Theoretical background of photonic Crystals: Bandgap and dispersion properties

Photonic crystals (PhCs), able to manipulate light at a scale on the order of the wavelength or even shorter, have the potential for developing new technologies and devices for a wide range of applications. In particular, PhCs have been used to investigate, both theoretically and experimentally, photonic sensors because of their peculiar properties, such as the capability of enhancing field-matter interaction and control over the group velocity. In this chapter the basic physics of photonic crystals with specific reference to the origin of the photonic band gap and to their design for achieving specific dispersion properties, is reviewed.