Radar cross section of discrete self-similar objects using a recursive electromagnetic analysis

We present a recursive method to explore the electromagnetic wave interaction with discrete self-similar - or pre-fractal - objects. In spite of their interesting properties, few authors have reported the electromagnetic properties of these multi-scale objects. One of the reasons is that the usual numerical methods are not well-adapted to the modeling of such objects because of the presence of many details at different scales. The new electromagnetic analysis proposed avoids this difficulty by taking advantage of the self-similarity properties of pre-fractal objects. The method consists in deriving an iterative process based on changing scale from the smallest to the largest one. This process is found to be analogous to the one that underlies the building of the studied self-similar object. To illustrate this mechanism, the radar cross section of fractal rings is presented and discussed.