Fractal geometries of complementary split-ring resonators

Complementary split-ring resonators (CSRRs) are typically used as negative-permittivity particles in microstrip left-handed structures. In this paper, novel CSRRs that use a square Sierpinski fractal curve are proposed and studied in detail. It is shown that the application of fractal geometries results in significant miniaturization of the metamaterial unit cell in comparison with conventional and equivalent meander structures. Multiple fractal CSRRs are also analyzed. The influence of different geometrical parameters and the order of the fractal curve on the performances are investigated, as well as the efficiency of excitation of the particles. When used in the design of left-handed transmission lines, fractal complementary split rings improve frequency selectivity in the upper transition band when compared to other nonfractal topologies. Index Terms--Fractals, metamaterials, microwave filters, splitring resonators.