Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime

TL;DR

This paper develops an exact nonlocal homogenization theory for composite media that accurately predicts electromagnetic wave behavior beyond the quasistatic limit, incorporating microstructural details and validated by simulations.

Contribution

It introduces a novel nonlocal homogenization approach extending beyond the quasistatic regime, capturing spatial dispersion and microstructural effects in composite media.

Findings

Accurate closed-form formulas for effective dielectric tensor beyond quasistatic limit.

Validation of formulas against full-wave simulations for 2D and 3D composites.

Disordered hyperuniform composites exhibit unique wave properties.

Abstract

We derive exact nonlocal expressions for the effective dielectric constant tensor ${\boldsymbol \varepsilon}_e({\bf k}_I, \omega)$ of disordered two-phase composites and metamaterials from first principles. This formalism extends the long-wavelength limitations of conventional homogenization estimates of ${\boldsymbol \varepsilon}_e({\bf k}_I, \omega)$ for arbitrary microstructures so that it can capture spatial dispersion well beyond the quasistatic regime (where $\omega$ 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 ${\varepsilon}_e({\bf k}_I,\omega)$ 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.