Extraordinary Optical and Transport Properties of Disordered Stealthy Hyperuniform Two-Phase Media

Abstract: Disordered stealthy hyperuniform (SHU) 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 strong-contrast expansion of a linear fractional form of the effective dynamic dielectric constant leads to accurate approximations for disordered two-phase composites when truncated at the two-point level for distinctly different microstructural symmetries in three dimensions. Here, we further elucidate the extraordinary optical and transport properties of disordered SHU media. Among other results, we prove in detail that SHU 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, the results for these SHU media imply that there can be no Anderson localization within the predicted perfect transparency interval in practice because the localization length is much larger than any practically large sample size. We further contrast and compare the extraordinary physical properties of SHU layered, transversely isotropic, and fully isotropic media to other model nonstealthy microstructures, including their attenuation characteristics, as measured by the imaginary part of effective dielectric constant, and transport properties, as measured by the time-dependent diffusion spreadability. We demonstrate cross-property relations between them: they are positively correlated as the structures span from nonhyperuniform, nonstealthy hyperuniform, and SHU media. Establishing cross-property relations for SHU media for other wave phenomena (e.g., elastodynamics) and transport properties will also be useful. Cross-property relations are generally useful because they enable one to estimate one property, given a measurement of another.