Fractal random cantor superlattices for the infrared

Abstract

Electromagnetics simulation has traditionally been tied to Euclidean geometry, where wave interaction with regular structures such as cylinders, spheres, cones, planes, and edges are considered. These Euclidean geometries can be combined to describe many man-made objects or to approximate complex objects that occur in nature. However, objects in nature contain complex structures that typically appear in multiple length-scales and are not well described using Euclidean geometry. These often spiky, wiggly, irregular structures are better represented by fractal geometry, which was introduced by Mandelbrot in the 1970s in order to describe geometries found in nature [1,2]. While fractal geometry is not rigorously defined, there are some typical characteristics in fractals, such as self-similarity across length-scales, an iterative construction of the fractal geometry, and a tendency to fill up space as many iterations of the geometry are constructed at progressively smaller length-scales [1].