3. Band diagrams of infinite crystals
3.1 Maxwell equations and Floquet-Bloch solutions
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 :
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Band diagrams of infinite crystals
Photonic crystals of finite size and periodicity defects
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