the absorption spectra at $2$ eV (green shades) and of the product (blue shades) between the absorption and the $4^{\rm th}$ power of the excitonic Hopfield coefficient of the chiralitonic state -see details in the Supporting Information (Sec. D) \[fig:3\].](Figure3_New.png){width="1\columnwidth"}

In view of chiral light-chiral matter interactions, we further investigate the interplay between this plasmonic chirality and the valley-contrasting chirality of the WS$_2$ monolayer. A first demonstration of such an interplay is found in the resonant second harmonic (SH) response of the strongly coupled system. Indeed, monolayer TMDs have been shown to give a high valley contrast in the generation of a SH signal resonant with their $A$-excitons [@Seyler2015]. As we show in Supporting Information (Sec. G) such high SH valley contrast are measured on a bare WS$_2$ monolayer. The optical selection rules for SH generation are opposite to those in linear absorption since the process involves two excitation photons, and are more robust since the SH process is instantaneous.

The angle resolved resonant SH signals are shown in Fig. \[fig:3\] (c) and (d) for right and left circularly polarized excitation. The SH signals are angularly exchanged when the spin of the excitation is reversed with a right vs. left 