Inverse Engineering of Optical Constants in Photochromic Micron-Scale Hybrid Films

TL;DR

This paper presents a data-driven method to extract effective optical constants from minimal measurements, enabling accurate modeling of complex hybrid photochromic films for optical modulation applications.

Contribution

It introduces a dual-state effective model that simplifies inhomogeneous hybrid films into homogeneous layers with pseudo-optical constants, validated through experimental data.

Findings

Accurately predicts optical modulation in hybrid films

Determines wavelength-dependent pseudo-optical constants

Provides a scalable framework for designing photochromic systems

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 non-uniformly 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 pseudo-refractive indices and pseudo-extinction coefficients for both pristine and UV-irradiated states. Through systematic optimization against experimental data from tungsten oxide-polyvinylpyrrolidone hybrid films, we determine wavelength-dependent pseudo-optical 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.