  Light-matter interactions can occur when an ensemble of molecular resonators
is placed in a confined electromagnetic field. In the strong coupling regime
the rapid exchange of energy between the molecules and the electromagnetic
field results in the emergence of hybrid light-matter states called polaritons.
Multiple criteria exist to define the strong coupling regime, usually by
comparing the splitting of the polariton bands with the linewidths of the
uncoupled modes. Here we highlight the limitations of these criteria and study
strong coupling using spectroscopic ellipsometry, a commonly used optical
characterisation technique. We identify a new signature of strong coupling in
ellipsometric phase spectra. Combining ellipsometric amplitude and phase
spectra yields a distinct topological feature that we suggest could serve as a
new criterion for strong coupling. Our results introduce the idea of
ellipsometric topology and could provide further insight into the transition
from the weak to strong coupling regime.
