Photonic crystals: An introductory survey

Photonic crystals, namely materials whose dielectric function is periodic in real space, are very suited to control light propagation and emission, as well as many linear and nonlinear processes involving radiation–matter interaction. This chapter gives an introduction to a few basic theoretical concepts related to photonic crystals of various dimensionalities. After presenting the general properties of Maxwell equations in periodic media, leading to the concepts of photonic bands and photonic band gaps (PBGs), we discuss the main features of photonic crystals in one, two, and three dimensions and in waveguide-embedded photonic crystals. We shall also treat defects and microcavities in photonic crystals, which lead to
localized defect modes within a PBG.