Production of optical phase space vortices with non-locally distributed mode converters

Optical vortices have been observed in a wide variety of optical systems. They can be observed directly in the wavefront of optical beams, or in the correlations between pairs of entangled photons. We present a novel optical vortex which appears in a non-local plane of the two-photon phase space, composed of a single degree of freedom of each photon of an entangled pair. The preparation of this vortex can be viewed as a 'non-local' or distributed mode converter. We show how these novel optical vortices of arbitrary order can be prepared in the spatial degrees of freedom of entangled photons.