Incremental Theory of Diffraction for Complex Point Source Illumination

The complex point source (CPS) is a solution of the Helmholtz equation obtained by analytical continuation of the free-space Green's function for complex position of the point source. The CPS representation of radiated fields can be used within a ray code to predict the interaction between an antenna and its actual environment, when standard diffraction formulations are extended to the CPS illumination. In the past, ray-based diffraction theories such as the geometrical theory of diffraction and its uniform version (UTD) were extended to complex point source fields, leaving, however, open some problematic issues concerning the "complex ray tracing''. In this paper, the generalization of the incremental theory of diffraction (ITD) to CPS is formulated. The total field scattered by the object is given in terms of line integration along edge discontinuities of ITD diffraction coefficients plus the discontinuous geometrical optics (GO). An incremental form of the discontinuous GO is also proposed to overcome GO "complex ray tracing'' difficulties. The final formulation is very simple and leads to accurate results that are successfully validated by comparison against a method of moment solution.