Efficient calculation of the band structure of artificial materials with cylindrical metallic inclusions

We present a new hybrid method that makes the calculation of the band structure of artificial materials with cylindrical metallic inclusions very efficient. We derive an auxiliary problem whose band structure is that of the metallic crystal along with several dispersionless bands. The eigenfunctions of the auxiliary problem have continuous derivatives up to order 2. Thus, the spectrum of the auxiliary problem can be efficiently computed using the plane-wave method. The band structure of the metallic crystal is then obtained by extracting from the computed results the dispersionless bands.