Time-division multiplexing of the orbital angular momentum of light

We present an optical setup for generating a sequence of light pulses in which the orbital angular momentum (OAM) degree of freedom is correlated with the temporal one. The setup is based on a single $q$-plate within a ring optical resonator. By this approach, we demonstrate the generation of a train of pulses carrying increasing values of OAM, or, alternatively, of a controlled temporal sequence of pulses having prescribed OAM superposition states. Finally, we exhibit an "OAM-to-time conversion" apparatus dividing different input OAM states into different time-bins. The latter application provides a simple approach to digital spiral spectroscopy of pulsed light.