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

TL;DR

This paper investigates the formation and characteristics of optical necklace modes in one-dimensional random superlattices, revealing how their order evolves with sample size and how additional resonances affect their structure.

Contribution

It introduces an empirical formula predicting optimal necklace order and explains the impact of extra resonances on necklace mode structure in disordered photonic systems.

Findings

Optimal necklace order increases with sample size.

Extra resonances are pushed to miniband edges, reducing necklace order.

Empirical formula accurately predicts necklace order.

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.