Fractal surfaces and electromagnetic extended boundary conditions

In this paper, we employ the extended boundary condition method with the Weierstrass-Mandelbrot (WM) fractal function to model and solve a relevant electromagnetic scattering problem. The key point of the procedure is the property of the WM to be an almost periodic function. This allows to generalize techniques employed for periodic problems and to express the field by means of a superposition of Floquet modes. The procedure is devised for the general case of dielectric surfaces. Criteria for assessing the validity of the method are discussed and provided. Validity of the method is confirmed by numerical results