Measurement of topological charges of optical vortices by antiphased semicircular slit pair

Determination of orbital angular momentum (OAM) states is a subject of crucial importance for their applications in areas ranging from classical physics to quantum information. Here, we propose the antiphase semicircular slit pair (ASSP) as a novel approach to determine the topological charge of OAM states. The ASSP contains two semicircular slits with a diameter increment and symmetrically arranged in upper and lower circle. It converts an incident OAM state into light field with two bright spots, of which the relative shift is twice as spot shift for a semicircular slit. Physically, we introduce the two models of equivalent spiral slit and the Young's-like interference, obtaining two approximate linear relations between the shift and the incident topological charge. Analytically, the antiphase of the diffracted fields for the two semicircular slits cancels a main Bessel vortex term, and doubles the complement fields contained in that for a single semicircular slit, realizing the field with two bright intensity spots with the relative shift doubled. The diffracted field is fundamentally approximated as the weighted superposition of finite Bessel vortex eigenstates. Using shift between the bright spots, the determination of topological charge of OAM states becomes a feasible and convenient, and the experimental measurement conforms to the theory with satisfying accuracy.