Helical-Phase Distinguishability for the Phase Distribution of Laguerre-Gaussian Beams

In the past few years, orbital angular momentum beams have contributed significantly to many applications in the optical-related fields due to their unique phase characteristics. Here, a novel approach about phase-helices structure for Laguerre-Gaussian beams carrying orbital angular momentum is presented. This proposal is based on numerical simulations to track the rotation of each helix in the phase and shows an impact on the rotational speed of the Laguerre-Gaussian phase distribution by using the characteristic of distinguishability of each helix. If the helices in the phase of a vortex cannot be distinguished, then the angular rotation speed of the phase distribution can be seen as independent of the azimuthal index l, due to its rotational symmetry, and it is called {\omega}indistinguishable. Oppositely, when the helices are distinguished from each other, the rotational speed is affected by this azimuthal index, and it becomes {\omega}distinguishable. This distinguishable theory can build a pathway to applications in the field of optical communications (as a coding system) and particle manipulation (changing the dynamics of off-beam trapped particles).