  We investigate optical parametric oscillations through four-wave mixing in
resonant cavities and photonic crystals. The theoretical analysis underlines
the relevant features of the phenomenon and the role of the density of states.
Using fully vectorial 3D time-domain simulations, including both dispersion and
nonlinear polarization, for the first time we address this process in a face
centered cubic lattice and in a photonic crystal slab. The results lead the way
to the development of novel parametric sources in isotropic media.
