摘要： Atomic vapours are an experimentally simple and ef?cient system in which to study nonlinear wave mixing. We study a four-wave mixing (FWM) process in rubidium vapour which ef?ciently converts 780 and 776 nm light to 420 nm and 5.2 μm ?elds [1]. In particular, we quantitatively investigate the transfer of orbital angular momentum (OAM) between the FWM ?elds. OAM, and structured light more generally, is an important research tool for optical manipulation, imaging and communication. Phase-matched nonlinear processes are both longitudinally and transversely phase coherent, and therefore OAM, which is associated with spiral phase fronts, must be conserved between the pump and generated ?elds [2]. This makes wave mixing an ideal tool for frequency conversion and generation of a variety of OAM states for use in both classical and quantum communication [3]. In our FWM process, conservation of OAM determines the total OAM carried by the 420 nm and 5.2 μm ?elds - but not how it is distributed between them. Fig. 1 (a) shows the intensity pro?le and interferogram (formed by interfering the beam with its mirror image) of the 420 nm ?eld when the pump beams each carry (cid:2)ˉh of OAM ((cid:2) = (cid:2)780 = (cid:2)776). We perform quantitative analysis of each interferogram to obtain the full Laguerre-Gauss mode decomposition of the 420 nm ?eld (Fig. 1 (b)). For small values of pump OAM, the 420 nm light is generated predominantly in one mode [4], but as the pump OAM increases the OAM spectrum broadens [5]. In order for OAM to be conserved, this indicates that the 420 nm and 5.2 μm light is generated in an OAM-entangled state. From the 420 nm mode decomposition we infer the spiral bandwidth (a measure of the number of entangled modes), Δ(cid:2)B, as well as the entanglement entropy, S, of this state. Both the experimental and theoretical results show that the generated state is strongly pump mode-dependent, with the spiral bandwidth increasing with increasing pump OAM. These results indicate that this system is likely to be an ef?cient source of OAM-entangled photon pairs with widely-disparate wavelengths.