Periodic oscillations in transmission decay of Anderson localized one-dimensional dielectric systems

It is well recognized that the transmittance of Anderson localized systems decays exponentially on average with sample size, showing large fluctuations brought up by extremely rare occurrences of necklaces of resonantly coupled states, possessing almost unity transmission. We show here that in a one-dimensional (1D) random photonic system with resonant layers these fluctuations appear to be very regular and have a period defined by the localization length xi of the system. We stress that necklace states are the origin of these well-defined oscillations. We predict that in such a random system efficient transmission channels form regularly each time the increasing sample length fits so-called optimal-order necklaces and demonstrate the phenomenon through numerical experiments. Our results provide new insight into the physics of Anderson localization in random systems with resonant units.