  We present a quantum mechanical description of parametric down-conversion and
phase-matching of Bloch-waves in non-linear photonic crystals. We discuss the
theory in one-dimensional Bragg structures giving a recipe for calculating the
down-converted emission strength and direction. We exemplify the discussion by
making explicit analytical predictions for the emission amplitude and direction
from a one-dimensional structure that consists of alternating layers of
Al0.4Ga0.6As and Air. We show that the emission is suitable for the extraction
of polarization-entangled photons.

Quantum Physics