Distribution of angular momentum and vortex morphology in optical beams

The amount of orbital angular momentum associated with an optical vortex depends on the helicity of the optical vortex, which forms part of the vortex morphology. It is shown that one can define a nontrivial morphology distribution for an optical beam, which, together with the distribution of the state of polarization, determines how the angular momentum is distributed over the cross-section of the beam. As an example, the morphology distribution of a Gaussian beam with an off-axis vortex is considered. Both the polarization distribution and the morphology distribution can be represented in terms of spinor fields. An expression is provided for the angular momentum distribution in terms of these spinor fields. It helps to reveal the relationship among the various spin representations. An interesting and potentially useful property of the morphology distribution is that one can in some cases associate a nontrivial monopole winding number with it.