SPECTRAL PROPERTIES OF CLASSICAL WAVES IN HIGH-CONTRAST PERIODIC MEDIA

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