Entangled photon pair generation by spontaneous parametric down-conversion in finite-length one-dimensional photonic crystals

A description of spontaneous parametric down-conversion in finite-length one-dimensional nonlinear photonic crystals is developed using semiclassical and quantum approaches. It is shown that if a suitable averaging is added to the semiclassical model, its results are in very good agreement with the quantum approach. We propose two structures made with GaN∕AlN that generate both degenerate and nondegenerate entangled photon pairs. Both structures are designed so as to achieve a high efficiency of the nonlinear process.