Optical angular momentum derivation and evolution from vector field superposition

Optical intrinsic angular momentum can be regarded as derivation from spatial superposition of optical vector fields embodied by spinning or/and spiraling the electric-field vector. We employ vectorial formulation derivation to comprehensively study all angular momentum contents of optical vector fields in arbitrary superposition states, including the longitudinal and transverse, spin and orbital (SAM and OAM) components. As for the orthogonal superposition fields, there inherently exists spin-orbit shift from longitudinal SAM to OAM, and the whole local spin flow manifests local multiple-fold helical trajectories. Especially, both the spin-orbit shift and transverse SAM could become considerable in the non-paraxial condition. Our studies here provide an explicit insight into the derivation and evolution, intrinsic correlations and salient features of various types of angular momentum components.