Parametric control of propagation of optical vortices through fibre ring resonators

Abstract

In this paper, we have studied transmission of optical vortices (OVs) through ring resonators (RRs) based on multimode fibres. Using the formalism of transfer matrix we have obtained in the scalar approximation the analytical expressions for amplitudes of transmitted OVs with opposite topological charges (TCs) as functions of RR’s parameters. We have calculated the orbital angular momentum (OAM) of the outcoming field and shown that by changing such parameters one can efficiently control its TC and continuously change its OAM. We have established that TC and OAM feature wavelength-scale sensitivity to variations of the ring’s length. We have demonstrated that this ability of RRs to influence OAM is due to a multipass interference assisted with TC inversion in the coupling area. We have also studied the effect of losses on the transmission of OVs through RRs and established that by controlling the attenuation parameter one can also control the TC of the outcoming field. Finally, we have solved the problem of OV transmission within the frameworks of a fully vectorial approach that allows for the spin–orbit interaction (SOI) in fibres. We have shown that accounting the SOI does not alter the main properties of RRs established with the use of the scalar approximation theory. We have shown that RRs, which operate on OAM modes, can be used for emulation of the quantum logical X, Y, S, T and Z gates. This can be useful for optical simulation of quantum computations.