Complex analysis between CV modes and OAM modes in fiber systems

As two groups of bases in fibers, cylindrical vector (CV) modes and the orbital angular momentum (OAM) modes can be transformed into each other. Several transformation relations have been studied in previous works, such as σ^+OAM+l=HEl+1,meven+iHEl+1,modd.${\hat \sigma ^ + }OA{M_{ + l}} = HE_{l + 1,m}^éven} + iHE_{l + 1,m}^ódd}.$ However, these relations are discussed in the limitation of equal amplitude, limited phase difference (kπ2, k∈Z)$\left( {{{k\pi } \over 2},{\rm{ }}k \in Z} \right)$ and finite (generally two) mode bases. Complete connection between the CV and OAM modes has not been found. In this paper, a four-dimensional complex space model is constructed to describe arbitrary CV and OAM modes. The reliability of the model is verified by previously reported results and our experiment results. The complete transformation relation between the CV modes and OAM modes is well described in the model. Furthermore, two common kinds of relations have been researched, that is, a single arbitrary polarized OAM mode and two arbitrary orthogonal polarized OAM modes and their corresponding CV modes. These two kinds of states include most of previously reported states, and some new states have not been reported.