Phononic and photonic band gap structures: modelling and applications

Photonic crystals (PhCs) are artificial materials with a permittivity which is a periodic function of the position, with a period comparable to the wavelength of light. The most interesting characteristic of such materials is the presence of photonic band gaps (PBGs). PhCs have very interesting properties of light confinement and localization together with the strong reduction of the device size, orders of magnitude less than the conventional photonic devices, allowing a potential very high scale of integration. These structures possess unique characteristics enabling to operate as optical waveguides, high Q resonators, selective filters, lens or superprism. The ability to mould and guide light leads naturally to novel applications in several fields. Band gap formation in periodic structures also pertains to elastic wave propagation. Composite materials with elastic coefficients which are periodic functions of the position are named phononic crystals. They have properties similar to those of photonic crystals and corresponding applications too. By properly choosing the parameters one may obtain phononic crystals (PhnCs) with specific frequency gaps. An elastic wave, whose frequency lies within an absolute gap of a phononic crystal, will be completely reflected by it. This property allows realizing non-absorbing mirrors of elastic waves and vibration-free cavities which might be useful in high-precision mechanical systems operating in a given frequency range. Moreover, one can use elastic waves to study phenomena such as those associated with disorder, in more or less the same manner as with electromagnetic waves. The authors present in this paper an introductory survey of the basic concepts of these new technologies with particular emphasis on their main applications, together with a description of some modelling approaches.