Diffraction from a truncated grounded dielectric slab: an efficient numerical analysis

The description of diffraction mechanisms at edges in a grounded dielectric slab is important in several engineering applications. The need for taking into account such effects may arise when considering actual patch antennas on finite substrates where these mechanisms may considerably affect the radiation pattern and have an influence on the directivity especially when surface waves are strongly excited. A formulation is suggested which allows for a dramatic reduction of the unknown quantity. The geometry which is treated consists on a grounded dielectric slab truncated on one side in both the dielectric and the ground plane, which is illuminated by an infinite line source placed at the substrate-air interface. By invoking the equivalence principle, the total space is separated (through an infinite surface in free-space) into into sub-regions in which the field can be calculated by standard Green´s functions. After that, the solution is obtained by solving via an ordinary method of moments (MoM) scheme the integral equations that represents the continuity of the tangential electric field through the surface which divides the regions. Due to the infiniteness of this surfaces, entire domain basis functions are used. The shape of them is chosen according to the behavior of the field diffracted at the edge, which consists in contributions coming from space field, surface waves, and leaky waves excitations.