  We investigate numerically the homogenized permittivities of composites made
of low index dielectric inclusions in a ferroelectric matrix under a static
electric field. A refined model is used to take into account the coupling
between the electrostatic problem and the electric field dependent permittivity
of the ferroelectric material, leading to a local field enhancement and
permittivity change in the ferroelectric. Periodic and pseudo-random structures
in two dimensions are investigated and we compute the effective permittivity,
losses, electrically induced anisotropy and tunability of those metamaterials.
We show that the tunability of such composites might be substantially enhanced
in the periodic case, whereas introducing disorder in the microstructure weaken
the effect of enhanced local permittivity change. Our results may be useful to
guide the synthesis of novel composite ceramics with improved characteristics
for controllable microwave devices.
