Computation of eigenmodes of photonic crystals by inversion of the Maxwell operator (Q556346)

A method to compute the lowest eigenvalues of the Maxwell operator in a periodic medium is described. The method is based on the iteration of the inverse operator. The inverse operator is compact, and estimates on the convergence of its largest eigenvalues are obtained. This method leads to fast computations, and a robust and superconvergent algorithm. The method is applied to the computation of the dispersion relations of a two-imensional photonic crystal. This work is part of a project intended to develop a holographic method for a direct growth of two-dimensional and three-dimensional photonic crystals by chemical vapor deposition.