Abstract
We investigate the band-gap structure of the frequency spectrum for waves in a high-contrast, two-component periodic medium. We consider two-dimensional photonic crystals consisting of a background medium which is perforated by an array of holes periodic along each of the two orthogonal coordinate axes. We perform a high-order sensitivity analysis with respect to the index ratio and small perturbations in the geometry of the holes. Our method, which is based on a boundary integral perturbation theory, gives a new tool for the optimal design problem in photonic crystals.