Effect of disorder and plasmonic confinement on mode localization in disordered arrays of hybrid waveguides

We study mode localization in a quasi-one-dimensional disordered array of titanium dioxide waveguides above a silver film embedded inside a fused silica matrix. Disorder is introduced by randomly offsetting waveguides from their periodic positions by up to 20% of the array period. Using a perturbative coupled mode theory with nearest-neighbor coupling, we study how mode localization changes with increasing disorder and array size. Our results show mode localization, as measured by both the average effective mode area and variance for all modes, intensifies with increasing disorder, especially for the fundamental modes with tighter plasmonic confinement. Remarkably, we find the average variance scales with the array size, resulting in a universal dependence of normalized variance on disorder for arrays of any size. These findings may have implications for designing photonic devices and developing efficient photodetectors.