Disordered stealthy hyperuniform two-phase media are a special subset of hyperuniform structures with novel physical properties due to their hybrid crystal-liquid nature. We have previously shown that the rapidly converging strong-contrast expansion of a linear fractional form of the effective dynamic dielectric constant εe(k1,ω) [Phys. Rev. X 11, 296 021002 (2021)] leads to accurate approximations for both hyperuniform and nonhyperuniform two-phase composite media when truncated at the two-point level for distinctly different types of microstructural symmetries in three dimensions. In this paper, we further elucidate the extraordinary optical and transport properties of disordered stealthy hyperuniform media. Among other results, we provide detailed proofs that stealthy hyperuniform layered and transversely isotropic media are perfectly transparent (i.e., no Anderson localization, in principle) within finite
wavenumber intervals through the third-order terms. Remarkably, these results imply that there can be no Anderson localization within the predicted perfect transparency interval in stealthy hyperuniform layered and transversely isotropic media in practice
because the localization length (associated with only possibly negligibly small higher-order contributions) should be very large compared to any practically large sample size. We further contrast and compare the extraordinary physical properties of
stealthy hyperuniform two-phase layered, transversely isotropic media, and fully 3D 
isotropic media to other model nonstealthy microstructures, including their attenuation
characteristics, as measured by the imaginary part of εe (k1 , ω), and transport properties,
as measured by the time-dependent diffusion spreadability S(t). We demonstrate that
there are cross-property relations between them, namely, we quantify how the imaginary
parts of εe(k1,ω) and the spreadability at long times are positively correlated as
the structures span from nonhyperuniform, nonstealthy hyperuniform, and stealthy
hyperuniform media. It will also be useful to establish cross-property relations for
stealthy hyperuniform media for other wave phenomena (e.g., elastodynamics) as well
as other transport properties. Cross-property relations are generally useful because they
enable one to estimate one property, given a measurement of another property.
