Band diagrams of infinite crystals
Photonic crystals and photon gaps - Fundamental aspects

We assume here that the photonic crystal is infinite in all directions. This infinite crystal is characterized by a relative dielectric permittivity ε _r (x, y, z), real and periodic along N directions (N = 1, 2 or 3) and invariant along the (3 - N) other directions orthogonal to these. We call a _i , i Îisin; (1, ..., N), the base vectors of the direct network. The reference frame thus formed by the vectors a _i is a priori neither normed nor orthogonal. An elementary crystal mesh is obtained from the a vectors defined by :