We propose a linear mapping relationship between the polarization of the fundamental mode and the cylindrical vector (CV) modes on the first-order Poincaré sphere (FOPS) in fiber. The new method is based on the four-dimensional complex Jones matrices in terms of the linearly polarized mode bases. With our theoretical model, an all-fiber approach to generate arbitrary CV beams on the FOPS is proposed theoretically and verified experimentally. In the experiment, through the combination of a mode c
