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 ${\tilde{\chi }}_V(k)\sim k^{\alpha }$ 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.

22 pages, 8+3 figures, one supplementary document and one supplementary data set

References in corpus (43)

• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Designer disordered materials with large complete photonic band gaps
• Hyperuniform States of Matter
• Isotropic Band Gaps and Freeform Waveguides Observed in Hyperuniform Disordered Photonic Solids
• Hyperuniformity in point patterns and two-phase random heterogeneous media
• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• Transport Phase Diagram and Anderson Localization in Hyperuniform Disordered Photonic Materials
• Hyperuniformity and its Generalizations
• Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
• Basic Understanding of Condensed Phases of Matter via Packing Models
• Light in correlated disordered media
• Hydrodynamics of Random-Organizing Hyperuniform Fluids
• Designing Disordered Hyperuniform Two-Phase Materials with Novel Physical Properties
• Inverse methods for design of soft materials
• Transport, Geometrical and Topological Properties of Stealthy Disordered Hyperuniform Two-Phase Systems
• Hyperuniform disordered phononic structures
• Light transport and localization in two-dimensional correlated disorder
• Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations
• Disordered Hyperuniform Heterogeneous Materials
• The Perfect Glass Paradigm: Disordered Hyperuniform Glasses Down to Absolute Zero
• Stealth acoustic materials
• Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime
• Structural Characterization of Many-Particle Systems on Approach to Hyperuniform States
• Enhanced Pinning For Vortices in Hyperuniform Substrates and Emergent Hyperuniform Vortex States
• Effective Electromagnetic Wave Properties of Disordered Stealthy Hyperuniform Layered Media Beyond the Quasistatic Regime
• Hyperuniformity with no fine tuning in sheared sedimenting suspensions
• New Tessellation-Based Procedure to Design Perfectly Hyperuniform Disordered Dispersions for Materials Discovery
• Absorption of scalar waves in correlated disordered media and its maximization using stealth hyperuniformity
• Tailoring correlations of the local density of states in disordered photonic materials
• Methodology to Construct Large Realizations of Perfectly Hyperuniform Disordered Packings
• Angular resolved light scattering from micron-sized colloidal assemblies
• Local Order Metrics for Two-Phase Media Across Length Scales
• Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime
• Extraordinary Optical and Transport Properties of Disordered Stealthy Hyperuniform Two-Phase Media
• Stealthy and hyperuniform isotropic photonic bandgap structure in 3D
• Effective Waves for Random Three-dimensional Particulate Materials
• Characterizing the Hyperuniformity of Ordered and Disordered Two-Phase Media
• Hyperuniformity and wave localization in pinwheel scattering arrays
• Multiscale Physics-Informed Neural Networks for the Inverse Design of Hyperuniform Optical Materials
• Hyperuniform scalar random fields for lensless, multispectral imaging systems
• Realizability of Iso-$g_2$ Processes via Effective Pair Interactions
• Existence of Nonequilibrium Glasses in the Degenerate Stealthy Hyperuniform Ground-State Manifold
• Reflection Measurement of the Scattering Mean Free Path at the Onset of Multiple Scattering