The dark spots of Arago

We explore the diffraction and propagation of Laguerre-Gaussian beams of varying azimuthal index past a circular obstacle both experimentally and numerically. When the beam and obstacle centers are aligned the famous spot of Arago, which arises for zero azimuthal index, is replaced for non-zero azimuthal indices by a dark spot of Arago, a simple consequence of the conserved phase singularity at the beam center. We explore how the dark spot of Arago behaves as the beam and obstacle centers are progressively misaligned, and find that the central dark spot may break into several dark spots of Arago for higher incident azimuthal index beams.