Where is the orbital angular momentum in vortex superposition states?

Abstract

In this paper, we explore the distribution of the orbital angular momentum (OAM) in the coaxial vortex superposition states based on the independent propagation principle of light in this interference process. We find that in this case, some specific singular points exist in the spatial intensity distribution. The first type of singular point is located at the center point of the spatial intensity distribution. The second type of specific singular point is at the critical location of the overlapping area in angular direction. By analogy with the angular momentum superposition of two axially rotating homogeneous disks with different radius in rigid body, We present a suggestion: the center point is located at the overlapping area of all the superposed components. Therefore, the topological charge value in the center point should be doubled by the actual number of superposition field components. The singular point at the critical location of the overlapping area in angular direction should also be co-owned by the superposition components outside the position of the ring (including the corresponding component of the ring). The total OAM is exactly equal to the sum of those two types contained in the superposition states, which is equal to the input OAM of the superposition state components. The conservation of the OAM in the coaxial interference process is demonstrated.