Scattering of Electromagnetic Waves by Cantor Screens: Rayleigh-Sommerfeld Integrals on Complex Domains

The scattering of light from fractal screens has been a topic of sustained interest in optics for many decades. A common thread weaving together much of the theoretical literature is the scalar approximation, wherein the polarization state of the electromagnetic field is not a primary concern. Experiments and their supporting analyses have also been confined largely to Fraunhofer [1,2] or, more recently, Fresnel [3] regimes. Here, these various simplifications are rolled back in order to address the scattering problem in a more fundamental way.