Spectral Properties of Classical Waves in High-Contrast Periodic Media

We introduce and investigate the band gap structure of the frequency spectrum for classical electromagnetic and acoustic waves in a high-contrast, two-component periodic medium. The asymptotics with respect to the high-contrast is considered. The limit medium is described in terms of appropriate self-adjoint operators and the convergence to the limit is proven. These limit operators give an idea of the spectral structure and suggest new numerical approaches as well. The results are obtained in arbitrary dimension and for rather general geometry of the medium. In particular, two-dimensional (2D) photonic band gap structures and their acoustic analogues are covered.