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

Abstract

We derive exact nonlocal expressions for the effective dielectric constant tensor ${\mathbf{\epsilon }}_e({\mathbf{k}}_I,\omega )$ of disordered two-phase composites and metamaterials from first principles. This formalism extends the long-wavelength limitations of conventional homogenization estimates of ${\mathbf{\epsilon }}_e({\mathbf{k}}_I,\omega )$ for arbitrary microstructures so that it can capture spatial dispersion well beyond the quasistatic regime (where $\omega$ and ${\mathbf{k}}_I$ are 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., $0\le |{\mathbf{k}}_I|\ell \lesssim 1$ (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 ${\epsilon }_e({\mathbf{k}}_I,\omega )$ 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.

26 pages, 13 figures (revised after the review process)

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