Statistics of Lyapunov exponent in random Fibonacci multilayer

We numerically investigated the localization properties of band-gap and band-edge modes in a one-dimensional random Fibonacci optical multilayer. The statistics of the Lyapunov exponent (LE) reveal distinct behaviors of localization effects for band-edge and band-gap modes as function of disorder strength. In particular, a deviation from the single parameter scaling theory (SPST) of localization was observed within a frequency window corresponding to the band-gap of an ordered Fibonacci multilayer. Different band-gaps show different SPST dynamics. To provide a physical explanation for the violation of SPST, a close correlation between the frequency distribution of the resonant modes in the band-gap and the variance of the LE has been found. The spatial distribution of resonant modes has been reported and discussed. Finally, the dynamics of the gap closing of the two main band-gaps as function of the disorder strength has been analyzed.