Transparency versus Anderson localization in one-dimensional disordered stealthy hyperuniform layered media

TL;DR

This study uses numerical simulations and transfer matrix methods to investigate electromagnetic wave propagation in disordered stealthy hyperuniform layered media, finding no evidence of Anderson localization or reduced transparency across a broad frequency range.

Contribution

It demonstrates that disordered stealthy hyperuniform layered media do not exhibit Anderson localization, contrasting with ordinary disordered systems, and validates the transfer matrix method for localization detection.

Findings

No Anderson localization observed in hyperuniform media

Transfer matrix method effectively detects localization

Contrast with localized behavior in ordinary disordered systems

Abstract

We present numerical simulations of disordered stealthy hyperuniform layered media ranging up to 10,000 thin slabs of high-dielectric constant separated by intervals of low dielectric constant that show no apparent evidence of Anderson localization of electromagnetic waves or deviations from transparency for a continuous band of frequencies ranging from zero up to some value $\omega_T$. The results are consistent with the strong-contrast formula including its tight upper bound on $\omega_T$ and with previous simulations on much smaller systems. We utilize a transfer matrix method to compute the Lyaponov exponents, which we show is a more reliable method for detecting Anderson localization by applying it to a range of systems with common types of disorder known to exhibit localization, such as perturbed periodic lattices. The Lyaponov exponents for these systems with ordinary disorder show clear evidence of localization, in contrast to the cases of perfectly periodically spaced slabs and disordered stealthy hyperuniform layered systems. As with any numerical study, one should be cautious about drawing definitive conclusions. There remains the challenge of determining whether one-dimensional disordered stealthy hyperuniform layered media possess a finite localization length on some scale much larger than our already large system size or, alternatively, are exceptions to the standard Anderson localization theorems.