Linearly damped modes at gap edges of photonic crystals.
It is shown that for one-dimensional dielectric photonic crystals, the Bloch modes, a vital tool in the analysis of these structures, cannot provide a complete representation of the electromagnetic field at the edges of bandgaps. On these points, the couple of Bloch modes representing the propagation on both sides of the crystal reduces to a single one, with a stationary field, and a complete representation of the field inside the crystal illuminated by a plane wave must include a linearly damped mode (LDM), the amplitude of which behaves linearly in space. The theory of transfer matrices and the use of basic properties of the field allow a precise description of the LDM from a few parameters. An extension to two-dimensional photonic crystals is proposed.
Maystre
Daniel
D
Institut Fresnel, UMR 6133, Aix-Marseille Université, CNRS, Domaine Universitaire de St. Jérôme, 13397 Marseille CEDEX 20, France. daniel.maystre@fresnel.fr
Hugonin
Jean-Paul
JP