Prediction of Effective Optical Properties of Composites via Nonlocal Strong-Contrast Expansions

The preponderance of previous treatments to predict the effective dielectric constant of composites apply to the quasistatic (long-wavelength) regime. Here we derive exact expressions for the nonlocal effective dielectric constants of two-phase composites at intermediate wavelengths by using the "strong-contrast" expansion formalism. From this formalism, we derive a family of series expansions that explicitly incorporate complete microstructural information of the composite via n-point correlation functions and hence accounts for multiple scattering to all orders well beyond the quasistatic regime. The fast convergence of this series enables us to extract an accurate approximation that depends on the two-point correlation function or its Fourier counterpart, called the "spectral density." Our formula thus extends previous quasistatic treatments that typically do not account for nontrivial microstructural information and/or are limited to small phase contrasts. We apply our formula to a variety of disordered models and discuss how to engineer composites with prescribed attenuation properties for electromagnetic waves.

Ref: S. Torquato and J. Kim, arXiv:2007.00701 (2020)