Truncated triangular diffraction lattices and orbital-angular-momentum detection of vortex SU(2) geometric modes.

We report, for the first time to the best of our knowledge, a truncated diffraction with a triangular aperture of the SU(2) geometric modes and propose a method to detect the complicated orbital angular momentum (OAM) of an SU(2) wave-packet. As a special vortex beam, a nonplanar SU(2) mode carrying special intensity and OAM distributions brings exotic patterns in a truncated diffraction lattice. A meshy structure is unveiled therein by adjusting the illuminated aperture in the vicinity of the partial OAM regions, which can be elaborately used to evaluate the partial topological charge and OAM of an SU(2) wave-packet by counting the dark holes in the mesh. Moreover, through controlling the size and position of the aperture at the center region, the truncated triangular lattice can be close to the classical spot-array lattice for measuring the center OAM. These effects being fully validated by theoretical simulations greatly extend the versatility of topological structures detecting special beams.