Iterative creation and sensing of twisted light.

The iterative interaction of a photon with a sample can lead to increased sensitivity in measuring the properties of the samples, such as its refractive index or birefringence. Here we show that this principle can also be used to generate and sense states of light. In particular, we demonstrate a technique to generate states with high orbital angular momentum using a single-vortex phase plate (VPP). This is accomplished by placing the phase plate in a self-imaging cavity such that light interacts with it multiple times; for an ideal phase plate, this is equivalent to iterative applications of the angular momentum operator. Using a discrete VPP, we show that our setup realizes a high-dimensional generalization of the Pauli matrix σ_x, and that the created states show sub-diffraction limited features that might find applications in structured illumination microscopy.