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A new approach to the design of graded Photonic Crystals (GPCs) devices isproposed by exploiting the inverse scattering framework as a synthesis tool.The introduced general methodology can be applied to arbitrary far-fieldspecifications, thus allowing to design non-canonical devices. In particular,two different strategies are developed which allow to deal with GPCs with bothgraded refractive index (GPC_R) and graded filling factor (GPC_F). In bothstrategies, the inverse scattering problem is solved by a proper reformulationof the Contrast Source Inversion method wherein a proper rescaling of theamplitude 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 basisfor the unknown contrast function and, then, simple analytical formulas areused to determine a GPC_F. The proposed approach is assessed through thesynthesis of an antenna generating ${\Sigma}/{\Delta}$ reconfigurable patterns.

Design of Graded Photonic Crystals Antennas via Inverse Scattering based techniques