Scattering from rough surfaces: A simple reflection phenomenon in fractional space

In this paper, scattering of incident plane waves from rough surfaces have been modeled in a fractional space. It is shown how wave scattering from a rough surface, could be a simple reflection problem in a fractional space. In the integer space, fluctuations of the surface result in wave scattering while in the fractional space these fluctuations are compensated by the geometry of the space. In the fractional space, reflection leads to the same results as the scattering in the integer space. To make it more clear, scattered wave function in the framework of Kirchhoff theory is considered in a fractional space and results are compared with those from a self-affine surfaces. Our results show that these two approaches are comparable.