Fractal surface scattering: A generalized Rayleigh solution

We consider the scattering of electromagnetic waves from perfectly conducting fractal surfaces. The surface is modeled by a multiscaled bandlimited continuous fractal function. We analytically develop a generalized Rayleigh solution for electromagnetic wave scattering from such fractal surfaces. After an examination of the convergence of the Rayleigh systems, we numerically calculate the coupling strengths and relate the angular scattering energy distribution to the fractal descriptors of the surface. We find that the slope of the coupling strengths as a function of their corresponding spatial frequencies on a logarithmic scale depends monotonically on the fractal dimension of the scattering surface.