AI 中文总结
该研究推导了适用于任意形状、多分散及非颗粒无序电介质的散射平均自由程预测公式，经模拟验证可准确预测波传输，为相关材料设计提供了微观结构途径。
AI 中文摘要
我们推导了维度d=1、2、3下统计均匀的两相电介质介质的散射平均自由程ℓ_s的预测公式。与仅适用于相同圆形或球形散射体的基于米氏（Mie）的估计不同，这些公式适用于任意形状和多分散的颗粒介质以及非颗粒介质，其微观结构通过谱密度进入公式。这些公式基于有效动态介电常数的精确强对比度展开。我们将其应用于五种非超均匀和超均匀模型，并使用时域有限差分法（finite-difference time-domain）模拟验证了选定案例。当k₁/s ≲ 1（其中k₁为入射波数，s为比表面积）时，预测结果与模拟吻合良好，且在适用情况下与米氏理论一致，同时提高了二维横磁极化下的精度；当k₁/s ≳ 1时，米氏估计更准确。对于在小k处满足χ̃_V(k)~k^α的超均匀介质，该理论预测ℓ_s~k₁^-(d+1+α)；隐身超均匀介质在有限波数区间内是透明的。这些结果提供了一种基于微观结构的途径，用于预测和设计一般无序电介质材料中的波传输。
英文摘要
We derive predictive formulas for the scattering mean free path $\ell_s$ of statistically homogeneous two-phase dielectric media in dimensions $d=1,2,3$. Unlike Mie-based estimates limited to identical circular or spherical scatterers, the formulas apply to arbitrarily shaped and polydisperse particulate media as well as nonparticulate media, with microstructure entering through the spectral density. The formulas are based on the exact strong-contrast expansion for the effective dynamic dielectric constant. We apply them to five nonhyperuniform and hyperuniform models and validate selected cases using finite-difference time-domain simulations. For $k_1/s \lesssim 1$, where $k_1$ is the incident wavenumber and $s$ is the specific surface, the predictions agree well with simulations and are consistent with Mie theory where applicable, while improving accuracy for two-dimensional transverse-magnetic polarization. Mie estimates become more accurate for $k_1/s \gtrsim 1$. For hyperuniform media with $\widetildeχ_V(k)\sim k^α$ at small $k$, the theory predicts $\ell_s\sim k_1^{-(d+1+α)}$; stealthy hyperuniform media are transparent over a finite wavenumber interval. These results provide a microstructure-based route to predict and design wave transport in general disordered dielectric materials.
Comments22 pages, 8+3 figures, one supplementary document and one supplementary data set
Journal refpublished: J. Kim and S. Torquato, Advanced Optical Materials, 14 e03370 (2026)
