Abstract
Abstract 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 ^ + O A M + l = H E l + 1 , m e v e n + i H E l + 1 , m o d d . ${\hat \sigma ^ + }OA{M_{ + l}} = HE_{l + 1,m}^{even} + iHE_{l + 1,m}^{odd}.$ However, these relations are discussed in the limitation of equal amplitude, limited phase difference ( k π 2 , 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.
Highlights
Cylindrical vector (CV) modes, as a group of intrinsic bases in fibers, have been studied for a long time [1]
Lth-order CV modes consist of four degenerated modes
No matter what the desired orbital angular momentum (OAM) modes in fibers are, there must be a specific group of intrinsic CV modes corresponding with them and that can be calculated
Summary
Cylindrical vector (CV) modes, as a group of intrinsic bases in fibers, have been studied for a long time [1]. For different points on the beam cross-section of CV modes, the polarization states vary from their azimuthal angles. These properties are unique compared with conventional light waves. To totally describe the lth-order electric field in fibers, we need combine the four degenerated CV modes in arbitrary amplitude and phase. This means we should consider the complex amplitudes of CV modes as arbitrary complex number and consider the four degenerated CV modes simultaneously. It leads to the benefit that the TCs are tunable between +l and −l
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