Adjusting the resonant frequency and loss of dendritic left-handed metamaterials with fractal dimension

Left-handed metamaterials (LHMs) with fractal dendritic cells have recently been demonstrated at both microwave and infrared frequencies. Here, we try to utilize only a single parameter, the fractal dimension, to manipulate the geometries of dendritic structures, and then adjust the resonant behaviors and lossy characteristics of the dendritic LHMs. Both the dendritic LHMs for electromagnetic wave parallel and normal incidences are discussed in this paper. As the fractal dimension increases, the left-handed resonant frequency of the dendritic LHMs decreases, and the lossy characteristics could be well adjusted. The method proposed in this paper could be an important guidance for LHMs' design, especially for the dendritic LHMs operating at optical frequencies.