The comparison of modes at flat bands in 2D photonic crystals and resonant modes of the single cylinder

By examining field distributions in photonic crystals and comparing the central frequency of bands with Mie resonant frequency, the origin of modes at flat bands of photonic crystals is closely investigated. It is shown that the flat bands are related to Mie resonances. And there is an optimum radius for certain refractive contrast and for certain radius there is also an optimum refractive contrast for tight-binding description.