Quantifying Non-Gaussian Diffusion in Transient Microscopy Using Excess Kurtosis.

Recent advances in transient microscopy have enabled high-resolution imaging of charge carrier dynamics. However, reliance on Gaussian fits to quantify population broadening can lead to misinterpretation when multiple species coexist. Transient scattering microscopy (TScM) provides a powerful alternative, yet its sensitivity to diverse species accentuates the limitations of traditional Gaussian fits. Here, we use TScM to visualize exciton transport in bulk transition metal dichalcogenides (TMDCs) and reveal that exciton populations exhibit non-Gaussian profiles by analyzing their excess kurtosis. Simulations incorporating anomalous diffusion reproduce these experimental observations and find that the signature of the kurtosis is distinct for coexisting populations and trap-dominated regimes. Additionally, we implement a discrete variable calculation to extract the variances which yields robust, consistent diffusivity values where Gaussian fits fail to do so. Our results establish kurtosis as a vital diagnostic parameter for identifying anomalous diffusion and demonstrate the necessity of moving beyond Gaussian approximations for analysis of TScM data.