A 2-D Extended Boundary Condition Method for scattering from perfectly conducting fractal surfaces

In this paper the field scattered by a 2-D Weierstrass-Mandelbrot (WM) perfectly conducting fractal surface is evaluated, by using the Extended Boundary Condition Method (EBCM). Integral equations are set in the frame of the extinction theorem. The surface fields are then evaluated by exploiting the WM property of being an almost periodic function. In principle, no assumptions on the surface roughness is made. Each component of the scattered field is expressed as a superposition of generalised Floquet modes, whose directions of propagation follow the grating equation and whose amplitudes are expressed in terms of matrixes with no finite, dimension. How to truncate the matrixes sets the validity limits. The reliability of the method is tested by means of an energy criterion.