Precisely measuring the orbital angular momentum of beams via weak measurement

Abstract

We proposed and analyzed a scheme of precisely measuring orbital angular momentum (OAM) of the vortex beams with the help of weak measurement process. The orbital angular momentum information $l$ of the unknown OAM state can be obtained by its spatial displacements. The valid condition of precisely measuring orbital angular momentum was completely discussed. Interestingly, it is shown that the measurement by using the two-dimensional spatial displacements jointly is very useful for precisely measuring the OAM state with a large orbital angular momentum $l$. The signal-to-noise ratio of the measurement can be enhanced by increasing the weak-coupling $\ensuremath{\gamma}$ linearly as the valid condition is still satisfied. For fixed $\ensuremath{\gamma}$, the maximal signal-to-noise ratio for each weak value increases with the decrease of the weak value.