Density-of-states and wave propagation in two-dimensional photonic crystals with positional disorder

Abstract

Most real-world structures are subject to some degree of imperfections. In a two-dimensional photonic crystal (PhC) the elements, rods in air or holes in a matrix, may be shifted from their ideal positions (positional disorder), or may vary in diameter (size disorder) as a consequence of the fabrication process. The disorder can have substantial influence on the properties of a PhC and on the performance of PhC-based devices. Here, we study this influence regarding the photonic density-of-states, the electromagnetic modes in the PhC and the wave propagation in the regime of negative refraction. At frequencies in the bands and in the disorder-induced band tails beam-like behaviour of the propagation is reduced and diffuse propagation appears at low degrees of disorder already. For applications where very well collimated light beams are needed, our results ask for narrow tolerances on the fabrication processes.