Compact source of narrow-band counterpropagating polarization-entangled photon pairs using a single dual-periodically-poled crystal

We propose a scheme for the generation of counterpropagating polarization-entangled photon pairs from a dual-periodically-poled crystal. Compared with the usual forward-wave-type source, this source, in the backward-wave way, has a much narrower bandwidth. With a 2-cm-long bulk crystal, the bandwidths of the example sources are estimated to be 3.6 GHz, and the spectral brightnesses are more than 100 pairs/(s GHz mW). Two concurrent quasi-phase-matched spontaneous parametric down-conversion processes in a single crystal enable our source to be compact and stable. This scheme does not rely on any state projection and applies to both degenerate and nondegenerate cases, facilitating applications of the entangled photons.