Characterizing interference effects of vortex beams based on the Sagnac interferometer

Orbital angular momentum (OAM) of photons has applications both in classical and quantum information due to its features of optical vortex and infinite dimensions. This paper studies the interference effects of optical vortex beams carrying mixed, conjugate, and single-mode OAM states based on the Sagnac interferometer with light sources of a laser and single photon. We compare our results with numerical simulations and show that the light intensity distribution and phase characteristics can directly characterize the absolute value of the topological charge (TC) carried by vortex beams. Furthermore, our scheme can also classify the photon with positive and negative signs of TC in the mixed mode OAM state by changing the relative phase. The results not only extend the manipulation methods for high-dimensional quantum states, but also lay a solid foundation for the application of vortex beams in a single-photon field.