Topological Charge and Asymptotic Phase Invariants of Vortex Laser Beams

It is well known that the orbital angular momentum (OAM) of a light field is conserved on propagation. In this work, in contrast to the OAM, we analytically study conservation of the topological charge (TC), which is often confused with OAM, but has quite different physical meaning. To this end, we propose a huge-ring approximation of the Huygens-Fresnel principle, when the observation point is located on an infinite-radius ring. Based on this approximation, our proof of TC conservation reveals that there exist other quantities that are also propagation-invariant, and the number of these invariants is theoretically infinite. Numerical simulation confirms the conservation of two such invariants for two light fields. The results of this work can find applications in optical data transmission to identify optical signals.

Automated summary

It is commonly known that the orbital angular momentum (OAM) of a light field is conserved during propagation, but the conservation of the topological charge (TC) is different and has unique physical meaning. The study reveals that there are other quantities that are also propagation-invariant, with theoretically infinite invariants. Numerical simulations confirm the conservation of two such invariants for two light fields, which can have applications in optical data transmission for identifying optical signals.