Scattering from fractally corrugated surfaces: an exact approach

We consider the scattering of optical or electromagnetic waves from perfectly conducting rough surfaces modeled by a multiscale fractal function through the use of the extended boundary condition method. This exact method is developed here through the expansion of the surface field in terms of generalized Floquet modes, which results in a closed-form solution that can be evaluated numerically. The method is validated by comparison with the Kirchhoff (approximate) method in its regime of validity and by calculation of the energy balance parameter.