We formulate a general method to analyze hybridization modes in metamaterials by employing electrical circuit models. By rewriting circuit equations for coupled inductor–capacitor circuit networks in the bra-ket notation, we show that there exists a good analogy between circuit models and quantum tight-binding models in solid-state physics. Our picture is also applicable to transmission systems that do not have tightly bound eigenmodes.
This analogy enables the synthesis of various electromagnetic metamaterials having dispersion relations similar to those for electrons in solids and consequently allows the systematic construction of metamaterials with desired characteristics. In this paper, we focus on the formation of flat bands in metamaterials with specific symmetries. The flat band, which corresponds to a slow group velocity of light or a heavy photon, is useful in designing functional metamaterials.