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

Abstract

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 ϵ_{e}(k_{I},ω) for arbitrary microstructures so that it can capture spatial dispersion well beyond the quasistatic regime (where ω and 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≤|k_{I}|ℓ≲1 (where ℓ 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 ϵ_{e}(k_{I},ω) 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.