Homogenization of metamaterials due to fractaloid structures in the microwave regime

A remarkable reduction of the resonance frequency is achieved by substitution of the usual split ring resonator by fractal structures. Due to the use of fractals of lower orders (called fractaloid structures) it is possible to reduce significantly the resonance frequencies, while the extension of the resonating structure remains constant. On the way to lower frequencies with great potential for medical applications, numerical and experimental results are presented with the aim of a higher degree of homogenization of metamaterials. Since the manipulation of epsilon(rel) is already known, we investigate in this work the precise control of mu(rel). A strategy to manipulate mu(rel) depends on the fact that both the resonance frequency and the magnetic resonance frequency of the structure are inversely proportional to the circumference. Due to fractaloid structures an exponential increase of the periphery and simultaneously a decrease of frequency is achieved. We present simulation results of a fractal metastructure where the well-known split ring resonator has been replaced by two concentric Koch snowflakes and their modifications. With respect to the wavelength of the lowest resonance frequency we achieve a higher degree of homogenization for both snowflake structures.