  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.
