Topological diagnosis of polymer composites via inversion of nonlinear dielectric mixing rules

Abstract

Accurate determination of the complex effective permittivity is fundamental to optical material engineering, but it remains a critical metrology challenge for heterogeneous systems. In polymer blends and optical composites, scattering and nonlinear dielectric effects severely distort spectral signatures, causing conventional linear unmixing and data-driven approaches to fail. Here, we present an inverse reconstruction framework that retrieves the broadband complex permittivity and constituent composition of strongly scattering mixtures directly from a single infrared (IR) extinction spectrum. The method integrates scattering theory, Lorentz oscillator modeling, and a generalized set of nonlinear effective medium approximations (EMAs) to simultaneously identify component spectra, estimate volume fractions, and, crucially, diagnose the underlying microstructure. The reconstruction algorithm demonstrates robust performance across synthetic two- and multi-component polymer blends, rigorously testing the efficacy of inverted, logarithmic, and cubic mixing regimes. By comparing the statistical causality and fitting quality of these competing EMAs, the framework uniquely provides a non-destructive, optical diagnosis of the blend's dominant interaction topology (e.g. co-continuous vs. stratified/series). The reconstructed permittivity spectra are dispersion-consistent and reveal physically interpretable optical properties across the full IR range. This framework establishes a new paradigm for inverse metrology in photonics, providing a necessary, physics-grounded foundation for the quantitative characterization and rational design of nonlinear optical composites. Specifically, by providing scattering-immune effective permittivity for forward modeling and delivering a physics-based diagnosis of the underlying microstructure, the framework enables engineers to reliably link fabrication parameters to the intended optical function.