Incremental theory of diffraction for complex source illumination

The effectiveness of Gaussian beams (GBs) to efficiently represent arbitrarily shaped antenna radiation patterns has been widely demonstrated in literature. GBs are solution of Maxwell equations only in the paraxial region but they are deeply concerned with the concept of the complex source point (CSP), whose field is Maxwellian throughout the space (also outside the paraxial region), as can be easily inferred via an analytic continuation of the source point Green's function when the source position is allowed to be complex. Such a GBs/CSPs representation can be used within a ray code to predict the interaction between antenna and the actual environment, if standard diffraction formulations are extended to the CSP case, i.e., when the illuminating source is treated as a CSP. The CSP extension of ray techniques like geometrical theory of diffraction (GTD) and its uniform version (UTD) appears to be substantially more problematic than that of incremental ray theories, such as physical theory of diffraction (PTD), incremental length diffraction coefficient (ILDC) and incremental theory of diffraction (ITD). In this paper we analyze this CSP extension of discrete and incremental ray techniques, with particular reference to the ITD formulation.