Homogenization of artificial media with a transmission line approach

The scientific research on metamaterials has achieved significant progress in recent years. In contrast, the related practical applications have encountered tough challenges. The insufficient homogeneity makes these artificial media lose its competitiveness to conventional continuous media. In this work, we propose a generalized approach to realize microwave metamaterials with ultra-subwavelength unit cells constructed with rolled-up transmission lines. As an illustration, we design and fabricate a bulk left-handed material sample with standard printed circuit board technique. With the 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. Simulation shows that by employing the planar process for semiconductor integrated circuits, this homogeneity can be further improved to a level of 1/300 of the wavelength at gigahertz frequencies. Our work also provides a new method for obtaining ultra-small microwave resonators, which can be widely used for all kinds of planar technologies.