Photonic band gap materials

Photonic band gap materials are periodic dielectric structures that control the propagation of electromagnetic waves. We describe the plane wave method, which allows to calculate the band structures of photonic crystals. By symmetry analysis and a perturbative approach, we predict the appearance of the low energy photonic band gaps of hexagonal structures. We propose new two-dimensional structures called graphite and boron nitride. Using a transfer matrix method, we calculate the transmission of the graphite structure and we show the crucial role of the coupling with external modes. We study the appearance of allowed modes in the photonic band gap by the introduction of localized defects in the periodicity. Finally, we discuss the properties of opals formed by self-organized silica microspheres, which are very promising for the fabrication of three-dimensional photonic crystals.