Scattering from fractal dielectric profiles: the extended boundary condition method

An electromagnetic model for the study of the scattering from natural rough surfaces is presented. The authors employ a Weierstrass-Mandelbrot (WM) fractal surface model in conjunction with the extended boundary condition method (EBCM). Dielectric profiles are considered. The property of the WM to be an almost periodic function allows one to generalise techniques employed for periodic functions. In particular, the authors express the scattered and transmitted fields as a superposition of Floquet modes, whose directions of propagation are evaluated by means of the grating equation, and whose amplitudes by means of the EBCM. The method leads the authors to express in matrix form the amplitude coefficients of the scattered and transmitted fields in terms of the amplitude coefficients of the known impinging field