论文标题
复合介质的非局部有效电磁波特征：超越绝对状态
Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime
论文作者
论文摘要
我们为有效的介电常数张量$ {\ boldsymbol \ varepsilon} _e（{\ bf k} _i，ω）$得出确切的非局部表达式。这种形式主义扩大了$ {\ boldsymbol \ varepsilon} _e的常规均质化估计的长波长限制（{\ bf k} _i，ω）$ $ to nutialary微观结构用于任意微观结构的$，以便它可以捕获空间分散范围以外的空间分散（其中$ω$ and $ω$和$Ω} \ bf，辐射）。这是通过得出非局部强对比的扩展来完成的，该扩展准确地解释了我们扩展的均化理论适用的波数范围的多个散射，即$ 0 \ le | {\ bf k} _i | \ ell \ lyssim 1 $（其中$ \ ell $是特征异质性长度比例）。由于此类扩展的快速连接属性，它们的下阶截断产生了$ {\ varepsilon} _e的准确封闭形式的近似公式（{\ bf k} _i，ω）$，通过光谱密度合并了微观结构信息，可以通过光谱密度进行任何复合材料，这易于对任何组成材料进行计算。这些微结构依赖性近似值的准确性是通过与复合介质的2D和3D有序模型和无序模型的全波形模拟方法进行比较的验证。因此，我们的封闭式公式使人们能够准确，有效地预测远远超出了绝对制度的有效波特性，而无需进行全面的模拟。除其他结果外，我们还表明，某些无序的超均匀颗粒复合材料表现出新的波浪特征。我们的结果表明，可以通过工程化微观结构以在规定的长度尺度上具有量身定制的空间相关性来设计无序复合材料的有效波特性。
We derive exact nonlocal expressions for the effective dielectric constant tensor ${\boldsymbol \varepsilon}_e({\bf k}_I, ω)$ of disordered two-phase composites and metamaterials from first principles. This formalism extends the long-wavelength limitations of conventional homogenization estimates of ${\boldsymbol \varepsilon}_e({\bf k}_I, ω)$ for arbitrary microstructures so that it can capture spatial dispersion well beyond the quasistatic regime (where $ω$ and ${\bf k}_I$ are frequency and wavevector of the incident radiation). This is done by deriving nonlocal strong-contrast expansions that exactly account for multiple scattering for the range of wavenumbers for which our extended homogenization theory applies, i.e., $0 \le |{\bf k}_I| \ell \lesssim 1$ (where $\ell$ is a characteristic heterogeneity length scale). Due to the fast-convergence properties of such expansions, their lower-order truncations yield accurate closed-form approximate formulas for ${\varepsilon}_e({\bf k}_I,ω)$ that incorporate microstructural information via 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 methods 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 without having to perform full-blown simulations. Among other results, we show that certain disordered hyperuniform particulate composites exhibit novel wave characteristics. 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.
