  The self-imaging, or Talbot Effect, that occurs with the propagation of
periodically structured waves has enabled several unique applications in
optical metrology, image processing, data transmission, and matter-wave
interferometry. In this work, we report on the first demonstration of a Talbot
Effect with single photons prepared in a lattice of orbital angular momentum
(OAM) states. We observe that upon propagation, the wavefronts of the single
photons manifest self-imaging whereby the OAM lattice intensity profile is
recovered. Furthermore, we show that the intensity at fractional Talbot
distances is indicative of a periodic helical phase structure corresponding to
a lattice of OAM states. This phenomenon is a powerful addition to the toolbox
of orbital angular momentum and spin-orbit techniques that have already enabled
many recent developments in quantum optics.
