Intensity and orbital angular momentum density of nonparaxial anomalous vortex beams

The intensity and the orbital angular momentum density of an anomalous vortex beam beyond the paraxial approximation are studied. By using the vectorial angular spectrum method, analytical expressions of the electric field of the nonparaxial anomalous vortex beam are derived. Based on the expressions, an analytical expression of the orbital angular momentum density of the nonparaxial anomalous vortex beam is deduced. Through the numerical simulation method, the intensity distribution and orbital angular momentum density distribution characteristics are studied, and then the effects of topological charge, beam order, and propagation distance on the distributions of the intensity and orbital angular momentum density are analyzed. The results show that the intensity distribution of an nonparaxial anomalous vortex beam is similar to that of an paraxial anomalous vortex beam, while the orbital angular momentum density distribution is not.