Formation of optimal-order necklace modes in one-dimensional random photonic superlattices

Abstract

We study the appearance of resonantly coupled optical modes, optical necklaces, in Anderson localized one-dimensional random superlattices through numerical calculations of the accumulated phase. The evolution of the optimal necklace order m* shows a gradual shift towards higher orders with increasing the sample size. We derive an empirical formula that predicts m* and discuss the situation when in a sample length L the number of degenerate in energy resonances exceeds the optimal one. We show how the \emph{extra} resonances are pushed out to the miniband edges of the necklace, thus reducing the order of the latter by multiples of two.

4 pages, 4 figures