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

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 long-wavelength limitations conventional homogenization estimates arbitrary microstructures so that it can capture spatial dispersion well beyond quasistatic regime (where $\omega$ ${\bf k}_I$ are frequency wavevector incident radiation). is done by deriving strong-contrast expansions exactly account multiple scattering range wavenumbers which our extended theory applies, i.e., $0 \le |{\bf k}_I| \ell \lesssim 1$ $\ell$ a characteristic heterogeneity length scale). Due to fast-convergence properties such expansions, their lower-order truncations yield accurate closed-form approximate formulas ${\varepsilon}_e({\bf k}_I,\omega)$ incorporate microstructural information via spectral density, easy compute any composite. The accuracy these microstructure-dependent approximations validated comparison full-waveform simulation methods both 2D 3D ordered models composite media. Thus, enable one predict accurately efficiently wave characteristics without having perform full-blown simulations. Among other results, we show certain hyperuniform particulate exhibit novel characteristics. Our results demonstrate design engineering microstructure possess tailored correlations at prescribed scales.