Analysis of the influence of a complex-shaped irregularity of a landscape on electromagnetic fields

A mathematical technique is developed for evaluating the influence exerted by a cylindrical irregularity of complex shape with the size less than or o f the order of the wavelength in a vacuum on electromagnetic fields. By a s pecial conformal mapping, the regularization of the Laplace operator is per formed. After inverting the singular part of the Helmholtz operator, the pr oblem is reduced to a Fredholm integral equation, which is solved by the co ntraction mapping method. As an example, for one class of irregularities, t he solution is constructed in a closed analytical form. The amplitudes and phases of the fields at the irregularity and its neighborhood are obtained.