A generalized uniform theory of diffraction method for complex illumination sources accounting for multiply-diffracted rays

A new formalism is presented that generalizes the use of the uniform theory of diffraction (UTD) to arbitrary illumination sources. The formalism returns the field in terms of a multipole expansion inside an extended observation region. When multiple UTD canonical objects are present, the multiply-diffracted rays can conveniently be superimposed. As an example, the scattering of a higher-order Hermite-Gaussian beam at a perfectly electrically conducting slit is examined.