Fractal metamaterial based on Sierpinski carpet

In this paper we implement the idea of fractal geometry in a metamaterial structure, a two-dimensional metamaterial formed by an array of parallel metallic cylinders - the wire medium (WM). This metamaterial has a stop-band at frequencies below an effective plasma frequency which is determined by the radius of the cylinders and the structural period. In contrast to the standard periodic WM, now we distribute the positions of the cylinders and their radii over the cross-section of the structure by following the Sierpinski carpet fractal pattern. It is shown that a WM with a fractal structure can perform similarly to the regular WM while opening new possibilities to make the structure lighter and using less material. The proposed structure also offers better control over the selection of the frequency range.