Spontaneous parametric down-conversion for an arbitrary monochromatic pump beam

Abstract

Signal-idler photon-pairs generated in spontaneous parametric down-conversion are considered for the case of an arbitrary monochromatic pump beam. It is shown that the quantum correlations between the signal and idler photons allow them to be mirror images of each other. A simple and very intuitive imaging formula is derived to describe this effect. In contrast to a conventional mirror, the down-conversion crystal acts as a volume reflector whose characteristics can be controlled by the spatial profile of the pump beam. For a very narrow pump beam the signal-idler photon-pairs suffer an effective aperture effect that reduces their momentum correlations in a prescribed manner.