  A new approach to the design of graded Photonic Crystals (GPCs) devices is
proposed by exploiting the inverse scattering framework as a synthesis tool.
The introduced general methodology can be applied to arbitrary far-field
specifications, thus allowing to design non-canonical devices. In particular,
two different strategies are developed which allow to deal with GPCs with both
graded refractive index (GPC_R) and graded filling factor (GPC_F). In both
strategies, the inverse scattering problem is solved by a proper reformulation
of the Contrast Source Inversion method wherein a proper rescaling of the
amplitude of the primary sources is pursued. In particular, in the first one,
the GPCs are obtained by exploiting homogenization theories. In the second one,
the GPC_R profile is synthesized by exploiting a suitable representation basis
for the unknown contrast function and, then, simple analytical formulas are
used to determine a GPC_F. The proposed approach is assessed through the
synthesis of an antenna generating ${\Sigma}/{\Delta}$ reconfigurable patterns.
