Theory of two-photon down-conversion in the presence of mirrors

A theory of two-photon down-conversion in the presence of mirrors is developed and applied to recent observations of Herzog et nl. [Phys. Rev. Lett. 72, 629 (1994)]. The experimentally observed results for counting and coincidence rates as functions of mirror-crystal separations are obtained, and it is shown how the same results may be derived in a simplified formulation that presumes phase-matched signal and idler modes. We account for the observed effects of the finite coherence length of the pump field as well as the signal and idler coherence lengths, which are much shorter than the pump coherence length and have a different physical origin. Our analysis also supports the interpretation of the phenomena observed as being analogous to the modification of single photon spontaneous emission of atoms in cavity QED.