An incremental theory of diffraction for edges in impedance surfaces

In this paper, an incremental theory of diffraction formulation is presented for defining incremental field contributions from local edge discontinuities in planar surfaces with impedance boundary conditions. By Fourier analysis, it is shown that the spectral integral representation of the exact solutions may also be represented as a spatial integral convolution along the longitudinal coordinates of the local edge Next, this latter exact formulation is interpreted as a linear, spatial superposition of incremental field contributions distributed all along the edge itself. Then, its integrand is directly used to define the relevant incremental field contribution. By applying a suitable asymptotic analysis, incremental diffraction coefficients are derived that, besides the Malyuzhinets special functions, involve only simple closed form expressions This formulation includes incremental contributions associated to the excitation and diffraction of surface waves In particular, explicit expressions are obtained for incremental surface wave contributions that arise from source-excited surface and space waves, as well as for incremental diffracted space waves excited by edge diffraction of surface waves.