Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime
IF 2.8 3区 材料科学Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY
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引用次数: 0
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.
托尔夸托和金[物理学]。Rev. X 11, 296 021002(2021)]导出了处理一般三维(3D)两相复合材料的有效动态介电常数张量的精确非局部强对比展开式,其有效范围远远超出长波长范围。在这里,我们证明了在两点和三点水平截断这种一般快速收敛序列是提取适合于各种微观结构对称性的精确近似的强大理论工具。我们分别导出了适用于层状介质中的横向极化和横向各向同性介质中的横向磁极化的封闭公式。我们使用这些公式来估计三维无序超均匀层状和横向各向同性介质模型的有效介电常数:非隐身超均匀和隐身超均匀(SHU)介质。特别是,我们表明SHU介质在有限的波数间隔内通过三阶项是完全透明的(通常意味着原则上没有安德森局域化)。对于这两个模型,我们验证了依赖于谱密度的二阶公式,通过与有限差分时域模拟显示出非常好的一致性,已经非常精确地超出了长波范围。二阶公式的高预测能力意味着高阶贡献可以忽略不计,因此,它非常准确地近似于多重散射效应。因此,在SHU介质中,在预测的完美透明区间内,在实践中不可能出现Anderson定位,因为与实际的大样本量相比,定位长度应该非常大。我们的预测理论为无序和统计各向异性结构的新型有效波特性的反设计提供了基础。
期刊介绍:
The Optical Society (OSA) publishes high-quality, peer-reviewed articles in its portfolio of journals, which serve the full breadth of the optics and photonics community.
Optical Materials Express (OMEx), OSA''s open-access, rapid-review journal, primarily emphasizes advances in both conventional and novel optical materials, their properties, theory and modeling, synthesis and fabrication approaches for optics and photonics; how such materials contribute to novel optical behavior; and how they enable new or improved optical devices. The journal covers a full range of topics, including, but not limited to:
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Optical Materials Express considers original research articles, feature issue contributions, invited reviews, and comments on published articles. The Journal also publishes occasional short, timely opinion articles from experts and thought-leaders in the field on current or emerging topic areas that are generating significant interest.