Statistics of equally weighted random paths on a class of self-similar structures

Abstract

In the companion paper, a coherent charge-current distribution for radiating electromagnetic wavelets was constructed on an oblate spheroidal surface S_a. Its main drawback was the necessity of including magnetic along with electric charges, making the sources impossible to realize. Here we show how this difficulty can be overcome by using Hertz potentials to generate a charge-current distribution due solely to bound electric charges. However, this distribution still appears difficult to realize because it consists of multiple surface layers on S_a. We show how it can be replaced by a simple volume distribution on a spheroidal shell. Our method generalizes the usual construction of equivalent Huygens sources, based on boundary conditions on an interface between electromagnetic media, by allowing the transition to be gradual without incurring addition complexity.