Determination of the optical properties of tungsten trioxide thin film using the transfer matrix method

Transfer-matrix method (TMM) in optics serves as a robust mathematical formalism for determining the transmittance of electromagnetic waves through a slab, thin film, or multi-layered structure. A plane electromagnetic (PEM) wave impinges at an angle to the normal of a slab or multi-layered structure and interacts with the material. A portion of this light passes through the first interface and then propagates in the material. Finally, it leaves the second interface of the material and carries information about the material. This formalism models the experimental transmittance spectra of \(WO_3\) $W{O}_3$ thin film prepared by a thermal evaporation method. The spectral variations of the transmission coefficient and refractive index of \(WO_3\) $W{O}_3$ are derived using the TMM approach, demonstrating concordance with the experimental data.