Ray Modes in Random Gap Systems

Abstract

A disordered photonic crystal with spectral degeneracies in the form of Dirac nodes is considered. Disorder can create a random gap at the Dirac nodes, which leads to the formation of random edge modes. We study the distribution of these edge modes and find from symmetry considerations that the discrete anisotropy of the photonic crystal is spontaneously broken for the propagation of photons from a local photon source. This effect can be understood as the spontaneous creation of a ray mode or as the creation of a one‐dimensional waveguide in a two‐dimensional photonic crystal through strong random scattering. The phenomenon must be distinguished from Anderson localization of photons in a single band crystal and can be considered as angular localization, since it creates geometric states rather than confining the photons to an area of the size of the localization length. The propagation of the photon intensity is described by a Fokker‐Planck equation, whose drift term is determined by the spectrum of the photonic crystal near the Dirac node.