Research on orbital angular momentum of off axial Gaussian vortex beam

By the theory of paraxial approximation for optical beam, the analytical expression of orbital angular momentum (OAM) of off axial Gaussian vortex beam is derived in the coordinates of centroid, based on which distribution of OAM of off axial vortex beam and its propagation are investigated. Numerical calculations show that the OAM of off axial vortex beam is not circularly symmetric. The contour of zero OAM is a close curve, inside which the OAM is positive and outside which the OAM is negative. With the increment of propagation length, the distribution of OAM of off axial vortex beam tends to be approximately right and left symmetric, and the bigger the topological charge is, the faster the distribution of OAM tends to form the characteristic of symmetry. Besides, the off axial distance also has influence on the distribution of OAM. On a certain observation plane, the absolute value of the minimum OAM (in negative area) will become closer to the absolute value of the maximum OAM (in positive area) if the off axial distance increases. The conclusion can provide guidance during the research on the interaction between off axial vortex beam and particles.