1.4.1. From dream

A 3D photonic crystal s optical index shows high contrast periodic modulation along the three dimensions of space. The main consequence lies in the new opportunity given to the eigenstates of three dimensional space to experience strong mutual coupling via diffraction processes, whereas the plane waves, eigenmodes of the homogeneous space with continuous transitional symmetry, ignore each other. Here we recall all the concepts and specifications of 1DPC analyzed in detail in section 1.3, but this time along the three dimensions of real space. As a celebrated example (this is the usual way in which 3DPC is introduced, though it is very restrictive), a 3D PC may show a full PBG for all directions of space, which means that it behaves as a perfect reflector for all angles of incidence, as illustrated in Figure 1.21.

Figure 1.21: A 3D photonic crystal may behave as an omni-directional perfect reflector in a finite spectral bandwidth. As shown in the figure, there exists a range of wavelengths (cross-hatched area) where reflectivity is uniform, for several directions of propagation

The concept of 3DPC was introduced in 1987 by E. Yablonovitch (YAB 87) and demonstrated experimentally for the first time in the field of microwaves in a photonic crystal called Yablonovite (YAB 91). The initial motivation was to gain full control of the spontaneous emission of an active emitting material: for example it can be fully inhibited if the active material is inserted in a photonic crystal showing...