Band structure computations of metallic photonic crystals with the multiple multipole method

A method for the computation of the band structure of two-dimensional photonic crystals is 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 (noncircular) elements. This method is based on the multiple multipole method. In order to find the solutions of the nonlinear 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 is demonstrated for two systems with different geometries: a square lattice of circular cross-section cylinders, and a triangular lattice of triangular cross-section cylinders. The case of metallic systems in H polarization, where surface plasmons may be excited, is chosen. The localized nature of the surface modes poses problems to other methods whereas the eigenvalues and eigenmodes are accurately computed with the proposed technique.