Theoretical prediction of the effective dynamic dielectric constant of disordered hyperuniform anisotropic composites beyond the long-wavelength regime [Invited]

Abstract

Torquato and Kim [Phys. Rev. X 11, 296 021002 (2021)10.1103/PhysRevX.11.021002] derived exact nonlocal strong-contrast expansions of the effective dynamic dielectric constant tensor ε e (k q ,ω) that treat general statistically anisoropic three-dimensional (3D) two-phase composite microstructures, which are valid well beyond the long-wavelength regime. Here, we demonstrate that truncating this general rapidly converging expansion at the two- and three-point levels is a powerful theoretical tool from which one can extract accurate approximations suited for various microstructural symmetries. Among other results, we show that such truncations yield closed-form formulas applicable to transverse polarization in layered media and transverse magnetic polarization in transversely isotropic media, respectively. We apply these formulas to estimate ε e (k q ,ω) for models of 3D disordered hyperuniform layered and transversely isotropic media: nonstealthy hyperuniform media and stealthy hyperuniform media. In particular, we show that stealthy hyperuniform layered and transversely isotropic media are perfectly transparent (trivially implying no Anderson localization, in principle) within finite wave number intervals through the third-order terms. For all models considered here, 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 (FDTD) simulations. The high predictive power of the second-order formula is due to the fact that higher-order contributions are negligibly small, implying that it very accurately approximates multiple scattering through all orders. This implies 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. Our predictive theory provides the foundation for the inverse design of novel effective wave characteristics of disordered and statistically anisotropic structures by engineering their spectral densities.

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

“…Specifically, we previously showed that second-order truncations, which depend on the microstructure via functionals involving the spectral density χV (k), already provide accurate approximations of ε e (k 1 , ω) beyond the long-wavelength regime for transverse electric (TE) polarization in transversely isotropic media [43] and transverse polarizations in layered [44] and fully 3D isotropic media [43]. Among other results, we predicted that stealthy hyperuniform two-phase dielectric composites possess the perfect transparency intervals [43,44,83]. As illustrated in figure 2, within such transparency intervals, the sinusoidal electric waves can propagate indefinitely without decaying (i.e.…”

“…In what follows, we present the key formulas for the effective dynamic dielectric constant tensor of layered and transversely isotropic media, which were extracted from the general strongcontrast expansion in [43,44,83]. We present relevant formulas at the three-point level to prove that SHU layered and transversely isotropic media are perfectly transparent within finite wavenumber intervals through the third-order terms in section 5.…”

“…We have previously shown that second-order strong-contrast formulas for SHU two-phase composites, i.e. those in which the spectral density obeys the condition (6), predict perfect transparency or, equivalently, a zero imaginary part of the effective dielectric constant, in a finite range of wavenumbers that is determined by the exclusion-region radius K. This was done specifically for TM [83] and TE [43] polarization in transversely isotropic media and transverse polarization in fully isotropic media [43] and layered media [44]. Across space dimensions, the predictions of such perfect transparency intervals have a similar form 9 :…”

“…k 1 = k 1 ẑ, where ẑ is a unit vector along the z-direction, which is the symmetry axis of the layered media. (The reader is referred to supplement1 of [83] for the formulas of obliquely incident waves.) Thus, these formulas depend on the wavenumber k 1 .…”

“…k 1 = k 1 ŷ, where ŷ is a unit vector along the ydirection. (The reader is referred to supplement1 of [83] for the formulas obliquely incident waves.) These formulas depend on the wavenumber k 1 in the reference phase q (= 1).…”