Polarization properties of superposed vector Laguerre-Guassian beams during propagation

We use analytical and numerical techniques to study the superposition of two vector Laguerre-Guassian (LG) beams. Vector LG beams contain rich polarization information and have many interesting intensity and polarization features. The composited electric field shows an inhomogeneous polarization distribution. We focus on looking for the distribution laws for the singularities obtained. The number and positions of singularity points are calculated and confirmed by numerical methods. We also study the fundamental cases for nonconcentric superposed vector LG beams and discover the difference distribution laws of several types of singular points in all the possible combinations.