In this paper, we study the design and homogenization of bianisotropic metamaterials originated from planar split-ring resonators, which would potentially meets the requirements of the emerging photonic topological insulators and some other types of extotic photonic materials with non-trivial states. We show that the off-diagonal elements in the magneto-electric tensor can be realized by combining the planar split-ring resonators with different orientations. To ease the fabrication process, a layer-bylayer design of metamaterials with desired bianisotropy is proposed. The design and homogenization procedure of such metamaterials are verified through effective parameter retrieval approach and computer based simulation. With the proposed structure, the complex magneto-electric coupling is realized in layered structures through planar techniques, which may be useful in the terahertz and optical range.
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