Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime

Abstract: 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.