  We present an effective model for a subwavelength periodically patterned
metallic layer, its cavities being filled with a nonlinear dielectric material,
which accounts for both the linear and second order behavior. The effective non
linear susceptibility for the homogenized layer is driven by the nonlinearity
of the dielectric material and by the geometrical parameters, thus leading to
much higher susceptibility than existing materials. This leads to a huge
enhancement of non linear processes when used together with resonances.
Furthermore, multiple resonances are taking place in the metallic cavities, and
we investigate the mode matching situations for frequency conversion processes
and show how it enhances further their efficiency.
