to minimum energy difference of the derivative reflectivity maps. This value is equal to the full width at half maximum (FWHM) $\hbar\gamma_{\rm exc}$ that we measured from the absorption spectrum of a bare WS$_2$ flake on a dielectric substrate.

![First derivative reflectivity maps in (a) left and (b) right circular polarizations, with the best fit coupled oscillator model drawn. \[fig:S1\]](FigureS1.png){width="1\columnwidth"}

On the low energy plasmonic asymptotes, we clearly observe the effect of the Bravais and OSO modes, partially overlapping in an asymmetric broadening of the branches. In this situation, a measure of the mode half-widths can be extracted from the (full) widths of the positive or negative regions of the first differential reflectivity maps. This procedure yields an energy half-width for the plasmonic modes of $\hbar\Gamma_{\rm OSO}/2=40$ meV. This width in energy can be related to an in-plane momentum width of ca. $0.5
~\mu\textrm{m}^{-1}$ via the plasmonic group velocity $v_G 
= \partial E/\partial k = 87$ meV$\cdot\mu$m, that we calculate from the branch curvature at $1.85$ eV. This in-plane momentum width results in a plasmonic propagation length of about $4 ~\mu$m. This value is in very good agreement with the measured PL extension above the structure, as discussed in section 