Computation of the diffraction from complex illumination sources in extended regions of space

In this paper, a two-dimensional high-frequency formalism is presented which describes the diffraction of arbitrary wavefronts incident on edges of an otherwise smooth surface. The diffracted field in all points of a predefined region of interest is expressed in terms of the generalized Huygens representation of the incident field and a limited set of translation coefficients that take into account the arbitrary nature of the incident wavefront and its diffraction. The method is based on the Uniform Theory of Diffraction (UTD) and can therefore be utilized for every canonical problem for which the UTD diffraction coefficient is known. Moreover, the proposed technique is easy to implement as only standard Fast Fourier Transform (FFT) routines are required. The technique's validity is confirmed both theoretically and numerically. It is shown that for fields emitted by a discrete line source and diffracted by a perfectly conducting wedge, the method is in excellent agreement with the analytic solution over the entire simulation domain, including regions near shadow and reflection boundaries. As an application example, the diffraction in the presence of a perfectly conducting wedge illuminated by a complex light source is analyzed, demonstrating the appositeness of the method.