Layer Potential Techniques in Spectral Analysis. Part II: Sensitivity Analysis of Spectral Properties of High Contrast Band-Gap Materials

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.

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