Static disorder-induced renormalization of polariton group velocity

Molecular exciton-polaritons exhibit long-range, ultrafast propagation, yet recent experiments have reported far slower propagation than expected. In this work, we implement a nonperturbative approach to quantify how static energetic disorder renormalizes polariton group velocity in strongly coupled microcavities. The method requires no exact diagonalization or master equation propagation and depends only on measurable parameters: the mean exciton energy and its probability distribution, the microcavity dispersion, and the Rabi splitting. Using parameters corresponding to recently probed organic microcavities, we show that exciton inhomogeneous broadening slows both lower and upper polaritons, particularly when the mean exciton energy fluctuation approaches the collective light-matter coupling strength. A detailed discussion and interpretation of these results is provided using perturbation theory in the limit of weak resonance scattering. The magnitude of the effects examined in this work supports the conclusion that most of the reported polaritonic slowdown arises from dynamical (phonon-assisted) disorder, with static energetic disorder contributing only secondarily.