Multi-band left-handed metamaterial inspired by tree-shaped fractal geometry

We report an alternative method of designing a new metamaterial with left handed (LH) characteristics over multi-band (MB) frequencies at microwave frequency regime. The resultant LH metamaterial (LHM) consisting of a single-sided tree-shaped fractal structure features triple magnetic resonances and one electric resonance apart from the lower metal plasma response, which is responsible for the three bands of negative refraction. The multi-resonant mechanism has been systematically studied to account for all electromagnetic behaviors, and capacitor–inductor circuit models are put forward for quantitative analysis. The LHM is balanced in the fundamental passband when only one layer is utilized, whereas the balanced condition is slightly broken when a collection of sub-wavelength cells are cascaded. The negative-zero-positive refraction of the fundamental LH band and the negative refraction of the higher LH band have been numerically validated by a prism-like LHM. For demonstration, a three-layer LHM slab sample is fabricated and measured. Consistent numerical and experimental results are observed. The method not requiring individual resonant particles and electrically continuous wires paves the way for a new route to compact MB LHM design.