Focal plane internal energy flows of singular beams in astigmatically aberrated low numerical aperture systems

Singular beams have circulating energy components. When such beams are focused by low numerical aperture systems suffering from astigmatic aberration, these circulating energy components get modified. The phase gradient introduced by this type of aberration splits the higher charge vortices. The dependence of the charge, the aberration coefficient, and the size of the aperture on the nature of the splitting process are reported in this paper. The transverse components of the Poynting vector fields that can be derived from the phase gradient vector field distributions are further decomposed into solenoidal and irrotational components using the Helmholtz-Hodge decomposition method. The solenoidal components relate to the orbital angular momentum of the beams, and the irrotational components are useful in the transport of intensity equations for phase retrieval.