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

Wave transport in one-dimensional (1D) systems, even with an arbitrarily small amount of disorder, is conventionally expected to exhibit localization at all frequencies. A recent strong-contrast expansion for the effective dynamic dielectric constant of disordered stealthy hyperuniform 1D (layered) two-phase dielectric media, exact through third order, predicts optical transparency over a continuous frequency band up to ω c , in agreement with simulations of systems containing a small number (50) of thin slabs. In this paper, we analyze simulations with up to 10,000 slabs and find no apparent evidence that higher-order terms induce Anderson localization or deviations from transparency over a continuous band extending from zero to a frequency ω T ≲ ω c , consistent with a tight upper bound predicted by the strong-contrast formula. We employ a transfer-matrix method to compute Lyapunov exponents, which we demonstrate is a more sensitive probe of Anderson localization by applying it to systems known to exhibit localization. The Lyapunov exponents show clear evidence of localization for layered media with ordinary disorder, but no such evidence when slabs are arranged periodically or in a disordered stealthy hyperuniform pattern. Although it remains challenging to determine whether 1D disordered stealthy hyperuniform layered media possess a finite localization length on scales beyond our already large system sizes, these findings may have practical implications for photonic and phononic material design.