Film and Substrate Spectral Optical Behaviors of a Tungsten Trioxide (WO3) Thin Layer Deposited on Fluorine-Doped Tin Oxide (FTO)–Coated Glass

Abstract

The effective optical constants (EOCs) of a 480 nm tungsten trioxide (WO₃ ) thin film deposited on fluorine-doped tin oxide (FTO)–coated glass were determined from collimated transmittance and reflectance measurements over the 250–2500 nm solar spectral range. The WO₃ EOCs were obtained by fitting the experimental spectra with the four-flux model (4FM), using previously determined optical constants of the FTO and glass layers as input parameters. This work extends previous analyses of FTO–glass bilayers to a more complex WO₃–FTO–glass trilayer configuration, enabling validation of the proposed framework under multilayer boundary conditions. A three-extinction matching requirement was identified from the agreement between extinction coefficients calculated from forward and backward 4FM collimated differential equations and from the EOCs under wavelength compression. In addition, a spectral limit of the optical behavior between film and substrate was consistently observed at wavelengths approximately three times the layer thickness for both FTO and WO₃ layers, confirming its applicability beyond bilayer systems. Thickness gradient plots of collimated light fluxes and complex electric fields revealed the transition from substrate-like incoherent behavior to film-like coherent behavior. In the coherent regime, complex electric fields were represented through wavelength-dependent Bode and Nyquist diagrams, allowing analysis of their magnitude–phase evolution within the multilayer structure. The results provide a consistent framework for determining EOCs and identifying optical regime transitions in multilayer systems, demonstrating applicability to trilayer electrochromic structures.

Received: 16 January 2026 | Revised: 30 April 2026 | Accepted: 27 May 2026

Conflicts of Interest

The author declares that he has no conflicts of interest to this work.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Author Contribution Statement

David Barrios-Puerto: Conceptualization, Methodology, Validation, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration.