MMP computations of photonic crystals: Band structure of perfect crystals and waveguides

In this paper, a method for the computation of the band structure of two-dimensional photonic crystals will be presented. It is well suited for crystals including materials with arbitrary frequency-dependent dielectric constants. The technique can be applied to study photonic crystals with irregularly shaped (non circular) elements. This method is based on the multiple multipole method (MMP) (5). In order to find the solutions of the non-linear eigenvalue problem, a multipolar source is introduced which acts as an excitation. By varying the frequency of the source, the various eigenmodes are excited and can be localized as resonances in an appropriately chosen function. The approach will be demonstrated for several systems including perfect photonic crytals and photonic crystals with defects. Various materials are investigated, such as non- dispersive dielectrics and highly dispersive metallic media.