Maximizing band gaps in two-dimensional photonic crystals

Photonic crystals are periodic structures composed of dielectric materials and designed to exhibit band gaps, i.e., ranges of frequencies in which electromagnetic waves cannot propagate, or other interesting spectral behavior. Structures with large band gaps are of great interest for many important applications. In this paper, the problem of designing structures that exhibit maximal band gaps is considered. Admissible structures are constrained to be composed of "mixtures" of two given dielectric materials. The optimal design problem is formulated, existence of a solution is proved, a simple optimization algorithm is described, and several numerical examples are presented.