Precision measurement theory of integer and fractional orbital angular momentum based on photonic spin Hall effect

Fractional vortex beams carrying fractional orbital angular momentum (OAM) serve as an indispensable part of integer vortex beams. Owing to their unique physical properties, these beams hold extensive potential for applications in optical communication and quantum information processing. However, the precise detection of the fractional OAM of the fractional vortex beam remains a significant and challenging issue due to the broken orthogonality of the OAM. Here we propose a straightforward yet highly effective method for the accurate measurement of integer and fractional OAM, based on the photonic spin Hall effect (SHE). It is found that the spin-dependent shift of the photonic SHE exhibits an increasing trend with the augmentation of the fractional topological charge (TC) for TC < 13 . When combined with weak measurement techniques, the results demonstrate that the amplified photonic SHE is nearly linearly correlated with the fractional TC. Consequently, we can accurately measure both positive and negative integer as well as fractional TC by utilizing the photonic SHE as a measurement pointer. These theoretical studies expand the practical applications of photonic SHE, and provide a reliable method for precision detection of fractional OAM. • We calculate the general expressions for the photonic spin Hall effect (SHE) transverse shifts of the fractional vortex beam carrying the fractional orbital angular momentum. • We establish a quantitative relationship between the fractional topological charge (TC) and the photonic SHE shifts and find that the photonic SHE shifts are sensitive to the fractional TC. • Combined with the weak measurement techniques, we can accurately measure both positive and negative integer as well as fractional TC with the photonic SHE as a measurement pointer.