Effective Electromagnetic Wave Properties of Disordered Stealthy Hyperuniform Layered Media Beyond the Quasistatic Regime

TL;DR

This paper develops a nonlocal theoretical model to predict electromagnetic wave transport in 1D disordered stealthy hyperuniform layered media beyond the quasistatic regime, validated by simulations, revealing perfect transparency intervals and enabling inverse design.

Contribution

It introduces the first exact nonlocal theory for 1D disordered stealthy hyperuniform media, deriving an approximation for the effective dielectric tensor valid beyond the quasistatic limit.

Findings

Excellent agreement between theory and FDTD simulations.

Stealthy hyperuniform media exhibit perfect transparency up to a finite wavenumber.

Non-stealthy media do not show perfect transparency.

Abstract

Disordered stealthy hyperuniform dielectric composites exhibit novel electromagnetic wave transport properties in two and three dimensions. Here, we carry out the first study of the electromagnetic properties of one-dimensional (1D) disordered stealthy hyperuniform layered media. From an exact nonlocal theory, we derive an approximation formula for the effective dynamic dielectric constant tensor ${\boldsymbol \varepsilon}_e({\bf k}_q,\omega)$ of general 1D media that is valid well beyond the quasistatic regime and apply it to 1D stealthy hyperuniform systems. We consider incident waves of transverse polarization, frequency $\omega$, and wavenumber $k_q$. Our formula for ${\boldsymbol \varepsilon}_e({k}_q,\omega)$, which is given in terms of the spectral density, leads to a closed-form relation for the transmittance $T$. Our theoretical predictions are in excellent agreement with finite-difference time-domain (FDTD) simulations. Stealthy hyperuniform layered media have perfect transparency intervals up to a finite wavenumber, implying no Anderson localization, but non-stealthy hyperuniform media are not perfectly transparent. Our predictive theory provides a new path for the inverse design of the wave characteristics of disordered layered media, which are readily fabricated, by engineering their spectral densities.