Topological Diagnosis of Optical Composites via Inversion of Nonlinear Dielectric Mixing Rules

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 from a single infrared extinction spectrum. The method integrates scattering theory, Lorentz oscillator modeling, and a generalized set of nonlinear effective medium approximations to 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.