Boundary element method for bandgap computation of photonic crystals

A boundary element method for computing bandgap structures of two-dimensional photonic crystals is developed. For photonic crystals composed of a square or triangular lattice of parallel cylinders with arbitrarily shaped cross-sections, the boundary integral equations are formulated for a unit cell. Constant boundary elements are adopted to discretize the boundaries. Applying the periodic boundary conditions and the interface conditions, we obtain a linear eigenvalue equation with relatively small matrices. The solution of the eigenvalue equation yields the Bloch wave vectors for given frequencies. The convergence of the method for the desired accuracy and efficiency is examined by some typical numerical examples. It is shown that the present method is efficient and accurate and thus provides a flexible treatment of electromagnetic waves in periodic structures with inclusions of arbitrary shape.