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.Comment: 4 pages, 4 figure