Dynamical Nature of Exciton-Polariton Coupling in WS₂ Nanoparticles

Semiconducting transition metal dichalcogenides can be synthesized in a wide range of structures and geometries, including closed cage nanostructures, such as nanotubes or fullerene-like nanoparticles (NSs). The latter is especially intriguing due to the stability, enhanced light-matter interactions, and ability to sustain exciton-polaritons (EPs) in ambient conditions, i. e., strong coupling of excitonic resonances to the optical cavity. Here we investigate the dynamics of EPs formation in WS₂ NPs in the time domain using femtosecond transient extinction spectroscopy. We develop a gamut of analytical methods and models with time-dependent parameters to extract the underlying non-equilibrium dynamics of EPs formation. We find that the formation of EPs in WS₂ NPs is not instantaneous but a gradual process that occurs only after several picoseconds. Specifically, for the short delay times, the light-matter interaction is guided by excitonic absorption, whereas for the long delay times, the process is controlled by polaritonic scattering. We discover that the coupling strength is a time-dependent entity and not a constant as is usually defined. Namely, there is a nonlinear coupling between excitonic and external modes and a notable transition from weak to strong coupling limit. Our results show that the time-dependent phenomenological dynamical model quantitatively reproduces the nonlinear dynamical coupling as well as the effects of the pump fluence on the coupling strength.