  Non-linear photonic crystals can be used to provide phase-matching for
frequency conversion in optically isotropic materials. The phase-matching
mechanism proposed here is a combination of form birefringence and phase
velocity dispersion in a periodic structure. Since the phase-matching relies on
the geometry of the photonic crystal, it becomes possible to use highly
non-linear materials. This is illustrated considering a one-dimensional
periodic Al$_{0.4}$Ga$_{0.6}$As / air structure for the generation of 1.5
$\mu$m light. We show that phase-matching conditions used in schemes to create
entangled photon pairs can be achieved in photonic crystals.
