Arithmetic operation of orbital angular momentum of light via slow-light four-wave mixing

Orbital angular momentum (OAM) of light has attracted much attention because of its applications in many fields. Electromagnetically induced transparency (EIT) is well known as an effective method to manipulate the light fields. Now there are some increasing interests in using the EIT technology to manipulate OAM. In this work, we experimentally report on arithmetic operation of OAM of light in a solid driven by EIT. In an EIT four-level double lambda configuration, we use the optical vortex beams carrying OAM to perform slow-light four-wave mixing (FWM) without experiencing EIT storage. The conservation of OAM is satisfied in this FWM process, and the topological charge of the generated FWM signal is determined by those of the applied fields. The slow-light FWM signal accumulates the total OAM of the applied laser fields. The arithmetic operation of addition, subtraction and cancellation of OAM is effectively performed in experiment. Such OAM manipulation could have practical applications in information processing and quantum information. • The vortex light with OAM is slowed via EIT in a rare-earth-ion-doped solid. • Slow-light four-wave mixing is demonstrated in an EIT double lambda system. • The OAM transfer is observed in slow-light four-wave mixing. • The arithmetic of addition, subtraction and cancellation of OAM is performed in experiment.