Fig. 1. Schematic drawing of waveguide superlattice structure. Direct coupling path and indirect coupling paths are illustrated by dashed and solid lines.

Fig. 2. Dielectric constant profile for (a) the superlattice, (b) an isolated waveguide #4, and (c) the dielectric c perturbation corresponding to the perturbation potential [ΔA]m4.

Fig. 3. Statistics of transmission fluctuation (indicated by error bars) for an SC5 superlattice, a=800  nm, σ=2  nm, lc=30  nm, L=500  μm.

Fig. 4. Statistics of transmission fluctuation for an SC5 superlattice (same parameters as Fig. 3 except L=1  mm).

Fig. 5. Statistics of transmission fluctuation for an SC5 superlattice (same parameters as Fig. 3 except L=3  mm).

Fig. 6. Distribution of T32 at given wavelength (nm) and L (μm). Plots in each row have the same λ; plots in each column have the same L.

Fig. 7. Statistical characteristics of the transmission T32(λ,L) as a function of L. (a) Standard deviation of T32 over all random configurations at three individual wavelengths. (b) Statistical characteristics of T32 calculated over all random configurations of roughness and over all wavelengths.

Fig. 8. Transmission spectra of T32 for five random configurations. (a) L=500  μm, (b) L=1  mm, (c) L=3  mm.