Internal energy flows of coma-affected singular beams in low-numerical-aperture systems

The circulating phase gradient component of a singular beam gets modified when focused by a low-numerical-aperature system suffering from coma aberration. The gradient due to this coma aberration splits the higher charge vortex into elementary vortices and distributes them spatially. This splitting depends on the charge and polarity of the incident singular beam as well as the sign and magnitude of the aberration coefficient. The transverse component of the Poynting vector field distribution at the focal plane is decomposed into the curl or solenoidal component and divergence or irrotational component using the Helmholtz-Hodge decomposition technique. The solenoidal component that relates to the orbital angular momentum carries the circulating energy, while the irrotational component shows the sources and sinks of the energy. Intriguing results of the study of energy flow around the edge dislocations apart from the point phase defects in the irrotational components are also presented.