that an uncoupled Bravais plasmonic branch is always superimposed to the plasmonic OSO mode, leading to asymmetric lineshapes clearly seen in Fig. \[fig:3\] (a) and (b). As shown in the Supporting Information (Sec. A), the anti-crossing can actually be fully resolved through a first-derivative analysis of our absorption spectra.

In such strong coupling conditions, the two dispersion diagrams also show a clear mirror symmetry breaking with respect to the normal incident axis ($k_x=0$) for the two opposite optical spins. This clearly demonstrates the capability of our structure to act as a spin-momentum locked polariton launcher. From the extracted linewidth that gives the lifetime of the chiralitonic mode and the curvature of the dispersion relation that provides its group velocity, we can estimate a chiraliton propagation length of the order of $4~\mu$m, in good agreement with the measured PL diffusion length presented in the Supporting Information (Sec. B).

![Angle-resolved absorption spectrum of the sample analyzed in (a) left and (b) right circular polarizations, with the best fit coupled oscillator model drawn. Angle-resolved resonant second harmonic spectrum for (c) right and (d) left circular excitations at $1.01$eV. Corresponding crosscuts are displayed with the angular profile of the SH signal (red curves), of 