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

The majority of previous formulas for the scattering mean free path (Formula presented.) were derived to treat ordinary disordered particulate media consisting of identical dielectric particles embedded in a matrix of another dielectric constant, including the well-known Mie estimate. We derive new approximate formulas for (Formula presented.) that apply to more general particulate media (e.g., arbitrarily shaped particles of different sizes) and non-particulate media in (Formula presented.) dimensions that accurately account for the microstructure via the spectral density. These approximations are based on the exact strong-contrast expansion for the effective dynamic dielectric constant [Torquato and Kim, Phys. Rev. X 11, 021002 (2021)]. To validate the versatility and accuracy of these new formulas for (Formula presented.), we apply them to five different model microstructures in two and three dimensions, including nonhyperuniform and hyperuniform particulate and non-particulate media. Using finite-difference time-domain (FDTD) simulations at selected volume fractions, we demonstrate that our predictive formulas for the scattering mean free path (Formula presented.) are accurate beyond the long-wavelength regime, that is, for (Formula presented.), where (Formula presented.) is the incident wavenumber, and (Formula presented.) denotes the specific surface of the microstructure. In this regime, the strong-contrast formulas are shown to be consistent with the predictions from the Mie theory but can be notably more accurate for 2D TM polarization modes. For the specific case of monodisperse sphere packings, this condition ((Formula presented.)) corresponds to a particle diameter-to-wavelength ratio of approximately 0.5 or smaller. However, the Mie estimates become more accurate for (Formula presented.). For hyperuniform media with a power-law spectral density (i.e., (Formula presented.) for small (Formula presented.)), our formulas predict a scaling behavior (Formula presented.). We also provide corresponding scalings laws for the other 2D and 3D nonhyperuniform and hyperuniform models considered here. Our work enables the inverse design of novel wave characteristics of disordered hyperuniform and nonhyperuniform media by engineering their spectral densities.