Predictive Formulas for Scattering Mean Free Path for General Disordered Dielectric Media Beyond the Long-Wavelength Regime

Abstract

We derive predictive formulas for the scattering mean free path $\ell_s$ of statistically homogeneous two-phase dielectric media in dimensions $d=1,2,3$. Unlike Mie-based estimates limited to identical circular or spherical scatterers, the formulas apply to arbitrarily shaped and polydisperse particulate media as well as nonparticulate media, with microstructure entering through the spectral density. The formulas are based on the exact strong-contrast expansion for the effective dynamic dielectric constant. We apply them to five nonhyperuniform and hyperuniform models and validate selected cases using finite-difference time-domain simulations. For $k_1/s \lesssim 1$, where $k_1$ is the incident wavenumber and $s$ is the specific surface, the predictions agree well with simulations and are consistent with Mie theory where applicable, while improving accuracy for two-dimensional transverse-magnetic polarization. Mie estimates become more accurate for $k_1/s \gtrsim 1$. For hyperuniform media with $\widetilde{\chi}_V(k)\sim k^\alpha$ at small $k$, the theory predicts $\ell_s\sim k_1^{-(d+1+\alpha)}$; stealthy hyperuniform media are transparent over a finite wavenumber interval. These results provide a microstructure-based route to predict and design wave transport in general disordered dielectric materials.