Spatiotemporal coherence properties of entangled light beams generated by parametric down-conversion

We investigate the amplitude and intensity spatiotemporal coherence and the photon coincidence rates of far-field down-converted light resulting from the interaction of a pump wave of finite spectral width with a nonlinear crystal of finite spatial width. We examine the interplay between energy and phase mismatches and their effects on the intrabeam and interbeam spatial and temporal coherence of the down-converted beams. We show that the down-converted light is spatially incoherent in the second order, and that the signal-idler fourth-order coherence extends over finite entanglement angles. We also study the effect of the apertures through which the down-converted light is collected, when they are centered at phase-matched or misaligned directions.