Electromagnetic Scattering from a Fractal Configuration

Electromagnetic scattering from a fractal configuration known as Ford Circles is studied. A scattering formalism is presented which leads to an expression for the scattering amplitude of an electromagnetic wave incident upon the fractal. The scattering amplitude is explicitly evaluated as a closed form expression in the dilute dielectric approximation. This expression is shown to be divergent, due to the infinite nature of the circumference of Ford Circles. The scattering amplitude expression in the case of Ford Discs, however, turns out to be finite, due to the finite area associated with the discs. The forward scattering amplitude, taken in the direction of the incident wave, is evaluated for Ford Circles and related to the total scattering cross section using the optical theorem. This leads to a final closed form expression for the scattering cross section from Ford Circles, which verifies that the total scattering cross section remains proportional to the volume of the scatterer even in the case of a fractal scatterer.