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

TL;DR

This paper reviews the fundamental principles of electromagnetic wave dispersion, causality, and analytical properties in photonic crystals, emphasizing their band structure and effects of absorption and dispersion.

Contribution

It provides a comprehensive review of dispersion laws, group velocity, and analytical properties in photonic crystals, including numerical illustrations.

Findings

Dispersion laws are fundamental to understanding photonic crystal behavior.

Absorption and dispersion extend the spectrum into the complex plane.

Numerical examples illustrate key properties of photonic crystal spectra.

Abstract

Photonic crystals are periodic structures which prevent light propagation along one or more directions in certain frequency intervals. Their band spectrum is usually analyzed using Floquet-Bloch decomposition. This spectrum is located on the real axis, and it enters the complex plane when absorption and dispersion is considered in the dielectric permittivity of material constituents. Here, we review fundamental definition and properties of dispersion law and group velocity in photonic crystals and we illustrate them with numerical examples.