Invited Article: Division and multiplication of the state order for data-carrying orbital angular momentum beams

We demonstrate all-optical division and multiplication of the state order ℓ for data-carrying orbital angular momentum (OAM) beams. We use linear optical transformations between log-polar and Cartesian coordinates to: (i) divide the OAM state order to convert the OAM order from 2 ℓ to ℓ ( ℓ = −5, −4, …, +4, +5), and (ii) multiply the OAM state order from ℓ to 2 ℓ . We analyze the OAM mode purity and the bit-error-rate performance of a classical two-mode OAM multiplexed link for the case of division and multiplication of the OAM state order. The experimental mode purity for halving and doubling OAM state order can reach around 87% and 40%, respectively. We further study the dependence of the OAM mode purity on the displacement of SLMs in simulation. The obtained results show that the transformation for doubling the OAM state order is more sensitive to the increase of the displacement than that for halving the OAM state order. The link bit error rates are below the forward error correction threshold of 3.8 × 10−3 for both channels.