Spectral domain full wave analysis of integrated planar structures with PBG substrates

In this paper a new analytical approach based on the Full Wave Analysis in the spectral domain of the integrated planar structure with PBG materials is presented. Starting from the curl Maxwell equations written for bi-dimensional inhomogeneous substrates and applying a bi-dimensional spatial Fourier transformation, a proper set of differential equations involving convolution operations is derived. Such a formulation allows to straightforwardly determine the spectral dyadic Green's function for a periodic integrated structure. The equivalence theorem and the image principle are also employed in order to obtain the radiation pattern due to an infinitesimal current source embedded in a medium with a harmonic variation of the relative permittivity. Finally, some numerical results showing the radiating behavior of this kind of structures are presented.