Ultrafast evolution of the complex dielectric function of monolayer WS₂ after photoexcitation

Transition metal dichalcogenides emerged as ideal materials for the investigation of exciton physics. Retrieving the excitonic signature in optical spectra, and tracking their time evolution upon photoexcitation requires appropriate analysis procedures, particularly when comparing different measurements, experimental techniques, samples, and substrates. In this work, we investigate the ultrafast time evolution of the exciton resonance of a monolayer of WS₂ deposited on fused silica and Si/SiO₂, and using two different measurement techniques: time-resolved reflectance and transmittance contrast. By modelling the dielectric function of the exciton with a Lorentz oscillator, using a Fresnell equations formalism, we derive analytical expressions of the exciton lineshape in both cases. The 2D linearized model introduced by Li et al. [Y. Li and T. F. Heinz, 2D Mater., 2018, 5, 025021] is used for the transmittance of the transparent substrate and a Fresnel transfer matrix method [O. Stenzel, The Physics of Thin Film Optical Spectra, Springer Series in Surface Science, 2016] is used to derive the reflectance in the case of the layered Si/SiO₂ substrate. By fitting two models to the time-dependent optical spectra, we extract and quantify the time evolution of the parameter describing the excitonic resonance. We find a remarkable agreement between the extracted dynamics from both experiments despite the different side conditions, showing the equivalence and reliability of the two analysis methods in use. With this work, we pave the way to the resilient comparison of the exciton dynamics from different samples, measurements technique and substrates.