Electromagnetic Diffraction by Fractal Dusts, Triangles and Carpets: A Kirchhoff Approach to Circulation

Abstract

The diffraction of plane waves by perfectly-conducting thin screens is of fundamental physical and mathematical interest in electromagnetics [1]. Classic laser-optics experiments involve both open (single- and double-slit arrangements) and closed (circular and regular-polygon) apertures, with analyses often being confined to the Fresnel [2] and Fraunhofer [3] regimes. Here, we consider a class of scattering problem involving fully-2D fractal screens, where the scatterer possesses the property of self-similarity. A more general formulation of the diffracted wave, based on Kirchhoff's theory and 3D Green's functions [4], is also deployed.