Role of volume and surface spontaneous parametric down-conversion in the generation of photon pairs in layered media

A rigorous description of volume and surface spontaneous parametric down-conversion in one-dimensional nonlinear layered structures is developed considering exact continuity relations for the fields' amplitudes at the boundaries. The nonlinear process is described by the quantum momentum operator that provides the Heisenberg equations whose solution is continuous at the boundaries. The transfer-matrix formalism is applied. The volume and surface contributions are clearly identified. Numerical analysis of a structure composed of 20 alternating GaN/AlN layers is given as an example.