  Torquato and Kim [Phys. Rev. X 11, 296 021002 (2021)] derived exact nonlocal
strong-contrast expansions of the effective dynamic dielectric constant tensor
that treat general three-dimensional (3D) two-phase composites, which are valid
well beyond the long-wavelength regime. Here, we demonstrate that truncating
this general rapidly converging series at the two- and three-point levels is a
powerful theoretical tool for extracting accurate approximations suited for
various microstructural symmetries. We derive such closed-form formulas
applicable to transverse polarization in layered media and transverse magnetic
polarization in transversely isotropic media, respectively. We use these
formulas to estimate effective dielectric constant for models of 3D disordered
hyperuniform layered and transversely isotropic media: nonstealthy hyperuniform
and stealthy hyperuniform (SHU) media. In particular, we show that SHU media
are perfectly transparent (trivially implying no Anderson localization, in
principle) within finite wave number intervals through the third-order terms.
For these two models, we validate that the second-order formulas, which depend
on the spectral density, are already very accurate well beyond the
long-wavelength regime by showing very good agreement with the
finite-difference time-domain simulations. The high predictive power of the
second-order formulas implies that higher-order contributions are negligibly
small, and thus, it very accurately approximates multiple scattering effects.
Therefore, there can be no Anderson localization in practice within the
predicted perfect transparency interval in SHU media because the localization
length should be very large compared to any practically large sample size. Our
predictive theory provides a foundation for the inverse design of novel
effective wave characteristics of disordered and statistically anisotropic
structures.
