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    Inverse engineering of optical constants in photochromic micron-scale hybrid films

    Bahrem Serhat Danis1,*, Amin Tabatabaei Mohseni2,3, Smagul Karazhanov3,4, and Esra Zayim5,†

    • *Contact author: bdanis23@ku.edu.tr
    • †Contact author: ozesra@itu.edu.tr

    Phys. Rev. E 114, 025406 – Published 11 August, 2026

    DOI: https://doi.org/10.1103/kmw2-2tx1

    Abstract

    Photochromic materials enable dynamic optical modulation through reversible transitions between distinct absorption states, with broad potential for smart windows, adaptive optics, and reconfigurable photonic devices. Micron-scale photochromic hybrid films present a particularly attractive platform for these applications, combining straightforward preparation with substantial optical modulation and scalability for high-volume fabrication. However, rational design of such films remains fundamentally constrained by the absence of well-defined optical constants. Unlike homogeneous thin films, micron-scale hybrid photochromic materials comprise active particles dispersed nonuniformly within polymer matrices. Conventional first-principles electromagnetic simulations face substantial computational costs and discrepancies between simulated and experimental particle distributions. Here, we introduce a data-driven framework that extracts effective optical constants directly from minimal experimental transmittance measurements. Our dual-state effective model approximates the complex inhomogeneous photochromic layer as a compressed homogeneous medium characterized by pseudorefractive indices and pseudoextinction coefficients for both pristine and UV-irradiated states. Through systematic optimization against experimental data from tungsten oxide–polyvinylpyrrolidone hybrid films, we determine wavelength-dependent pseudooptical constants and compression ratios that enable accurate prediction of optical modulation within the tested thickness range. Our methodology establishes a framework for engineering hybrid photochromic systems and demonstrates how data-driven modeling can overcome limitations in characterizing complex nanostructured materials.

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