Radio wave diffraction from impedance surfaces with one dimensional general impedance variation

The problem of plane wave diffraction from shorelines in planar land-sea boundaries, using the Wiener-Hopf technique, was addressed by Bazer et al. (1962). Geometrical theory of diffraction (GTD) methods, while accurate at high frequencies, have only been applied to problems where abrupt variations in a surface are present. An analytical formulation is developed to predict the diffraction from a surface impedance discontinuity, of an arbitrary profile, such as rivers, shorelines, or troughs, when excited by a small dipole of arbitrary orientation. Basically the river is modeled as an impedance change in an infinite impedance plane, representing the ground plane. An integral equation is developed in the Fourier domain for ease of analysis and then solved analytically using a perturbation technique, assuming a one dimensional impedance variation. Recursive expressions for the induced current of any order, for arbitrary impedance variations, are shown. Using these currents, the far field expressions for plane wave excitation are evaluated using the stationary phase technique. The derivation is then extended to small dipole excitation represented by a continuous spectrum of plane waves, again using the stationary phase to calculate the diffracted fields. Results for both plane wave and dipole excitation are shown.