Ultra sub-wavelength gigahertz resonator for constructing silicon-substrate metamaterials

The insufficient homogeneity of metamaterials is one of the most important factors that plagues their engineering applications. Here, we propose an approach to realize silicon-substrate metamaterials with ultra-subwavelength gigahertz resonators constructed with rolled-up transmission lines. Simulation shows that by employing the Cu damascene process in silicon technology, the homogeneity of the unit cells can be reduced to be smaller than 1/300 of the wavelength. As an experimental verification, we design and fabricate a bulk left-handed material sample based on standard printed circuit board technique. With a normalized periodicity of the unit cells ranging from 1/61 to 1/48 of wavelength, the negative refractive index can be clearly measured in the frequency range between 1.02 and 1.3 GHz.