We derive exact nonlocal homogenized constitutive relations for the effective electromagnetic wave properties of disordered two-phase composites and metamaterials from first principles. This exact formalism enables us to extend the long-wavelength limitations of conventional homogenization estimates of the effective dynamic dielectric constant tensor ${\mathit{ϵ}}_e({\mathbf{k}}_I,\omega )$ for arbitrary microstructures so that it can capture spatial dispersion well beyond the quasistatic regime (where $\omega$ and ${\mathbf{k}}_I$ are the frequency and wave vector of the incident radiation). We accomplish this task by deriving nonlocal strong-contrast expansions that exactly account for complete microstructural information (infinite set of $n$-point correlation functions) and hence multiple scattering to all orders for the range of wave numbers for which our extended homogenization theory applies, i.e., $0\le |{\mathbf{k}}_I|\ell \lesssim 1$ (where $\ell$ is a characteristic heterogeneity length scale). Because of the fast-convergence properties of such expansions, their lower-order truncations yield accurate closed-form approximate formulas for ${\mathit{ϵ}}_e({\mathbf{k}}_I,\omega )$ that apply for a wide class of microstructures. These nonlocal formulas are resummed representations of the strong-contrast expansions that still accurately capture multiple scattering to all orders via the microstructural information embodied in the spectral density, which is easy to compute for any composite. The accuracy of these microstructure-dependent approximations is validated by comparison to full-waveform simulation computations for both 2D and 3D ordered and disordered models of composite media. Thus, our closed-form formulas enable one to predict accurately and efficiently the effective wave characteristics well beyond the quasistatic regime for a wide class of composite microstructures without having to perform full-blown simulations. We find that disordered hyperuniform media are generally less lossy than their nonhyperuniform counterparts. We also show that certain disordered hyperuniform particulate composites exhibit novel wave characteristics, including the capacity to act as low-pass filters that transmit waves “isotropically” up to a selected wave number and refractive indices that abruptly change over a narrow range of wave numbers. Our results demonstrate that one can design the effective wave characteristics of a disordered composite by engineering the microstructure to possess tailored spatial correlations at prescribed length scales. Thus, our findings can accelerate the discovery of novel electromagnetic composites.

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复合介质的非局部有效电磁波特性：准静态范围之外

我们从第一原理中得出了无序两相复合材料和超材料的有效电磁波特性的精确非局部均质本构关系。这种精确的形式主义使我们能够扩展有效动态介电常数张量的常规均质化估计的长波长限制${\mathit{ϵ}}_{Ë}（{\mathbf{ķ}}_{\mathrm{一世}}，\omega ）$ 适用于任意微结构，因此它可以捕获超出准静态范围（其中 $\omega$ 和 ${\mathbf{ķ}}_{\mathrm{一世}}$是入射辐射的频率和波矢）。我们通过导出恰好说明完整的微结构信息（无穷大集合）的非局部强对比度扩展来完成此任务。$ñ$点相关函数），因此在我们扩展的均质化理论适用的波数范围内，所有阶次的多重散射，即 $0\le |{\mathbf{ķ}}_{\mathrm{一世}}|\ell \lesssim \mathrm{1个}$ （在哪里 $\ell$是特征性异质性长度尺度）。由于此类展开的快速收敛性质，它们的低阶截断可得出精确的闭式近似公式${\mathit{ϵ}}_{Ë}（{\mathbf{ķ}}_{\mathrm{一世}}，\omega ）$适用于各种各样的微结构。这些非局部公式是强对比度展开式的恢复表示，仍可以通过包含在光谱密度中的微结构信息准确地捕获多个散射到所有阶次，对于任何复合物都易于计算。通过与复合介质的2D和3D有序和无序模型的全波形仿真计算进行比较，可以验证这些与微结构有关的近似值的准确性。因此，我们的封闭式公式使人们能够准确而有效地预测有效波特性，远远超出了适用于各种复合材料微结构的准静态范围，而无需执行全面的模拟。我们发现无序的超均匀介质通常比非超均匀介质的损失少。我们还表明，某些无序的超均匀颗粒复合材料表现出新颖的波特征，包括充当低通滤波器的能力，该滤波器可以“各向同性”地传输高达选定波数的波，并且折射率会在窄波数范围内突然变化。我们的结果表明，可以通过对微结构进行工程设计以在规定的长度尺度上拥有量身定制的空间相关性，来设计无序复合材料的有效波动特性。因此，我们的发现可以加速新型电磁复合材料的发现。包括充当低通滤波器的能力，这些滤波器可以“各向同性”地传输高达选定波数的波，以及在窄波数范围内突然变化的折射率。我们的结果表明，可以通过对微结构进行工程设计以在规定的长度尺度上拥有量身定制的空间相关性，来设计无序复合材料的有效波动特性。因此，我们的发现可以加速新型电磁复合材料的发现。包括充当低通滤波器的能力，这些滤波器可以“各向同性”地传输高达选定波数的波，以及在窄波数范围内突然变化的折射率。我们的结果表明，可以通过对微结构进行工程设计以在规定的长度尺度上拥有量身定制的空间相关性，来设计无序复合材料的有效波动特性。因此，我们的发现可以加速新型电磁复合材料的发现。