Photonic bands in two-dimensional metallodielectric photonic crystals composed of metal coated cylinders

Photonic bands in two-dimensional metallodielectric (MD) periodic systems composed of metal coated cylinders are investigated theoretically based on frequency dependent plane-wave expansion method. For the case of E-polarization, although the thickness of metal coating is less than half of the cylinder's radius, most of MD photonic bands are the same as photonic bands composed of pure metal cylinders. This property provides us with a way to substitute metal photonic crystals with MD photonic crystals in many applications. In addition, flatbands are discovered in MD photonic band structures, which can be tuned by changing the thickness of metal coating while other photonic bands do not change their positions. For the case of H-polarization, the lowest frequency band gap (between the first and the second bands) can open up when the thickness of metal coating is thick enough. According to approximate calculation based on Maxwell-Garnett type effective medium theory and comparison with recent studies on three-dimensional MD photonic band structures, we predict that the lowest frequency band gap is not because of Bragg scattering but result from the individual metal coated dielectric cylinders, so that the gap is independent on geometry of photonic crystal lattices. Then, numerical calculation validates that our prediction is right.