Extraordinary optical and transport properties of disordered stealthy hyperuniform two-phase media

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 ϵ e k 1 , ω (Torquato and Kim 2021 Phys. Rev. X 11 021002) 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 three-dimensional isotropic media to other model nonstealthy microstructures, including their attenuation characteristics, as measured by the imaginary part of ϵ e k 1 , 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 ϵ e k 1 , 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.