Electromagnetic phenomenological study of photonic band structures

It is shown, in the case of one-dimensional photonic crystals, that the tra nsmission gaps are caused by the existence of resonance phenomena inside th e layers which constitute the crystal. From a mathematical point of view, t hese resonances are associated with poles and zeros in the complex plane of the wavenumber k. Transmission gaps are located outside these resonance re gions. A phenomenological formula allows us to represent quantitatively the transmission inside the gaps. Finally, a synthetic explanation of the prop erties of doped and non-doped crystals is proposed and it is shown that the transmission peaks inside the gaps of doped photonic crystals are caused b y a shift of poles and zeros located inside the resonance regions of non-do ped crystals.