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Photonic crystals are periodic structures which prevent light propagationalong one or more directions in certain frequency intervals. Their bandspectrum is usually analyzed using Floquet-Bloch decomposition. This spectrumis located on the real axis, and it enters the complex plane when absorptionand dispersion is considered in the dielectric permittivity of materialconstituents. Here, we review fundamental definition and properties ofdispersion law and group velocity in photonic crystals and we illustrate themwith numerical examples.

Electromagnetic waves in photonic crystals: laws of dispersion, causality and analytical properties