Local density of states of chiral Hall edge states in gyrotropic photonic clusters

We have constructed the Green's tensor for two-dimensional gyrotropic photonic clusters and have calculated their optical local density of states (LDOS). For clusters that support the chiral Hall edge states we calculate the LDOS as a function of wavelength, position, size, and shape of the cluster. It is shown that the LDOS of Hall edge states is a strong function of the cluster shape and position. The LDOS can be orders of magnitude higher at the edges of the cluster compared to the free space value while it vanishes towards the cluster center. It is shown that the LDOS in such photonic clusters can withstand a very strong disorder due to their topological protection. The spatial profiles of chiral Hall edge modes, their quality factors, and their excitations have been calculated. Both gyroelectric and gyromagnetic (ferrite) clusters have been treated.