classical and quantum information applications where high OAM modes are needed.
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