The effect of disorder on the local density of states in two-dimensional quasi-periodic photonic crystals

We analyse the effect of disorder in radius, dielectric constant and spatial position of high refractive index cylinders, forming several types of quasi-periodic photonic crystals, on its local density of states (LDOS). We focus on the two lowest frequency regions where the LDOS is small for TM-polarized light, where the electric field is parallel to the cylinder axis. It turned out that these spectral regions are almost independent of the strength of position disorder but vanish quickly for the two other disorder types. Hence, we conclude that in such crystals the spectral domains with small LDOS are primarily associated with Mie resonances of a single cylinder. This behaviour is compared to a photonic crystal made of air holes in a high refractive index background medium, a structure where Bragg reflection evokes band gaps.