Figure 5

Average localization lengths for TM (a) and TE (b) modes for different values of randomness α = 0.2 – 1. In the panel (a), black vertical lines show band edges in the absence of randomness (i.e. for α = 0) whereas cyan vertical lines show the positions of points where lines corresponding to different α cross. In the panel (b), black vertical lines show the edges of a partial spectral gap existing for the propagation in the ΓX direction. The vertical lines shown in this figure divide the spectrum of our system in frequency bands (5 for TM modes and 3 for TE modes, marked by Roman numerals I–V) in which the behavior of the system is found to be different.